ALBERT

Description: A systematic crosschecking of the NBS oxalic acid standard, the ANU Sucrose secondary standard, and the RB oak tree rings grown in 1858 ± 5 and 1890 ± 5 has been performed using the proportional counter technique. Details on the counter gas (methane) purification are given. Corrections of count rates due to changes of barometric pressure and ambient temperature are applied and discussed. Results of measurements are presented and the ratios between mean activities of the NBS oxalic, ANU sucrose and RB oak samples are given.

Description: The following list includes some measurements made during 1975-1978 since our last list (R, 1978, v 20, p 62-67) in the National Radiocarbon Laboratory of the Ecole Nationale Supérieure de Géologie Appliquée et de Prospection Minière (ENSG) de Nancy.

Description: Most of the 14C measurements reported here were made between October 1977 and October 1978. Equipment, measurement, and treatment of samples are as reported previously (R, 1968, v 10, p 36-37; 1976, v 18, p 290) except for some minor improvements of the electronic equipment.

Description: Radiocarbon measurements have been continued on a variety of projects and materials. Chemical and counting procedures remain the same as indicated in R, v 20, p 274-282. Dates are calculated using the Libby 14C half-life of 5568 years; errors are reported as one-standard deviation (1σ) based only on statistical counting uncertainties in background, modern standard, and sample activities. All samples for which 13C/12C ratios are available are corrected for isotopic fractionation by normalizing to —25‰. A 400-year reservoir age correction has been applied to marine carbonates.

Description: The following list contains dates of organogenous sediments (peat and sapropel from the Karelian ASSR) made in 1972 to 1977 with the aim of studying the history of the development of peat bogs in the Holocene (Elina, 1969; 1971a,b; Pyavchenko et al, 1976). Samples were collected with Hiller or Instorf samplers. Borings were made in the deepest parts of the peat bogs.

Description: Temple's radiocarbon dating facility is housed in the Department of Geology on the Main Campus. The laboratory was established to support research in late Pleistocene and Holocene Geology, Archaeology, and Anthropology.

Description: Along SE coast of Australia a variety of Holocene barriers composed of siliceous sand and shell detritus occur within bedrock-confined embayments. On basis of morphostratigraphy 4 barrier types are recognized: prograded, stationary, receded and episodic transgressive dunes. Several subtypes are also distinguished. Composite bay barriers involving partial eolian reworking of a prograded barrier constitute most complex examples of Holocene depositional sequences on this coast. The present list is a preliminary attempt at defining the age structure of a group of such barriers (excepting receded type). Ages are reported in conventional years bp. Text references to ages and age ranges are environmental effect corrected ages bp* and yr* (as recommended by Stuiver and Polach, 1977), using 450 ± 35 yr as postulated by Gillespie and Polach (in press) in order to relate Australian oceanic environment shells to terrestrial environment wood. δ13C errors, where based on measurement, are always ± 0.2% and are not shown in the text; when based on estimated values (Est) the error is given.

Description: Radiocarbon measurements have been continued on a variety of projects and materials. Chemical and counting procedures remain the same as indicated in R, v 20, p 274-282. Dates are calculated using the Libby 14C half-life of 5568 years; errors are reported as one-standard deviation (1σ) based only on statistical counting uncertainties in background, modern standard, and sample activities. All samples for which 13C/12C ratios are available are corrected for isotopic fractionation by normalizing to —25‰. A 400 year reservoir age correction has been applied to marine carbonates.

Description: The dates in this list follow on, approximately chronologically, from Harwell II (R, 1977, v 19, p 400-423) and refer principally to measurements carried out in the period 1975-6. Laboratory techniques have remained essentially unchanged from earlier reports but a full description of the setting-up philosophy and operating procedure of the liquid scintillation counting systems has now been published separately (Otlet and Warchal, 1977).

Description: The dating equipment and operating conditions remain essentially as described in R, 1970, v 12, p 285-286, except that the samples are now measured at either 76, 152 or 380cm Hg at 20°C to allow for the variation in sample size. The calculation of results and correction for isotopic enrichment remain as previously described in R, 1973, v 15, p 212.

Description: The following date list covers certain samples dated by this laboratory from Nov 1975 through December 1977. All archaeological, all geological, and some of the geochemical samples measured during that period are included here. Measurements of tree-ring samples analyzed through Sept 1977 have been published previously (Suess, 1978); later measurements of wood samples will be included in the next list. Data and interpretation of 14C in the CaCO3 of annual coral growth have been published (Druffel & Linick, 1978) with further coral data to be published in the future.

