ALBERT

Description: It is well known that 14C dating of fossil bone with seriously depleted protein levels, or bone that has been consolidated with preservatives, can produce erroneous results. In the tropics, warm and moist soil conditions lead to constant reworking of organic matter and add to the danger of bone contamination. Because of this, 14C dating of preservative-impregnated bone from such areas has rarely been successful. We report here a set of AMS dates on both unconsolidated animal bone and polyvinyl acetate/polyvinyl alcohol (PVA/PV-OH) impregnated human burials from the Maya site of Cuello, Belize. The steps needed to purify the samples are described, together with details on the use of qualitative infra-red (IR) spectra as a means of assessing sample purity.

Description: This is the third of the series of lists of English archaeologic dates submitted to Harwell for measurement by the Historic Buildings and Monuments Commission for England and Wales within a prescribed contractual period. This list of 155 dates covers the period April 1987 to March 1988 and results are reported whether the associated projects are completed or on-going.

Description: The results in this list come from our earlier years of operation and form part of the special series of lists being prepared to clear the backlog of unpublished dates from this laboratory, in this case 49 samples coming from sites in and around Northampton, UK. They originate from excavations directed by John Williams and Helen M Bamford of the Northampton Development Corporation between 1973 and 1982, and all were submitted for measurement and paid for by the Ancient Monuments Laboratory of the Historic Buildings and Monuments Commission for England and Wales.

Description: Detailed stable oxygen isotope analyses coupled with AMS 14C measurements on an eastern Mediterranean sapropel S1 sequence indicate that adverse bottom conditions persisted for ca 8000 years. AMS dates on additional sequences show that complete bottom anoxia lasted for 300-800 years. The S1 event is not synchronous throughout the eastern Mediterranean, but started earlier in the deeper parts of the basin.

Description: The results presented in this list were obtained from 1986 to 1989. Equipment, measurement and treatment of samples are as reported previously (Kanwiszer & Trzeciak 1984: 111). Age calculations are based on a contemporary value equal to 95% of the activity of NBS oxalic acid standard and on the conventional half-life for 14C of 5568 ± 30 years. Results are reported in years before 1950 (years BP). Errors quoted (± 1σ) include standard deviations of count rates for the unknown sample, contemporary standard and background. The dates are not corrected for 13C fractionation. Descriptions and comments are based on information supplied by submitters of samples.

Description: We report 63 new radiocarbon analyses of samples from São Miguel, the largest (ca 62 × 13km) and most populous (ca 150,000 inhabitants) island in the Azores archipelago (Fig 1). The samples are mainly carbonized tree roots and other plant material collected from beneath 20 mafic lava flows and spatter deposits and from within and beneath 42 trachytic pyroclastic flow, pyroclastic surge, mudflow, pumice-fall, and lacustrine deposits and lava flows. One calcite date is reported. The samples were collected during geologic mapping of the entire island (Moore, in press A; sample locations are shown on this map). Nine 1:25,000-scale topographic maps, published in 1983 by the Portuguese Army Cartographic Service, cover the island; samples and locations described below refer to these named sheets.

Description: A suite of 23 14C age determinations, from a well-stratified rockshelter and from 3 pollen cores on Mangaia Island is reported. The rockshelter has yielded significant evidence for avifaunal extinctions during the period cal. A.D. 1000-1600. The Lake Tiriara pollen cores span a period from ca. 6500 cal. b.p. to the present, and palynological analysis of the TIR 1 core indicates major anthropogenic disturbance on the island's vegetation after ca. 1600 cal. B.P. These sites, and the radiocarbon ages associated with them, provide the first chronologically secure evidence for human impacts on the island ecosystems of the southern Cook Islands.

Description: This list includes dates from Italy, Libyan Sahara, Niger and the Dahlak Islands, obtained from 1976 to 1980, using the benzene scintillation method.Chemical processing from sample to benzene follows procedures of Alessio et al (1978a). Standard pretreatment for wood and charcoal included boiling with 5–10% HCL.

Description: The Radiocarbon Laboratory at the University of Barcelona began its serial measurements in 1985. The following list contains dates obtained between 1985 and 1987. Both archaeological and geological samples were dated.The measurement technique we use is liquid scintillation counting of benzene. A previous paper (Mestres, García & Rauret 1991) describes sample pretreatment, synthesis and counting protocols and equipment.

Description: The following list consists of dates, obtained by liquid scintillation counting of benzene, for archaeologic samples mostly measured between June 1987 and October 1989.Charcoal and grain samples were pretreated with 1M HCl followed by washing in water and, where considered necessary, with dilute alkali for the removal of humic acids. Wood samples were treated either in the same way, or, where large enough, were reduced to cellulose by the action of chlorine dioxide produced in situ. All antler and bone samples were treated with cold dilute acid. The term ‘collagen’ is used throughout to mean the acid insoluble organic fraction produced by this treatment. Peat samples were treated with dilute acid and alkali to separate the humin and humic acid fractions, which were dated individually.

Description: We converted to CO2 samples of organic materials, Quaternary carbonate rocks and carbonates extracted from groundwater. We measured 14C radioactivity in a proportional counter with an effective volume of 723ml filled to 0.28MPa. A mechanical box with an inside cylinder of a plastic scintillator, 4cm thick, arranged in anticoincidence provides the shielding. We present a review of radiocarbon ages of Quaternary and archaeological samples.

Description: High count rates of lithium ions in an AMS measurement system for 14C were traced to the lithium content in the quartz tubes used in the graphitization of the samples. The lithium contamination was nearly eliminated by the use of borosilicate glass reaction tubes at a lower reaction temperature. The ion beam current and the measurement precision of the isotope ratio were not affected.

Description: AMS 14C measurements on pteropod shells from eastern North Atlantic deep-sea cores reveal distinct periods of aragonite preservation during the last 16,000 years. Most preservation spikes coincide with documented periods of climatic change on a scale of 2 × 101 to 2 × 103 years.

Description: This list includes some significant measurements carried out by CRAD Radiocarbon Laboratory from 1979 to 1985. The dates were obtained by liquid scintillation counting of benzene using the laboratory procedures described in previous lists (Barbina et al 1982: 214-216; Barbina, Calligaris & Ciuti 1979). Samples were pretreated according to generally applied methods, depending on type of material and particular archaeologic and geologic features.

Description: In 1983, the University of Barcelona, the Institut d'Estudis Catalans and the Department of Culture of the Generalitat de Catalunya agreed to establish a laboratory for radiocarbon measurement at the Analytical Chemistry Department of the University of Barcelona. The liquid scintillation technique was chosen for radiocarbon counting. The counting laboratory is in the basement of a six-story building.

Description: The bifurcation structure of two-dimensional, pressure-driven flows through a horizontal, rectangular duct that is heated with a uniform flux in the axial direction and a uniform temperature around the periphery is examined. The solution structure of the flow in a square duct is determined for Grashof numbers (Or) in the range of 0 to 1O6 using an arclength continuation scheme. The structure is much more complicated than reported earlier by Nandakumar, Masliyah & Law (1985). The primary branch with two limit points and a hysteresis behaviour between the two-and four-cell flow structure that was computed by Nandakumar et al. is confirmed. An additional symmetric solution branch, which is disconnected from the primary branch (or rather connected via an asymmetric solution branch), is found. This has a two-cell flow structure at one end, a four-cell flow structure at the other, and three limit points are located on the path. Two asymmetric solution branches emanating from symmetry-breaking bifurcation points are also found for a square duct. Thus a much richer solution structure is found with up to five solutions over certain ranges of Gr. A determination of linear stability indicates that all two-dimensional solutions develop some form of unstable mode by the time Gr is increased to about 220000. In particular, the four-cell becomes unstable to asymmetric perturbations. The paths of the singular points are tracked with respect to variation in the aspect ratio using the fold-following algorithm. Transcritical points are found at aspect ratios of 1.408 and 1.456 respectively for Prandtl numbers Pr = 0.73 and 5. Above these aspect ratios the four-cell solution is no longer on the primary branch. Some of the fold curves are connected in such a way as to form a tilted cusp. When the channel cross-section is tilted even slightly (1°) with respect to the gravity vector, the bifurcation points unfold and the two-cell solution evolves smoothly as the Grashof number is increased. The four-cell solutions then become genuinely disconnected from the primary branch. The uniqueness range in Grashof number increases with increasing tilt, decreasing aspect ratio and decreasing Prandtl number. © 1991, Cambridge University Press. All rights reserved.

Description: The mass transport of a diffusible substance during volume-cycled oscillatory flow in a thin-walled viscoelastic tube is studied. A small-amplitude, long-wavelength travelling wave is generated by the oscillatory pressure gradient. Lubrication theory is employed for slow axial variations to derive regular perturbation solutions to the Navier-Stokes equations. The convection-diffusion equation is solved in a similar manner, assuming uniform steady end concentrations and no wall flux. From the velocity and concentration fields, the time-average rate of axial mass transport is calculated, and its dependence on oscillation frequency, tube stiffness, and stroke amplitude is investigated. The general result is that transport is enhanced less for softer tubes than for stiffer ones and that mass flow rate as a function of frequency reaches a local maximal value. The results are related to gas transport in pulmonary airways during high-frequency ventilation. © 1991, Cambridge University Press. All rights reserved.

Description: We investigate the stretching and breakup of a drop freely suspended in a viscous fluid undergoing chaotic advection. Droplets stretch into filaments acted on by a complex flow history leading to exponential length increase, folding, and eventual breakup; following breakup, chaotic stirring disperses the fragments throughout the flow. These events are studied by experiments conducted in a time-periodic two-dimensional low-Reynolds-number chaotic flow. Studies are restricted to viscosity ratios p such that 0.01 〈 p 〈 2.8. The experimental results are highly reproducible and illustrate new qualitative aspects with respect to the case of stretching and breakup in linear flows. For example, breakup near folds is associated with a change of sign in stretching rate; this mode of breakup leads to the formation of rather large drops. The dominant breakup mechanism, however, is capillary wave instabilities in highly stretched filaments. Other modes of breakup, such as necking and end-pinching occur as well. We find that drops in low-viscosity-ratio systems, p 〈 1, extend relatively little, O (101−102), before they break, resulting in the formation of large droplets that may or may not break again; droplets in systems with p 〉 1, on the other hand, stretch substantially, O (102–104), before they break, producing very small fragments that rarely break again. This results in a more non-uniform equilibrium drop size distribution than in the case of low-viscosity-ratio systems where there is a succession of breakup events. We find as well that the mean drop size decreases as the viscosity ratio increases. The experimental results are interpreted in terms of a simple model assuming that moderately extended filaments behave passively; this is an excellent approximation especially for low-viscosity-ratio drops. The repetitive nature of stretching and folding, as well as of the breakup process itself, suggests self-similarity. We find that, indeed, upon scaling, the drop size distributions corresponding to different viscosity ratios can be collapsed into a master curve. © 1991, Cambridge University Press. All rights reserved.

Description: The description of the slow viscous flow due to the axisymmetric or asymmetric translation of an annular disk involves the solution of respectively one or two sets of triple integral equations involving Bessel functions. An efficient method is presented for transforming each set into a Fredholm integral equation of the second kind. Simple, regular kernels are obtained and the required physical constants are readily available. The method is also applied to the pressure-driven extrusion flow through an annular hole in a wall. The velocity profiles in the holes are found to be flatter than expected with correspondingly sharper variation near a rim. For the sideways motion of a disk, an exact solution is given with bounded velocities and both components of the rim pressure singularity minimized. The additional drag experienced by this disk when the fluid is bounded by walls parallel to the motion is then determined by solving a pair of integral equations, according to methods given in an earlier paper. © 1991, Cambridge University Press. All rights reserved.

Description: We present the results of a study of the inviscid spatial stability of a parallel three-dimensional compressible mixing layer. The parameters of this study are the Mach number of the fast stream, the ratio of the speed of the slow stream to that of the fast stream, the ratio of the temperature of the slow stream to that of the fast stream, the direction of the crossflow in the fast stream, the frequency, and the direction of propagation of the disturbance wave. Stability characteristics of the flow as a function of these parameters are given. Certain theoretical results are presented which show the interrelations between these parameters and their effects on the stability characteristics. In particular, the three-dimensional stability problem for a three-dimensional mixing layer at Mach zero can be transformed to a two-dimensional stability problem for an equivalent two-dimensional mean flow. There exists a one-parameter family of curves such that for any given direction of mean flow and of wave propagation one can apply this transformation and obtain the growth rate from the universal curves. For supersonic convective Mach numbers, certain combinations of crossflow angle and propagation angle of the disturbance can increase the growth rates by a factor of about two, and thus enhance mixing. © 1991, Cambridge University Press. All rights reserved.

Description: We implement a linear stability analysis of the convective instability in superposed horizontal fluid and porous layers with throughflow in the vertical direction. It is found that in such a physical configuration both stabilizing and destabilizing factors due to vertical throughflow can be enhanced so that a more precise control of the buoyantly driven instability in either a fluid or a porous layer is possible. For ζ = 0.1 (ζ, the depth ratio, defined as the ratio of the fluid-layer depth to the porous-layer depth), the onset of convection occurs in both fluid and porous layers, the relation between the critical Rayleigh number Rcm and the throughflow strength γm is linear and the Prandtl-number (Prm) effect is insignificant. For ζ ≥ 0.2, the onset of convection is largely confined to the fluid layer, and the relation becomes Rcm ∼ γ2m for most of the cases considered except for Prm = 0.1 with large positive γm where the relation Rcm ∼ γ3m holds. The destabilizing mechanisms proposed by Nield (1987 a, b) due to throughflow are confirmed by the numerical results if considered from the viewpoint of the whole system. Nevertheless, from the viewpoint of each single layer, a different explanation can be obtained.

Description: Buoyancy-driven flow on a heated inclined plate can become unstable to static longitudinal roll instability at a critical distance, measured by Rc, from the leading edge. Experiments in water by Sparrow & HUSAR (1969) indicate that these rolls undergo a second transition further downstream such that adjacent rolls merge and their spanwise wavelength is doubled. We study this secondary bifurcation phenomenon here with a set of model equations by first constructing the full eigenspectrum and eigenfunctions with a Chebyshev-Tau spectral method and then deriving the pertinent amplitude equations. By stipulating that the dimensional cross-stream wavelength of the rolls remains constant beyond Rc which is consistent with experimental observation, we show that the finite-amplitude primary rolls are destabilized by the ⅓ subharmonic mode at another critical distance R1/2 from the edge. This 1/2 mode is shown to have an asymmetric spatial phase shift of 1/2 π relative to the original 1 mode of the primary rolls, thus explaining the unique dislocation of tracer streaks after the rolls coalesce in the experiments. Also consistent with experimental observation is the theoretical result that the merged rolls are annihilated downstream by a saddle-node bifurcation before further wavelength doubling can occur. Simple amplitude criteria and critical distances from the leading edge for the various transitions are derived and compared to experimental values. © 1991, Cambridge University Press. All rights reserved.

Description: An example is presented of a separated flow in an unbounded domain in which, as the Reynolds number becomes large, the separated region remains of size 0(1) and tends to a non-trivial Prandtl-Batchelor flow. The multigrid method is used to obtain rapid convergence to the solution of the discretized Navier-Stokes equations at Reynolds numbers of up to 5000. Extremely fine grids and tests of an integral property of the flow ensure accuracy. The flow exhibits the separation of a boundary layer with ensuing formation of a downstream eddy and reattachment of a free shear layer. The asymptotic (‘triple deck’) theory of laminar separation from a leading edge, due to Sychev (1979), is clarified and compared to the numerical solutions. Much better qualitative agreement is obtained than has been reported previously. Together with a plausible choice of two free parameters, the data can be extrapolated to infinite Reynolds number, giving quantitative agreement with triple-deck theory with errors of 20% or less. The development, of a region of constant vorticity is observed in the downstream eddy, and the global infinite-Reynolds-number limit is a Prandtl-Batchelor flow; however, when the plate is stationary, the occurrence of secondary separation suggests that the limiting flow contains an infinite sequence of eddies behind the separation point. Secondary separation can be averted by driving the plate, and in this case the limit is a single-vortex Prandtl-Batchelor flow of the type found by Moore, Saffman & Tanveer (1988); detailed, encouraging comparisons are made to the vortex-sheet strength and position. Altering the boundary condition on the plate gives viscous eddies that approximate different members of the family of inviscid solutions. © 1991, Cambridge University Press. All rights reserved.

Description: We analyse the dilute, steady, fully developed flow of relatively massive particles in a turbulent gas in the context of a vertical pipe. The idea is that the exchange of momentum in collisions between the grains and between the grains and the wall plays a significant role in the balance of forces in the particle phase. Consequently, the particle phase is considered to be a dilute system of colliding grains, in which the velocity fluctuations are produced by collisions rather than by the gas turbulence. The balance equations for rapid granular flow are modified to incorporate the drag force from the gas, and boundary conditions, based on collisional exchanges of momentum and energy at the wall, are employed. The turbulence of the gas is treated using a one-equation closure. A numerical solution of the resulting governing equations provides velocity and turbulent energy profiles in agreement with the measurements of Tsuji et al. M984b. © 1991, Cambridge University Press. All rights reserved.

Description: The inviscid instability of a longitudinal vortex structure within a steady boundary layer is investigated. The instability has wavelength comparable with the boundary-layer thickness so that a quasi-parallel approach to the instability problem can be justified. The generalization of the Rayleigh equation to such a flow is obtained and solved for the case when the vortex structure is induced by curvature. Two distinct modes of instability are found; these modes correspond with experimental observations on the breakdown process for Görtler vortices. © 1991, Cambridge University Press. All rights reserved.

Description: Chemical reactions in shock waves can be strongly affected by minute impurity concentrations. Thus it is not adequate to take into account the additional impurity electron production in relaxation studies simply by global adjustment of the atom—atom excitation cross-section constant to the measured electron density. A definite improvement, however, can only be achieved if the ionization relaxation model is extended to include all relevant impurity atom reactions. Consequently we treated the real test gas as a mixture of krypton and impurity carbon atoms. For the carbon model it is important to take the lower real excitation levels into consideration. Carrying out a sensitivity analysis we were able to reduce the number of reactions substantially. A comparison with experimental electron density profiles yielded 3. 0 × 10–-6 m2/J for the Kr—Kr excitation cross-section constant as well as values for the C—Kr constants. For a temperature of about 8000 K and an impurity concentration of about 40 p. p. m. it is shown that the impurity reactions dominate the electron production in the initial relaxation zone. This effect causes a pronounced decrease of the relaxation time with increasing concentration. By comparing computational results of the Kr—C model with those of the simplistic pure Kr model it is possible to explain the dependence of the Kr-Kr excitation cross-section constant on the impurity concentration and the plasma temperature. © 1991, Cambridge University Press. All rights reserved.

Description: We consider the waves generated by transcritical flow past a constriction in a channel, or by ships or surface pressure distributions travelling at transcritical speeds. The two-dimensionality of the upstream advancing nonlinear waves, which has been observed both experimentally and numerically by several authors, is described by a modal decomposition of the flow response. We show that the lowest transverse mode may evolve nonlinearly, leading to a two-dimensional response upstream, with the higher transverse modes swept downstream. This description is supported by comparing the initial evolution of the solutions to the corresponding linear and nonlinear problems. Averaging across the channel demonstrates that the three-dimensional problem may be related to the corresponding two-dimensional problem with an additional effective forcing coming from the nonlinear coupling of the higher modes to the lowest two-dimensional mode. This coupling leads to a dependence of the upstream solutions on the channel width as well as the Froude number. Solutions are also obtained for two-layer fluids in which cubic nonlinearity is also important. The inclusion of cubic nonlinearity permits the generation of two-dimensional fronts upstream, and demonstrates that the transition from three- to two-dimensional solutions upstream is not specific to Boussinesq solitary waves. © 1991, Cambridge University Press. All rights reserved.

Description: The frequency response of the shear layers separating from a circular cylinder subject to small-amplitude rotational oscillations has been investigated experimentally in water for the Reynolds number (Re) range 250 to 1200. A hot-film anemometer was placed in the separated shear layers from 1 to 1.5 diameters downstream of the cylinder, and connected to a lock-in analyser. By referencing the lock-in analyser to the cylinder oscillations, the amplitude and phase of the response to different frequency oscillations were measured directly. It is shown that rotational oscillations corresponding to cylinder peripheral speeds between 0.5 and 3% of the free stream can be used to influence the primary (Karman) mode of vortex generation. For Re greater than =500, such oscillations can also force the shear-layer vortices associated with the instability of the separating shear layers. Corresponding to the primary and shear-layer modes are two distinct peaks in response amplitude versus frequency curves, and two very different phase versus frequency curves. The response of the shear layers (and near wake) in the range of Karman frequency suggests qualitative similarities with the response of an oscillator near resonance. Forced oscillations in the higher-frequency shear-layer mode range are simply convected by the shear layers. Close to the cylinder, the shear-layer response is shown to be comparable to that of generic free shear layers studied by others. © 1991, Cambridge University Press. All rights reserved.

Description: A spectral scheme is developed to study the mass transport in three-dimensional water waves where the steady flow is assumed to be periodic in two horizontal directions. The velocity-vorticity formulation is adopted for the numerical solution, and boundary conditions for the vorticity are derived to enforce the no-slip conditions. The numerical scheme is used to calculate the mass transport under two intersecting wave trains; the resulting flow is reminiscent of the Langmuir circulation patterns. The scheme is then applied to study the steady flow in a three-dimensional standing wave. © 1991, Cambridge University Press. All rights reserved.

Description: The unsteady boundary-layer flow produced by a two-dimensional vortex in motion above an infinite plane wall in an otherwise stagnant fluid is considered in the limit of infinite Reynolds number. This study is part of a continuing investigation into the nature of the physical processes that occur near the surface in transitional and fully turbulent boundary layers. The adverse pressure gradient due to the vortex leads to the development of a zone of recirculation in the viscous flow near the surface, and the boundary-layer flow then focuses rapidly toward an eruption along a band which is very narrow in the streamwise direction. The evolution of the unsteady boundary layer is posed in Lagrangian coordinates and computed using an efficient, factored ADI numerical method. The boundary-layer solution is found to develop a separation singularity and to evolve toward a terminal stage which is generic in two-dimensional unsteady flows. The computed results are compared with the results of asymptotic theory of two-dimensional boundary-layer separation and the agreement is found to be excellent. © 1991, Cambridge University Press. All rights reserved.

Description: An extension of an axial viewing optical technique (first used by Lee, Adrian & HANRATTY) is described which allows the determination of the turbulence characteristics of solid particles being transported by water in a pipe. Measurements are presented of the mean radial velocity, the mean rate of change radial velocity, the mean-square of the radial and circumferential fluctuations, the Eulerian turbulent diffusion coefficient, and the Lagrangian turbulent diffusion coefficient. A particular focus is to explore the influence of slip velocity for particles which have small time constants. It is found that with increasing slip velocity the magnitude of the turbulent velocity fluctuations remains unchanged but that the turbulent diffusivity decreases. The measurements of the average rate of change of particle velocity are consistent with the notion that particles move from regions of high fluid turbulence to regions of low fluid turbulence. Measurements of the root-mean-square of the fluctuations of the rate of change of particle velocity allow an estimation of the average magnitude of the particle slip in a highly turbulent flow, which needs to be known to analyse the motion of particles not experiencing a Stokes drag. © 1991, Cambridge University Press. All rights reserved.

Description: An investigation was undertaken to improve our understanding of low-Reynolds-number turbulent boundary layers flowing over a smooth flat surface in nominally zero pressure gradients. In practice, such flows generally occur in close proximity to a tripping device and, though it was known that the flows are affected by the actual low value of the Reynolds number, it was realized that they may also be affected by the type of tripping device used and variations in free-stream velocity for a given device. Consequently, the experimental programme was devised to investigate systematically the effects of each of these three factors independently. Three different types of device were chosen a wire, distributed grit and cylindrical pins. Mean-flow, broadband-turbulence and spectral measurements were taken, mostly for values of Re varying between about 715 and about 2810. It was found that the mean-flow and broadband-turbulence data showed variations withi?0, as expected. Spectra were plotted using scaling given by Perry, Henbest & Chong (1986) and were compared with their models which were developed for high-Reynolds-number flows. For the turbulent wall region, spectra showed reasonably good agreement with their model. For the fully turbulent region, spectra did show some appreciable deviations from their model, owing to low-Reynolds-number effects. Mean-flow profiles, broadband-turbulence profiles and spectra were found to be affected very little by the type of device used for Rd« 1020 and above, indicating an absence of dependence on flow history for this Rerange. These types of measurements were also compared at both Re « 1020 and Re« 2175 to see if they were dependent on how Re was formed (i.e. the combination of velocity and momentum thickness used to determine Re). There were noticeable differences for Re % 1020, but these differences were only convincing for the pins, and there was a general overall improvement in agreement for Rti« 2175. © 1991, Cambridge University Press. All rights reserved.

Description: Mass transport in various kind of two-dimensional water waves is studied. The characteristics of the governing equations for the mass transport depend on the ratio of viscous lengthscale to the amplitude of the free-surface displacement. When this ratio is small, the nonlinearity is important and the mass transport flow acquires a boundary-layer character. Numerical schemes are developed to investigate mass transport in a partially reflected wave and above a hump in the seabed. When the mass transport is periodic in the horizontal direction, a spectral scheme based on a Fourier–Chebyshev expansion, is presented for the solution of the equations. For the ease of a hump on the seabed, the flow domain is divided into three regions. Using the spectral scheme, the mass transport in the uniform-depth regions is calculated first. and the results are used to compute the steady flow in the inhomogeneous flow region which encloses the hump on the seabed.

Description: Air bubbles released from an underwater nozzle emit an acoustical pulse which is of interest both for the study of bubble detachment and for elucidating the mechanism of sound generation by a newly formed bubble. In this paper we calculate theoretically the sequence of bubble shapes from a given nozzle and show that there is for each nozzle a bubble of maximum volume Vmax. Assuming that the bubble becomes detached at its ‘neck’, and that the volume of the detached bubble equals the volume V* of the undetached bubble above its ‘neck’, we determine for each nozzle diameter D an acoustic frequency f* corresponding to ‘slow’ bubble release. Experiments show that the acoustic frequency, hence the bubble size, depends on the rate of air flow to the bubble, but for slow rates of flow the frequency f is very close to the theoretical frequency f*. High-speed photographs suggest that when the bubble pinches off, the limiting form of the surface is almost a cone. This is accounted for by assuming a line sink along the axis of symmetry. Immediately following pinch-off there is evidence of the formation of an axial jet going upwards into the bubble. This may play a part in stimulating the emission of sound. © 1991, Cambridge University Press. All rights reserved.

Description: Two-layer hydraulics is developed for problems in which the moving layers can have stagnant layers above and below, the two internal wave modes can have comparable speeds and the total depth of the moving layers may vary. The general development allows both Boussinesq and non-Boussinesq problems to be studied. Solutions are presented in the Froude-number plane and the effect of different layer densities on the form of the solution space is shown. The theory is applied to two-layer plunging flows and a variety of controlled solutions are found. Solutions for the 21/2-layer theory and the plunging flow theory are demonstrated experimentally. Shear instability is often observed in the divergent section of the channel. © 1991, Cambridge University Press. All rights reserved.

Description: It has been shown experimentally (Lee et al. 1982) that water drops with injected air bubbles inside them may be forced dynamically to assume the spherosymmetric shape. Linear analysis is unable to predict a centring mechanism, but provides two distinct modes of oscillation. Weakly nonlinear theory (Tsamopoulos & BROWN 1987) indicates that centring of the bubble inside the drop occurs when the two interfaces move out of phase. A hybrid boundary element-finite element schemes is used here to study the complete effect of nonlinearity on the dynamics of the motion. The gas inside the liquid shell may be considered either incompressible or compressible by using a polytropic relation. In both cases, the present calculations show that besides the fast oscillation of the shell due to an initial disturbance, a slow oscillatory motion of the centres of the bubble and the drop is induced around the concentric configuration. This occurs in both modes of oscillation and is a direct result of Bernoulli’s law. Furthermore, when this slow oscillation is damped by viscous forces, it is anticipated that it will lead to a spherosymmetric shape. © 1991, Cambridge University Press. All rights reserved.

Description: When a tube, sealed at one end and open to a quiescent environment at the other, is rotated about its axis, fluid flows from the open end along the axis towards the sealed end and returns in an annular boundary layer on the cylindrical wall. This paper describes the first known study to be made of this self-induced flow. Numerical solutions of the Navier-Stokes equations are shown to be in mainly good agreement with experimental results obtained using flow visualization and laser-Doppler anemometry in a rotating glass tube. The self-induced flow in the tube can be described in terms of the length-to-radius ratio, 0, and the Ekman number, E. However, for large values of G (G ≥ 20), the flow outside the boundary layer on the endwall of the tube can be characterized by a single, modified, Ekman number, E*, where E* = O.2) Although most of the fluid entering the open end of the tube is entrained into the annular (Stewartson-type) boundary layer, for small values of E* (E* 〈 0.2) some flow reaches the sealed end. For this so-called ‘short-tube case’, the flow in the boundary layer on the endwall is shown to be similar to that associated with a disk rotating in a quiescent environment: the free disk. The self-induced flow for the short-tube case is believed to be responsible for the ‘hot-poker effect’ used, on some jet engines, to provide ice protection for the nose bullet. © 1991, Cambridge University Press. All rights reserved.

Description: It is well known that the spectral peak of wind-induced gravity waves on the sea surface tends to shift to lower frequencies as the fetch increases. In past theories the nonlinear dynamics subsequent to Benjamin-Feir instability has been found to initiate the downshift in narrow-banded waves in the absence of wind. However, these weakly nonlinear theories all predict the downshift to be only the first phase of an almost cyclic process. Limited by the length of a wave tank, existing experiments are usually made with relatively steep waves which often break. Although there is a theory on how breaking adds dissipation to stop the reversal of the initial trend of downshift, the details of breaking must be crudely characterized by semi-empirical hypotheses. Since the direct role of wind itself must be relevant to the entire development of wind-wave spectrum, we examine here the effect of wind on the nonlinear evolution of unstable sidebands in narrow-banded waves. We assume that the waves do not break and consider the case where the nonlinear effects that initiate the downshift, energy input by wind and damping by internal dissipation all occur on the same timescale. This means that not only must the waves be mild but the wind stress intensity must also lie within a certain narrow range. With these limitations we couple the air flow above the waves with Dysthe’s extension of the cubic Schrodinger equation, and examine the initial as well as the long-time evolution of a mechanically generated wavetrain. For a variety of wind intensities, downshift is indeed found to be enhanced and rendered long lasting. © 1991, Cambridge University Press. All rights reserved.

Description: Results of two field experiments in the North Sea are presented. Pressure was measured at two fixed heights above the mean water level and correlated with simultaneous wave height measurements. Roughly 90 hours of data have been analysed and the results are in agreement with earlier results obtained by Snyder et al. (1981). Measurements over swell give no indication of wave decay or growth for waves travelling faster than the wind or against the wind. © 1991, Cambridge University Press. All rights reserved.

Description: Two-dimensional free-surface flows, which are uniform far upstream in a channel of finite depth that ends suddenly, are computed numerically. The ending is in the form of a vertical wall, which may force the flow upward before it falls down forever as a jet under the effect of gravity. Both subcritical and supercritical solutions are presented. The subcritical solutions are a one-parameter family of solutions, the single parameter being the ratio between the height of the wall and the height of the uniform flow far upstream. On the other hand, the supercritical solutions are a two-parameter family of solutions, the second parameter being the Froude number. Moreover, for some combinations of the parameters, it is shown that the solution is not unique. © 1991, Cambridge University Press. All rights reserved.

Description: Over the past decade and a half, analyses of the dynamics of fluids containing moving contact lines have specified hydrodynamic models of the fluids in a rather small region surrounding the contact lines (referred to as the inner region) which necessarily differ from the usual model. If this were not done, a singularity would have arisen, making it impossible to satisfy the contact-angle boundary condition, a condition that can be important for determining the shape of the fluid interface of the entire body of fluid (the outer region). Unfortunately, the nature of the fluids within the inner region under dynamic conditions has not received appreciable experimental attention. Consequently, the validity of these novel models has yet to be tested. The objective of this experimental investigation is to determine the validity of the expression appearing in the literature for the slope of the fluid interface in the region of overlap between the inner and outer regions, for small capillary number. This in part involves the experimental determination of a constant traditionally evaluated by matching the solutions in the inner and outer regions. Establishing the correctness of this expression would justify its use as a boundary condition for the shape of the fluid interface in the outer region, thus eliminating the need to analyse the dynamics of the fluid in the inner region. Our experiments consisted of immersing a glass tube, tilted at an angle to the horizontal, at a constant speed, into a bath of silicone oil. The slope of the air-silicone oil interface was measured at distances from the contact line ranging between 0.013a and 0.17 a, where a denotes the capillary length, the lengthscale of the outer region (1511 μm). Experiments were performed at speeds corresponding to capillary numbers ranging between 2.8 x 10–4and 8.3 x 10–3. Good agreement is achieved between theory and experiment, with a systematic deviation appearing only at the highest speed. The latter may be a consequence of the inadequacy of the theory at that value of the capillary number. © 1991, Cambridge University Press. All rights reserved.

Description: For the free creeping viscous incompressible plane flow of a finite region, bounded by a simple smooth closed curve and driven solely by surface tension, analyzed previously, the shape evolution was described in terms of a time-dependent mapping function z = Ω(ξ, t) of the unit circle, conformal on| ξ| ≤ 1. An equation giving the time evolution of the map, typically in parametric form, was derived. In this article, the flow of the infinite region exterior to a hypotrochoid is given. This includes the elliptic hole, which shrinks at a constant rate with a constant aspect ratio. The theory is extended to a class of semi-infinite regions, mapped from Im ξ ≤ 0, and used to solve the flow in a half-space bounded by a certain groove. The depth of the groove ultimately decays inversely with time. © 1991, Cambridge University Press. All rights reserved.

Description: The interaction of two identical circular viscous vortex rings starting in a side-by-side configuration is investigated by solving the Navier-Stokes equation using a spectral method with 643 grid points. This study covers initial Reynolds numbers (ratio of circulation to viscosity) up to 1153. The vortices undergo two successive reconnections, fusion and fission, as has been visualized experimentally, but the simulation shows topological details not observed in experiments. The shapes of the evolving vortex rings are different for different initial conditions, but the mechanism of the reconnection is explained by bridging (Melander & HUSSAIN 1988) except that the bridges are created on the front of the dipole close to the position of the maximum strain rate. Spatial structures of various field quantities are compared. It is found that domains of high energy dissipation and high enstrophy production overlap, and that they are highly localized in space compared with the regions of concentrated vorticity. The kinetic energy decays according to the same power laws as found in fully developed turbulence, consistent with concentrated regions of energy dissipation. The main vortex cores survive for a relatively long time. On the other hand, the helicity density which is higher in roots of bridges and threads (or legs) changes rapidly in time. The high-helicity-density and high-energy-dissipation regions overlap significantly although their peaks do not always do so. Thus a long-lived structure may carry high-vorticity rather than necessarily high-helicity density. It is shown that the time evolution of concentration of a passive scalar is quite different from that of the vorticity field, confirming our longstanding warning against relying too heavily on flow visualization in laboratory experiments for studying vortex dynamics and coherent structures. © 1991, Cambridge University Press. All rights reserved.

Description: The evolution equation is derived for a weakly nonlinear coastal Kelvin wave propagating in slowly varying topography in an f-plane ocean. For weak transverse variations in the topography, the wave evolution is governed by a perturbed Korteweg-de Vries equation. In the absence of transverse variation, wave dispersion vanishes and the evolution equation reduces to a nonlinear advection equation with variable coefficients. As a general property of these equations, the total mass flux associated with the Kelvin wave is not conserved; residual mass must be generated. It is shown by an asymptotic analysis that this residual mass field is in balance with a mean geostrophic current long after the passage of the Kelvin wave. This result is verified using a numerical model. The physical mechanism evolved in the generation of the residual mass can be understood in terms of potential vorticity conservation. © 1991, Cambridge University Press. All rights reserved.

Description: The dependence of the parameters of capillary-gravity ripples on the characteristics of the steep surface waves (in the range 4–20 cm) that excite them is found. For steep 4–6 cm waves calculations are performed on the basis of the improved first Stokes method. Qualitative coincidence of the theoretical results with the experimental data is shown. For 7–20 cm waves the results are obtained by the multiple-scale method where the large-scale motion and the driving force for the ripple are found by the improved first Stokes method. Qualitative agreement between theory and experiment in this wavelength range is achieved. © 1991, Cambridge University Press. All rights reserved.

Description: We study the in inviscid mechanisms governing the three-dimensional evolution of an axisymmetric jet by means of vortex filament simulations. The spatially periodic calculations provide a detailed picture of the processes leading to the concentration, reorientation, and stretching of the vorticity. In the purely axisymmetric case, a wavy perturbation in the streamwise direction leads to the formation of vortex rings connected by braid regions, which become depleted of vorticity. The curvature of the jet shear layer leads to a loss of symmetry as compared to a plane shear layer, and the position of the free stagnation point forming in the braid region is shifted towards the jet axis. As a result, the upstream neighbourhood of a vortex ring is depleted of vorticity at a faster rate than the downstream side. When the jet is also subjected to a sinusoidal perturbation in the azimuthal direction, it develops regions of counter-rotating streamwise vorticity, whose sign is determined by a competition between global and local induction effects. In a way very similar to plane shear layers, the streamwise braid vorticity collapses into counter-rotating round vortex tubes under the influence of the extensional strain. In addition, the cores of the vortex rings develop a wavy dislocation. As expected, the vortex ring evolution depends on the ratio R/θ of the jet radius and the jet shear-layer thickness. When forced with a certain azimuthal wavenumber, a jet corresponding to R/θ = 22.6 develops vortex rings that slowly rotate around their unperturbed centreline, thus preventing a vortex ring instability from growing. For R/θ = 11.3, on the other hand, we observe an exponentially growing ring waviness, indicating a vortex ring instability. Comparison with stability theory yields poor agreement for the wavenumber, but better agreement for the growth rate. The growth of the momentum thickness is much more dramatic in the second case. Furthermore, it is found that the rate at which streamwise vorticity develops is strongly affected by the ratio of the streamwise and azimuthal perturbation amplitudes. © 1991, Cambridge University Press. All rights reserved.

Description: Disturbed flow over a rotating disk can lead to transition of the von Kirmin boundary layer at a much lower Reynolds number, Re, (i.e. smaller radius) than that due to the well-known Type 1 stationary mode of instability. This early transition is due to the excitation of the Type 2 instability, similar to that found in the Ekman layer. Detailed numerical values of the growth rates, phase speeds, group velocities, neutral curves, and other characteristics of these two instabilities have been calculated over a wide range of parameters. Neutral curves for the Ekman and Bodewadt boundary layers also are presented. The minimum critical Reynolds numbers for the von Kármán Ekman and Bödewadt layers are Rec(2)= 69.4, 54.3, and 15.1 with wavelengths L = 22.5, 20.1, and 16.6 and at angles e = —19.0°, — 23.1°, and —33.2°, respectively. These minimum critical values frequently do not well describe laboratory observations, however, because at larger Re other modes grow more rapidly and dominate the flow. The computed results are in excellent agreement with laboratory observations wherever comparison is possible. The growth of representative Type 1 instabilities with radius is shown to lead to N-factors greater than 9 at Re = 520 as appears to be necessary for transition to turbulence by the interaction of Type 1 with the basic flow. The growth of Type 2 instabilities with radius can lead to three additional mechanisms of transition. The necessary levels of excitation of Type 2 for these different mechanisms are estimated. A sequence of photographs from a cine film illustrate one of the transition mechanisms discussed: the interaction of Type 2 instabilities and a secondary instability that is nearly perpendicular to the Type 2 vortices. © 1991, Cambridge University Press. All rights reserved.

Description: The effects of compressibility on free (unsteady) viscous heat-conducting vortices are investigated. Analytical solutions are found in the limit of large, but finite, Reynolds number, and small, but finite, Mach number. The analysis shows that the spreading of the vortex causes a radial flow. This flow is given by the solution of an ordinary differential equation (valid for any Mach number), which gives the dependence of the radial velocity on the tangential velocity, density, and temperature profiles of the vortex; estimates of the radial velocity found by solving this equation are found to be in good agreement with numerical solutions of the full equations. The experiments of Mandella (1987) also report a radial flow in the vortex, but their estimates are much larger than the analytical predictions, and it is found that the flow inferred from the experiments violates the Second Law of Thermodynamics for two-dimensional axisymmetric flow. It is speculated that three-dimensionality is the cause of this discrepancy. To obtain detailed analytical solutions, the equations for the viscous evolution are expanded in powers of Mach number, M. Solutions valid to 0(M2), are discussed for vortices with finite circulation. Two specific initial conditions — vortices with initially uniform entropy and with initially uniform density — are analysed in detail. It is shown that swirling axisymmetric compressible flows generate negative radial velocities far from the vortex core owing to viscous effects, regardless of the initial distributions of vorticity, density and entropy. © 1991, Cambridge University Press. All rights reserved.

Description: The quantitative effects of uniform strain and background rotation on the stability of a strip of constant vorticity (a simple shear layer) are examined. The thickness of the strip decreases in time under the strain, so it is necessary to formulate the linear stability analysis for a time-dependent basic flow. The results show that even a strain rate γ (scaled with the vorticity of the strip) as small as 0.25 suppresses the conventional Rayleigh shear instability mechanism, in the sense that the r.m.s. wave steepness cannot amplify by more than a certain factor, and must eventually decay. For γ 〈 0.25 the amplification factor increases as γ decreases; however, it is only 3 when γ ė 0.065. Numerical simulations confirm the predictions of linear theory at small steepness and predict a threshold value necessary for the formation of coherent vortices. The results help to explain the impression from numerous simulations of two-dimensional turbulence reported in the literature that filaments of vorticity infrequently roll up into vortices. The stabilization effect may be expected to extend to two- and three-dimensional quasi-geostrophic flows.

Description: The events which are responsible for strong Reynolds-stress production in the nearwall region of a bounded turbulent shear flow have been investigated in a turbulent boundary layer at a Reynolds number based on momentum thickness of Reθ = 4650. The coherent structures associated with the production process have been studied using the quadrant detection technique. All three velocity components were measured in a three-dimensional sampling volume about the point of detection. The conditional ensemble-averaged velocity field associated with the detection of a sweep or an ejection is presented and compared with non-conditioned space—time correlations. Conditional space—time probability density distributions were calculated at all measurement locations based on the occurrence of a Reynolds-stressproducing event at the detection point. The resulting three-dimensional representation of the conditional probability demonstrates that a significant fraction of the events are relatively large in scale, that a hierarchy of sizes exists and that there is a link between the outer flow and the “bursting” process. However, many investigators have shown that the “bursting” frequency scales with wall variables. Therefore all indications suggest that the scales are generated by a wall-layer mechanism but grow to sizes and convect with velocities scaling with the outer layer. © 1991, Cambridge University Press. All rights reserved.

Description: A dilute dispersion containing drops of one fluid dispersed in a second, immiscible fluid is considered. The drops are sufficiently small that inertia is negligible and that they remain spherical. Two drops of different size are in relative motion due to either Brownian diffusion or gravitational sedimentation. When the drops become close, they interact with each other owing to hydrodynamic disturbances and van der Waals attractions, and, under favourable conditions, they will collide with each other and coalesce. The rate at which two drops collide is predicted by solving the diffusion equation for Brownian coalescence, and by using a trajectory analysis to follow the relative motion of pairs of drops for gravity-induced coalescence. The emphasis of our analysis is on the effects of drop interactions on their collision rate, and these are described by the collision efficiency. Since the hydrodynamic resistance to the drop relative motion reduces with a decreasing ratio of the viscosities of the drop fluid and the surrounding fluid, the collision efficiency increases with decreasing viscosity ratio. A qualitative difference in the collision behaviour of viscous drops from that of rigid spheres is demonstrated; finite collision rates for drops are predicted even in the absence of attractive forces, provided that drop deformation is negligible, whereas rigid particles with smooth surfaces will not come into contact in a fluid continuum unless an attractive force is present which is able to overcome the lubrication forces resisting the relative motion. Hydrodynamic interactions between two spherical drops are accounted for exactly by determining the two-sphere relative mobility functions from previous solutions for two drops moving along and normal to their line of centres. These solutions are based on the method of reflections for widely separated drops, lubrication theory for drops in near-contact, and bispherical coordinates for general separations. The hydrodynamic interactions have a greater effect on reducing the rate of gravity collisions than the rate of Brownian collisions. © 1991, Cambridge University Press. All rights reserved.

Description: A layer of volatile viscous liquid drains down a uniformly heated inclined plate. Long-wave instabilities of the uniform film are studied by deriving an evolution equation for two-dimensional disturbances. This equation incorporates viscosity, gravity, surface tension, thermocapillarity, and evaporation effects. The linear theory derived from this describes the competition among the instabilities. Numerical solution of the evolution equation describes the finite-amplitude behaviour that determines the propensity for dryout of the film. Among the phenomena that appear are the tendency to wave breaking, the creation of secondary structures, and the pre-emption of dryout by mean flow. © 1991, Cambridge University Press. All rights reserved.

Description: The vortices near the origin of an initially laminar mixing layer have a single frequency with a well-defined phase; i.e. there is little phase jitter. Further downstream, however, the phase jitter increases suddenly. Even when the flow is forced, this same transition is observed. The forcing partially loses its influence because of the decorrelation of the phase between the forcing signal and the passing coherent structures. In the present investigation, this phenomenon is documented and the physical mechanism responsible for the phase decorrelation is identified. © 1991, Cambridge University Press. All rights reserved.

Description: We explain the emergence of organized structures in two-dimensional turbulent flows by a theory of equilibrium statistical mechanics. This theory takes into account all the known constants of the motion for the Euler equations. The microscopic states are all the possible vorticity fields, while a macroscopic state is defined as a probability distribution of vorticity at each point of the domain, which describes in a statistical sense the fine-scale vorticity fluctuations. The organized structure appears as a state of maximal entropy, with the constraints of all the constants of the motion. The vorticity field obtained as the local average of this optimal macrostate is a steady solution of the Euler equation. The variational problem provides an explicit relationship between stream function and vorticity, which characterizes this steady state. Inertial structures in geophysical fluid dynamics can be predicted, using a generalization of the theory to potential vorticity. © 1991, Cambridge University Press. All rights reserved.

Description: It is known that the mixing or spreading rate of free mixing layers decreases with an increase in the convective Mach number of the flow. At supersonic convective Mach number the natural rate of mixing of the shear layers is very small. It is believed that the decrease in mixing rate is directly related to the decrease in the rate of growth of the instabilities of these flows. In an earlier study (Tam & Hu 1989) it was found that inside a rectangular channel supersonic free shear layers can support two families of instability waves and two families of acoustic wave modes. In this paper the possibility of driving these normal acoustic wave modes into resonant instability by using a periodic Mach wave system is investigated. The Mach waves can be generated by wavy walls. By properly choosing the wavelength of the periodic Mach wave system mutual secular excitation of two selected acoustic wave modes can be achieved. In undergoing resonant instability, the acoustic modes are locked into mutual simultaneous forcing. The periodic Mach waves serve as a catalyst without actually being involved in energy transfer. The resonant instability process is analysed by the method of multiple scales. Numerical results indicate that by using wavy walls with an amplitude-to-wavelength ratio of 11/2% it is possible to obtain a total spatial growth of e9 folds over a distance of ten channel heights. This offers reasonable promise for mixing enhancement. The results of a parametric study of the effects of flow Mach numbers, temperature ratio, shear-layer thickness, modal numbers as well as three-dimensional effects on the spatial growth rate of the resonant instability are reported and examined so as to provide basic information needed for future feasibility analysis. © 1991, Cambridge University Press. All rights reserved.

Description: Results from laboratory experiments on oscillatory flows over topography in a rapidly rotating cylinder of homogeneous liquid are presented and compared with weakly nonlinear and low-order theories. With periodic forcing, the motion can be either periodic or chaotic. In the periodic regime, linear Rossby waves excited by the sloshing flow over shallow bottom topography become resonant at forcing frequencies that are integer multiples of the natural free Rossby wave frequency. As the topographic effect or the forcing amplitude is increased, the maximum response is shifted away from the linearly resonant frequency to higher periods for azimuthal topographic wavenumbers of 1 and to lower periods for topographic zonal wavenumbers exceeding 1, in agreement with theory. The simple theories which use slippery sidewalls do not describe the observed chaotic flows. These complex states are associated with the development of small-scale vortices in the sidewall boundary layer that are shed into the interior. For both periodic and chaotic flows, long-time particle paths can contain significant chaotic components which are revealed in direct Poincare sections constructed from observations of surface floats. © 1991, Cambridge University Press. All rights reserved.

Description: Cavitation has been observed in the trailing vortex system of an elliptic planform hydrofoil. A complex dependence on Reynolds number and gas content is noted at inception. Some of the observations can be related to tension effects associated with the lack of sufficiently large-sized nuclei. Inception measurements are compared with estimates of pressure in the vortex obtained from LDV measurements of velocity within the vortex. It is concluded that a complete correlation is not possible without knowledge of the fluctuating levels of pressure in tip-vortex flows. When cavitation is fully developed, the observed tip-vortex trajectory shows a surprising lack of dependence on any of the physical parameters varied, such as angle of attack, Reynolds number, cavitation number, and dissolved gas content. © 1991, Cambridge University Press. All rights reserved.

Description: Generalized Taylor dispersion theory is extended so as to enable the analysis of the transport in unbounded homogeneous shear flows of Brownian particles possessing internal degrees of freedom (e.g. rigid non-spherical particles possessing orientational degrees of freedom, flexible particles possessing conformational degrees of freedom, etc.). Taylor dispersion phenomena originate from the coupling between the dependence of the translational velocity of such particles in physical space upon the internal variables and the stochastic sampling of the internal space resulting from the internal diffusion process.Employing a codeformational reference frame (i.e. one deforming with the sheared fluid) and assuming that the eigenvalues of the (constant) velocity gradient are purely imaginary, we establish the existence of a coarse-grained, purely physical-space description of the more detailed physical-internal space (microscale) transport process. This macroscale description takes the form of a convective–diffusive ‘model’ problem occurring exclusively in physical space, one whose formulation and solution are independent of the internal (‘local’-space) degrees of freedom.An Einstein-type diffusion relation is obtained for the long-time limit of the temporal rate of change of the mean-square particle displacement in physical space. Despite the nonlinear (in time) asymptotic behaviour of this displacement, its Oldroyd time derivative (which is the appropriate one in the codeformational view adopted) tends to a constant, time-independent limit which is independent of the initial internal coordinates of the Brownian particle at zero time.The dyadic dispersion-like coefficient representing this asymptotic limit is, in general, not a positive-definite quantity. This apparently paradoxical behaviour arises due to the failure of the growth in particle spread to be monotonic with time as a consequence of the coupling between the Taylor dispersion mechanism and the shear field. As such, a redefinition of the solute's dispersivity dyadic (appearing as a phenomenological coefficient in the coarse-grained model constitutive equation) is proposed. This definition provides additional insight into its physical (Lagrangian) significance as well as rendering this dyadic coefficient positive-definite, thus ensuring that solutions of the convective–diffusive model problem are well behaved. No restrictions are imposed upon the magnitude of the rotary Péclet number, which represents the relative intensities of the respective shear and diffusive effects upon which the solute dispersivity and mean particle sedimentation velocity both depend.The results of the general theory are illustrated by the (relatively) elementary problem of the sedimentation in a homogeneous unbounded shear field of a size-fluctuating porous Brownian sphere (which body serves to model the behaviour of a macromolecular coil). It is demonstrated that the well-known case of the translational diffusion in a homogeneous shear flow of a rigid, non- fluctuating sphere (for which the Taylor mechanism is absent) is a particular case thereof.

Description: We generalize the class of models of the wall layer of Aubry et al. (1988), based on the proper orthogonal decomposition, to permit uncoupled evolution of streamwise and cross-stream disturbances. Since the Reynolds stress is no longer constrained, in the absence of streamwise spatial variations all perturbation velocity components eventually decay to zero. However, their transient behaviour is dominated by ‘ghosts’ of the non-trivial fixed points and attracting heteroclinic cycles which are characteristic features of those models based on empirical eigenfunctions whose individual velocity components are fixed. This suggests that the intermittent events observed in Aubry et al. do not arise solely because of the effective closure assumption incorporated in those models, but are rooted deeper in the dynamical phenomenon of the wall region. © 1991, Cambridge University Press. All rights reserved.

Description: This article considers certain two-dimensional, irrotational, steady flows in fluid regions of finite depth and infinite horizontal extent. Geometrical information about these flows and their singularities is obtained, using a variant of a classical comparison principle. The results are applied to three types of problems: (i) supercritical solitary waves carrying planing surfaces or surfboards, (ii) supercritical flows past ship hulls and (iii) supercritical interfacial solitary waves in systems consisting of two immiscible fluids. © 1991, Cambridge University Press. All rights reserved.

Description: A complete second-order solution is presented for the two-dimensional wave motion forced by a generic planar wavemaker. The wavemaker is doubly articulated and includes both piston and hinged wavemakers of variable draught. It is shown that the first-order evanescent eigenseries cannot be neglected when computing the amplitude of the second-order free wave. A previously neglected, time-independent solution that is required to satisfy an inhomogeneous kinematic boundary condition on the wavemaker as well as an inhomogeneous Neumann boundary condition on the free surface is examined in detail for the first time. This time-independent solution is found to accurately estimate the mean return flow in a closed wave flume computed by the Eulerian method. This mean return current due to Stokes drift is usually estimated using the principle of kinematic conservation of mass flux. Even though the first-order eigenseries will converge for any geometry of a generic planar wavemaker, the second-order solutions obtained from Stokes perturbation expansions will not converge for all planar wavemaker geometries. © 1991, Cambridge University Press. All rights reserved.

Description: Extensive experimental studies are presented of the effects of prolonged streamline divergence on developing turbulent boundary layers. The experiment was arranged as source flow over a flat plate with a maximum divergence parameter of about 0.075. Mild, but alternating in sign, upstream-pressure-gradient effects on diverging boundary layers are also discussed. It appears that two overlapping stages of development are involved. The initial stage covers a distance of about 20 initial boundary-layer thicknesses (δ0) from the start of divergence, where the coupled effects of pressure gradient and divergence are present. In this region there is a fairly large reduction in divergence parameter, Re(Reynolds number based on momentum thickness) remains constant (« 1400) and the boundary-layer properties change rapidly. In the second region, which lasts nearly to the end of the diverging section, the pressure-gradient effects are negligible, the rate of decrease in divergence parameter is very small and Reincreases gradually. Up to the last measurement station (« 10050) the flow is still considered to be at a low Reynolds number (R0« 2000). For almost the entire length of this region, the profiles of non-dimensional eddy viscosity appear to be self-similar, but have larger values than for the unperturbed flow. Also in this region, beyond 3550, the wake parameter, which has reduced significantly, becomes nearly constant and independent of Re. On the other hand the entrainment rate attains a constant value at around 50δ0. It appears that the boundary layer reaches a state of equilibrium. It is suggested that this is the result of an enhanced turbulent diffusion to the outer layer. Spectral measurements show that divergence affects mainly the low-wavenumber, large-scale motions. However, there is no change in large-eddy configurations, since the dimensionless structure parameters show only negligible deviations from the unperturbed values. © 1991, Cambridge University Press. All rights reserved.

Description: We modify a recent theory of Longuet-Higgins (1989a, b) to study the resonant interaction between an isotropic mode and one or two distortional modes of an oscillating bubble in water when the isotropic mode is forced by ambient sound. Gravity and buoyant rise are ignored. The energy exchange between modes is strong enough so that both (or all three) can attain comparable amplitudes after a long time. We show that for two-mode interactions the mode-coupling equations are similar to those studied in other physical contexts such as nonlinear optics, coupled oscillators and standing waves in a basin. Instability around fixed points is examined for various bubble radii, phase mismatch, and detuning of the external forcing. Numerical evidences of chaotic bubble oscillations and sound radiation are discussed. It is found that in a certain parameter domain, Hopf bifurcations are possible, and chaos is reached via a period-doubling sequence. However, when there are three interacting modes, each of the two distortion modes interacts with the breathing mode directly and the route to chaos is via a quasi-periodic 2-torus. Possible relevance of this theory to the observed erratic drifting of a bubble is discussed. © 1991, Cambridge University Press. All rights reserved.

Description: It is a well-known observation in fluidization technology, axial filters and the blood microcirculation that the discharge concentration of a particulate suspension through a small circular side pore which is fed by a large main tube can be significantly lower than the feed concentration. Two underlying mechanisms are believed to be responsible for this exit concentration defect: the fluid skimming from the particle-free layer at the main tube wall and the particle screening due to the hydrodynamic interaction with the pore entrance. In this paper we shall focus our attention only on the first mechanism and shall present a theory which relates the discharge concentration to the dimensionless volume discharge rate 2πQ through the side pore (scaled to the wall shear rate in the main tube and the pore radius) and the ratio of the particle to pore entrance diameters, under creeping flow conditions and for small particle concentrations. First, the shape of the capture tube cross-section upstream of the pore is computed on the basis of a simplified three-dimensional velocity field which neglects the disturbance produced by the orifice on the incoming shear flow. Surprisingly simple closed-form expressions for this shape are derived as Q→∞ or as Q→0. Also, using a recently developed exact solution for the simple shear flow past an orifice (Davis 1991), we are able to rigorously demonstrate that, even for small Q, the disturbance produced by the orifice on the shear flow has only a minor effect on the capture tube cross-section far upstream. This simplified flow field is then used to construct a three-dimensional theory for the discharge concentration defect due to pure fluid skimming for a dilute suspension of spheres. The qualitative features of the theoretical predictions show the same trends as the experimental observations in the microcirculation, although the limits of this theory are well below the observed hematocrit concentrations and the particles are taken as rigid spheres. © 1991, Cambridge University Press. All rights reserved.

Description: Longitudinal rolls represent the preferred form of convection in a horizontal fluid layer heated from below in the presence of parallel shear flows for sufficiently low Reynolds numbers and for a finite range of the Rayleigh number above the critical value Rαc. In this paper properties of the longitudinal rolls and their stability with respect to three-dimensional disturbances are investigated in the case of Poiseuille flow. While the convective heat transport is independent of the Reynolds number, the mass flux through the channel at a given Reynolds number decreases with increasing Rayleigh number. A wavy instability is found to set in at a finite Reynolds number and relatively low Rayleigh numbers, depending on the Prandtl number P. In particular, the stability region for longitudinal rolls is analysed for P = 0.025, 0.1, 0.71, 2.5, and 7. For sufficiently small Reynolds number the oscillatory, the skewed varicose or the knot instability can precede the wavy instability. For P = 7 the wavy instability is preceded by a modified knot instability throughout the Reynolds-number range that has been investigated. In spite of the difference in symmetry, the results for Poiseuille flow resemble those obtained earlier in the case of plane Couette flow. © 1991, Cambridge University Press. All rights reserved.

Description: The development of turbulent spots in plane Couette flow was studied by means of direct numerical simulation. The Reynolds number was varied between 300 and 1500 (based on half the velocity difference between the two surfaces and half the gap width) in order to determine the lowest possible Reynolds number for which localized turbulent regions can persist, i.e. a critical Reynolds number, and to determine basic characteristics of the spot in plane Couette flow. It was found that spots can be sustained for Reynolds numbers above approximately 375 and that the shape is elliptical with a streamwise elongation that is more accentuated for high Reynolds numbers. At large times though there appears to be a slow approach towards a circular spot shape. Various other features of this spot suggest that it may be classified as an interesting intermediate case between the Poiseuille and boundary-layer spots. In the absence of experiments for this case the present results represent a true prediction of the physical situation. © 1991, Cambridge University Press. All rights reserved.

Description: Directional solidification experiments have been carried out using the analogue casting system of NH4Cl-H20 solution by cooling it from below with a constant-temperature surface ranging from —31.5 °C to +11.9 °C. The NH4Cl concentration was 26% in all solutions, with a liquidustemperature of 15 °C. It was found that finger convection occurred in the fluid region just above the mushy layer in all experiments. Plume convection with associated chimneys in the mush occurred in experiments with bottom temperatures as high as +11.0°C. However, when the bottom temperature was raised to +11.9°C, no plume convection was observed, although finger convection continued as usual. A method has been devised to determine the porosity of the mush by computed tomography. Using the mean value of the porosity across the mush layer and the permeability calculated by the Kozeny-Carman relationship, the critical solute Rayleigh number across the mush layer for onset of plume convection was estimated to be between 200 and 250. © 1991, Cambridge University Press. All rights reserved.

Description: We consider the problem of steady Euler flows in a torus. We show that in the absence of a direction of symmetry the solution for the vorticity contains δ-function singularities at the rational surfaces of the torus. We study the effect of a small but finite viscosity on these singularities. The solutions near a rational surface contain cat’s eyes or islands, well known in the classical theory of critical layers. When the islands are small, their widths can be computed by a boundary-layer analysis. We show that the islands at neighbouring rational surfaces generally overlap. Thus, steady toroidal flows exhibit a tendency towards Beltramization. © 1991, Cambridge University Press. All rights reserved.

Description: A boundary-integral method is developed for computing first-order and mean second-order wave forces on floating bodies with small forward speed in three dimensions. The method is based on applying Green’s theorem and linearizing the Green function and velocity potential in the forward speed. The velocity potential on the wetted body surface is then given as the solution of two sets of integral equations with unknowns only on the body. The equations contain no water-line integral, and the free-surface integral decays rapidly. The Timman-Newman symmetry relations for the added mass and damping coefficients are extended to the case when the double-body flow around the body is included in the free-surface condition. The linear wave exciting forces are found both by pressure integration and by a generalized far-field form of the Haskind relations. The mean drift force is found by far-field analysis. All the derivations are made for an arbitrary wave heading. A boundary-element program utilizing the new method has been developed. Numerical results and convergence tests are presented for several body geometries. It is found that the wave exciting forces and the mean drift forces are most influenced by a small forward speed. Values of the wave drift damping coefficient are computed. It is found that interference phenomena may lead to negative wave drift damping for bodies of complicated shape. © 1991, Cambridge University Press. All rights reserved.

Description: A previous study revealed that only maximization of the efficiency function, from among a large class of mean field moments, results in both a logarithmic law and a velocity defect law in turbulent Poiseuille channel flow. The efficiency function, $, is the product of a drag coefficient and the ratio of the fluctuation and mean dissipation rate integrals. Here, maximum $ is explored in Couette flow to test its generality as a statistical stability criterion for turbulent shear flows. The optimal flow exhibits a logarithmic law but does not have a velocity defect law. A decreasingvelocity defect is predicted for Reynolds numbers up to 30000. This prediction is shownto be supported by the existing data, which are limited to Reynolds numbers less than 20000. © 1991, Cambridge University Press. All rights reserved.

Description: The problem of the dynamics of elliptical-vortex solutions of the rotating shallow water equations is solved in Lagrangian coordinates using methods of Hamiltonian mechanics. All such solutions are shown to be quasi-periodic by reducing the problem to quadratures in terms of physically meaningful variables. All of the relative Equilibria - including the well-known rodon solution - are shown to be orbitally Lyapunov stable to perturbations in the class of elliptical-vortex solutions. © 1991, Cambridge University Press. All rights reserved.

Description: The modelling of the pressure-strain correlation of turbulence is examined from a basic theoretical standpoint with a view toward developing improved second-order closure models. Invariance considerations along with elementary dynamical systems theory are used in the analysis of the standard hierarchy of closure models. In these commonly used models, the pressure-strain correlation is assumed to be a linear function of the mean velocity gradients with coefficients that depend algebraically on the anisotropy tensor. It is proven that for plane homogeneous turbulent flows the equilibrium structure of this hierarchy of models is encapsulated by a relatively simple model which is only quadratically nonlinear in the anisotropy tensor. This new quadratic model - the SSG model - appears to yield improved results over the Launder, Reece & Rodi model (as well as more recent models that have a considerably more complex nonlinear structure) in five independent homogeneous turbulent flows. However, some deficiencies still remain for the description of rotating turbulent shear flows that are intrinsic to this general hierarchy of models and, hence, cannot be overcome by the mere introduction of more complex nonlinearities. It is thus argued that the recent trend of adding substantially more complex nonlinear terms containing the anisotropy tensor may be of questionable value in the modelling of the pressure-strain correlation. Possible alternative approaches are discussed briefly. © 1991, Cambridge University Press. All rights reserved.

Description: A general solution of the three-dimensional Stokes equations is developed for the viscous flow past a square array of circular cylindrical fibres confined between toparallel walls. This doubly periodic solution, which is an extension of the theory developed by Lee & Fung (1969) for flow around a single fibre, successfully describes the transition in behaviour from the Hele-§haw potential flow limit (aspect ratio B ≪ 1) to the viscous two-dimensional limiting case (B ≫ 1, Sangani & Acrivos 1982) for the hydrodynamic interaction between the fibres. These results are also compared with the solution of the Brinkman equation for the flow through a porous medium in a channel. This comparison shows that the Brinkman approximation is very good when B 5, but breaks down when B ≤ 0(1). A new interpolation formula is proposed for this last regime. Numerical results for the detailed velocity profiles, the drag coefficient and the Darcy permeability K p are presented. It is shown that the velocity component perpendicular to the parallel walls is only significant within the viscous layers surrounding the fibres, whose thickness is of the order of half the channel height B'. One finds thatwhen the aspect ratio B 5, the neglect of the vertical velocity component vzcan lead tolarge errors in the satisfaction of the no-slip boundary conditions on the surfaces of the fibres and large deviations from the approximate solution in Lee (1969), in which vzand the normal pressure field are neglected. The numerical results show that the drag coefficient of the fibrous bed increases dramatically when the open gap between adjacent fibres Af becomes smaller than B\\\\ The predictions of the new theory are used to examine the possibility that a cross-bridging slender fibre matrix can exist in the intercellular cleft of capillary endothelium as proposed by Curry & Michel (1980. © 1991, Cambridge University Press. All rights reserved.

Description: Measurements of wall pressure, and mean and r.m.s. velocities of the confined flow about a disk of 50 % area blockage have been carried out for two Newtonian fluids and four concentrations of a shear-thinning weakly elastic polymer in aqueous solution encompassing a Reynolds-number range from 220 to 138000. The flows of Newtonian and non-Newtonian fluids were found to be increasingly dependent on Reynolds numbers below 50000, with a decrease in the length of the recirculation region and dampening of the normal Reynolds stresses. At Reynolds numbers less than 25000, the recirculation bubble lengthened and all turbulence components were suppressed with increased polymer concentration so that, at a Reynolds number of 8000, the maximum values of turbulent kinetic energy were 35 and 45% lower than that for water, with 0.2% and 0.4% solutions of the polymer. Non-Newtonian effects were found to be important in regions of low local strain rates in low-Reynolds-number flows, especially inside the recirculation bubble and close to the shear layer, and are represented by both an increase in viscous diffusion and a decrease in turbulent diffusion to, respectively, 6% and 18% of the largest term of the momentum balance with a 0.4% polymer solution at a Reynolds number of 7700. The asymmetry and unsteadiness of the flow at Reynolds numbers between 400 and 6000 is shown to be an aerodynamic effect which increases in range and amplitude with the more concentrated polymer solutions. © 1991, Cambridge University Press. All rights reserved.

Description: The collapse of a spherical vapour cavity in the vicinity of a compliant boundary is examined numerically. The fluid is treated as a potential flow and a boundary-element method is used to solve Laplace's equation for the velocity potential. Full nonlinear boundary conditions are applied on the surface of the cavity. The compliant wall is modelled as a membrane with a spring foundation. At the interface between the fluid and the membrane, the pressure and vertical velocity in the flow are matched to the pressure and vertical velocity of the membrane using linearized conditions. The results of calculations are presented which show the effect of the parameters describing the flow (the initial cavity size and position, the fluid density and the pressure driving the collapse) and the parameters describing the compliant wall (the mass per unit area, membrane tension, spring constant and coating radius) on the interaction between the two. When the wall is rigid, the collapse of the cavity is characterized by the formation of a re-entrant jet that is directed toward the wall. However, if the properties of the compliant wall are chosen properly, the collapse can be made to occur spherically, as if the cavity were in an infinite fluid, or with the re-entrant jet directed away from the wall, as if the cavity were adjacent to a free surface. This behaviour is in qualitative agreement with the experiments of Gibson & Blake (1982) and Shima, et al. (1989). Calculations of the transfer of energy between the flow and the coating are also presented. © 1991, Cambridge University Press. All rights reserved.

Description: In this paper we examine the linear stability of an annular film surrounding a dielectric-fluid core in a tube in the presence of double layers of charges at the film core and at the film—tube interfaces, when the fluid—fluid interface is of low tension. In the absence of electrostatic forces, the surface tension force arising from the circumferential curvature destabilizes, and that from the axial curvature stabilizes the system. The competition is such that waves larger than the unperturbed interface circumference are unstable and those shorter are stable. For charged layers in the film, two cases are examined (i) double-layer repulsion where the volume charge density is everywhere of the same sign and (ii) double-layer attraction where the diffusive layers next to the film interfaces are of opposite signs. In the first case, double-layer repulsion and surface tension lowering stabilize the destabilizing action of the circumferential component of the surface tension force, and a window of stability can exist. In the case of double layers of opposite signs, double-layer attraction destabilizes the system, and growth rates larger than those caused by pure capillarity can arise. Finally, for the case of a core bounded by an infinite electrolyte, surface tension lowering stabilizes the destabilizing action of the circumferential component of the surface tension force and destabilizes the longitudinal one, although the magnitudes of these effects may differ. As a result the thread can become unstable to waves shorter than the interface circumference. © 1991, Cambridge University Press. All rights reserved.

Description: A spatially developing countercurrent mixing layer was established experimentally by applying suction to the periphery of an axisymmetric jet. A laminar mixing region was studied in detail for a velocity ratio R = AU/2Ū between 1 and 1.5, where ΔU describes the intensity of the shear across the layer and Ū is the average speed of the two streams. Above a critical velocity ratio RCT = 1.32 the shear layer displays energetic oscillations at a discrete frequency which are the result of very organized axisymmetric vortex structures in the mixing layer. The spatialorder of the primary vortices inhibits the pairing process and dramatically alters the spatial developmentof the shear layer downstream. Consequently, the turbulence level inthe jet core is significantly reduced, as is the decay rate of the mean velocity on thejet centreline. The response of the shear layer to controlled external forcing indicates that the shear layer oscillations at supercritical velocity ratios are self-excited. The experimentally determined critical velocity ratio of 1.32, established for very thin axisymmetric shear layers, compares favourably with the theoretically predicted valueof 1.315 for thetransition from convective to absolute instability in plane mixing layers (Huerre & Monkewitz 1985). © 1991, Cambridge University Press. All rights reserved.

Description: This paper examines the three-dimensional wave packets which are generated by an initially localized pulse disturbance in an incompressible parallel flow and described by a double Fourier integral in the wavenumber space. It aims to clear up some confusion arising from the asymptotic evaluation of this integral by the method of steepest descent. In this asymptotic analysis, the calculation of the eigenvalues can be facilitated by making use of the Squire transformation. It is demonstrated that the use of the Squire transformation introduces branch points in the saddle-point equation that links the physical coordinates to the saddle-point value, regardless of whether the flow is viscous or in viscid. It is shown that the correct branch should be chosen according to the principle of analytic continuation. The saddle-point values for the three-dimensional problem should be considered to be the analytic continuation of those for the two-dimensional case where the saddle-point values can be uniquely determined. The three-dimensional wave packets in an inviscid wake flow are examined; their behaviour at large time is calculated asymptotically by the method of steepest descent in terms of the two-dimensional eigenvalue relation. © 1991, Cambridge University Press. All rights reserved.

Description: There are two separate mechanisms which can generate a boundary flow in a non-rotating, stratified fluid. The Phillips–Wunsch boundary flow arises in a stratified, quiescent fluid along a sloping boundary. Isopycnals are deflected from the horizontal in order to satisfy the zero normal mass flux condition at the boundary; this produces a horizontal density gradient which drives a boundary flow. The second mechanism arises when there is an independently generated turbulent boundary layer at the wall such that the eddy diffusion coefficients decay away from the wall; if the vertical density gradient is non-uniform the greater eddy diffusion coefficients near the wall result in a greater accumulation or diminution of density near the wall. This produces a horizontal density gradient which drives a boundary flow, even at a vertical wall. The turbulent Phillips Wunsch flow, in which there is a vigorous recirculation in the boundary layer, develops if the wall is sloping. This recirculation produces an additional dispersive mass flux along the wall, which also generates a net volume flux along the wall if the density gradient is non-uniform.We investigate the effect of these boundary flows upon the mixing of the fluid in the interior of a closed vessel. The mixing in the interior fluid resulting from the laminar Phillips–Wunsch-driven boundary flow is governed by [ ho_t = frac{kappa_{ m m}}{A}( ho z A)_z. ] The turbulence-driven boundary flow mixes the interior fluid according to [ ho_frac{1}{A}left(kappa_{ m e} ho zintdelta,{ m d}s ight)z. ] Here ρ is the density, κm and κe are the far-field (molecular) and effective boundary (eddy) diffusivities, including the dispersion, A is the cross-sectional area of the basin and ∫ δ ds is the cross-sectional area of the boundary layer. The interior fluid is only mixed significantly faster than the rate of molecular diffusion if there is a turbulent boundary layer at the sidewalls of the containing vessel which either (i) varies in intensity with depth in the vessel or (ii) is mixing a non-uniform density gradient. These mixing phenomena are consistent with published experimental data and we consider the effect of such mixing in the ocean.

Description: This paper presents and discusses the results of an extensive experimental investigation of a flat-plate turbulent boundary subjected to an adverse pressure gradient sufficiently strong to lead to the formation of a large separated region. The pressure gradient was produced by applying strong suction through a porous cylinder fitted with a rear flap and mounted above the boundary layer and with its axis in the spanwise direction. Attention is concentrated on the structure of the turbulent flow within the separated region and it is shown that many features are similar to those that occur in separated regions produced in a very dissimilar manner. These include the fact that structure parameters, like Reynolds stress ratios, respond markedly to the re-entrainment of turbulent fluid transported upstream from the reattachment region, the absence of any logarithmic region in the thin wall boundary layer beneath the recirculation zone and the lack of any effective viscous scaling in this wall region, and the presence of a significant low-frequency motion having timescales much longer than those of the large-eddy structures around reattachment. Similarities with boundary layers separating under the action of much weaker pressure gradients are also found, despite the fact that the nature of the flow around separation is quite different. These similarities and also some noticeable differences are discussed in the paper, which concludes with some inferences concerning the application of turbulence models to separated flows. © 1991, Cambridge University Press. All rights reserved.

Description: Turbulent boundary–layer fluctuations in the incompressive domain are expressed in terms of fluctuating velocity–product ‘sources’ in order to elucidate relative characteristics of fluctuating wall–shear stress and pressure in the subconvective range of streamwise wavenumbers. Appropriate viscous wall conditions are applied, and results are obtained to lowest order in this Strouhal–scaled wavenumber which serves as the expansion parameter. The spectral amplitudes of pressure and of the shear stress component directed along the wavevector both contain additive terms proportional to source integrals with exponential wall–distance weighting characteristic respectively of the irrotational and the rotational fields. At low wavenumbers, barring unexpected relative smallness of the pertinent boundary–layer source term, the rotational terms become dominant. There the wall pressure and shear–stress component have spectra that approach the same non–vanishing, wavevector-white but generally viscous–scale–dependent level and are totally coherent with phase difference 1-2π. The other, irrotational contributions to the shear–stress and pressure amplitudes likewise bear a simple and previously known, generally wavevector and frequency–dependent, ratio to one another. In an inviscid limit this contribution to the pressure amplitude reduces to the one obtained previously from inviscid treatments. A representative class of models is introduced for the source spectrum, and the resulting rotational contribution to the spectral density of wall pressure and K–aligned shear stress at low (but incompressive) wavenumbers is estimated. It is suggested that this contribution may predominate and account for measured low-wavenumber levels of wall pressure. © 1991, Cambridge University Press. All rights reserved.

Description: An experimental observation of the flow following the discharge of firearms has been carried out by means of ultra-high-speed visualization. The theory of similarity has been applied in order to define the rules governing the tests on models, chiefly for gun firing-air intake interference problems. When the blast effect predominates, no geometric similarity is required between the simulation gun and the simulated one, so the model and the simulation gun can have different scales. It is shown that the main parameter characterizing the blast effect is the energy rate at the muzzle which can be considered as a point source of energy caused by a very hot gas. So, the muzzle wave tends asymptotically toward the blast wave of a non-instantaneous intense point explosion. Specific experiments confirm this assertion. All previous results allow a theoretical modelling of gun-firing aerodynamic phenomena which will be presented in a separate paper. © 1991, Cambridge University Press. All rights reserved.

Description: A Fizeau optical interferometer has been used to visualize the wake behind a circular cylinder at low Reynolds numbers Re. As well as showing the vortex shedding mechanism and development of the far wake in a new light, the shed vortex strength and age were derived from the results. The vortex velocity distributions, at downstream distances of 5 to 16 diameters, were found to be those of convected Oseen vortices. These measurements confirmed the existence of a transition at Re « 100, which reflects the emergence of convection as the dominant process in the near wake. © 1991, Cambridge University Press. All rights reserved.

Description: We have performed high-resolution numerical simulations of supersonic slip surfaces to confirm and illuminate earlier analytic nonlinear stability calculations of such structures. This analytic work was in turn inspired by earlier computer simulations reported in Woodward (1985) and Woodward et al. (1987). In particular Artola & Majda (1987) examined the response of a supersonic slip surface to an incident train of small-amplitude nonlinear sound waves. They found analytic solutions which indicate that nonlinear resonance occurs at three angles of incidence which depend upon the Mach number of the relative motion. The two-dimensional simulations described here numerically solve this problem for a Mach-4 flow using the piecewise-parabolic method (Colella & Woodward 1984; Woodward & Colella 1984). The simulations show that sound waves incident at a predicted resonance angle excite nonlinear behaviour in the slip surface. At these angles the amplitude of the reflected waves is much greater than the incident wave amplitude (i.e. a shock forms). The observed resonance is fairly broad, but the resonance narrows as the strength of the incident waves is reduced. The nature of the nonlinear kink modes observed in the simulations is similar to that discussed by Artola & Majda. Most of the modes move in either direction with speeds near the predicted value. Speeds of other than this value are observed, but the disagreement is not serious in view of the strongly nonlinear behaviour seen in the simulations but not treated in the analytic work. The stationary modes seen in the analytic results are perhaps observed as transient structures. They may eventually dominate the flow at late times (Woodward et al. 1987). The role of the kink modes in the stability of slab jets is discussed, and it is argued that the stationary modes are more disruptive than the propagating modes. © 1991, Cambridge University Press. All rights reserved.