Description: Most of the dates reported in this list were obtained between November 1975 and December 1976. All samples were subjected to standard de Vries pretreatment. Age calculations are based on a contemporary value equal to 0.95 of the activity of NBS oxalic acid standard and on the Libby value for the half-life of radiocarbon. Results are reported as conventional radiocarbon dates in years before ad 1950. All measurements were made with our L1 counter (Mościcki & Zastawny, 1976). Counting rates of all samples were normalized to the standard value of CO2 pressure and corrected for the counting efficiency (Pazdur et al, 1978). Errors quoted (±1σ) include estimated overall standard deviations of count rates for the unknown sample, contemporary standard and background (Pazdur, & Walanus, in press). No corrections for 13C/12C ratio were made for measurements reported in this list. The value of δ13C for our NBS oxalic acid standard is equal to — 19.41% relative to the PDB standard. The descriptions of the samples are based on information provided by the submitters.

Description: This list includes results of measurements made during 1974-1978. When requested, MASCA corrected dates (Ralph et al, 1973) are reported.

Description: The following date list presents results obtained during 1975-1977. The facilities at Glasgow have been further developed and include a gas counting system utilizing CO2 as counting material and two liquid scintillation counting laboratories based on synthesis of benzene. The results presented here were obtained using the liquid scintillation system only. Sample pretreatment varied according to individual sample type, whether wood or charcoal. The majority of samples were of preserved wood. After manual removal of gross contamination, samples of wood were finely chopped and digested in boiling, 2M KOH solution. The dehumified wood was then separated by filtration, thoroughly washed with distilled water and dilute hydrochloric acid, and then bleached in a solution of NaClO2/HCl at 80°C for 48 hours. Pure, white wood cellulose was obtained by filtration and washed with a large volume of distilled water. The cellulose, typically 40% by weight of the original material, was then dried overnight in an oven at 80°C. Samples of charcoal were closely examined for non-contemporaneous contamination and then subjected to successive treatments with hot, dilute (1M) KOH and HCL, respectively. The remaining charcoal was then dried overnight at 80°C.

Description: Procedures and equipment have been described in previous date lists. Except as otherwise indicated, wood, charcoal and peat samples are pretreated with dilute NaOH and dilute H3PO4 before conversion to the counting gas methane; marls and lake cores are treated with acid only. Very calcareous materials are treated with HCl instead of H3PO4.

Description: This list reports certain 14C measurements completed by November 1978; other projects completed by this time will be reported later. Age calculations are based on 14C half-life of 5568yr and modern standard of 95% NBS oxalic acid, supplemented by tree rings of pre-industrial wood from a log cut in the 1850's (Tx-540; R, 1970, v 12, p 249). Deviations reported are based on counting statistics of sample, background and modern, and are ± 1σ, except that when sample count approaches either modern or background, 2σ limits are reported. Unless noted, 12C/13C measurements were not made and results are not corrected for 13C fractionation (assumed ratio = −25‰ WRT PDB). Our laboratory uses liquid scintillation counting of benzene, with Li2C2 and vanadium-activated catalyst in preparation; chemical yields range between 95% and 99%. Three counters are employed; a Packard Tri-Carb Model 3002 and 2 Beckman LS320 spectrometers obtained through a grant from the National Science Foundation.

Description: The following list consists entirely of dates for archaeologic samples from the prehistoric flint mining site of Grime's Graves, Weeting, Thetford, Norfolk, England (52° 30' N, 0° 40' E, Natl Grid Ref TL 816898), measured over the period from August 1973 to December 1977,* all the samples having been excavated between 1972 and 1976. The dates were obtained by liquid scintillation counting of benzene using a Model 3315 Packard Tricarb Liquid Scintillation Spectrometer linked to a Hewlett Packard 2100A computer system for on-line processing of counting data (Hall & Hewson, 1977). The laboratory procedures used were those outlined in the two previous lists (R, 1976, v 18, p 16; 1977, v 19, p 143).

Description: Measurements have continued with the same proportional counter system, pretreatment procedure, methane preparation and measurement, and calculation, as described previously (R, 1970, v 12, p 298-318). Uncertainties quoted are single standard deviations originating from standard, sample, background counting rates and half-life. No 13C/12C ratios were measured.

Description: The following list contains dates of samples measured since our previous list (R, 1977, v 19, p 465-475). As before, age calculations are based on the Libby half-life, 5570 ± 30 years, and reported in years before 1950. The modern standard is 0.95 of the activity of NBS oxalic acid. Solid sample pretreatment, combustion and counting technique are essentially the same as described in R, 1971, v 13, p 135-140. Groundwater samples were prepared following the procedure adopted by the IAEA (IAEA, 1977). Carbonates and hydrocarbonates from water samples were precipitated by adding saturated barium chloride solution while the alkalinity was adjusted to pH = 8 by adding carbonate-free saturated solution of sodium hydroxide. The precipitation was enhanced by adding iron salts and Praestol as coagulating medium. Carbon dioxide was evolved by acidification of the precipitate and converted to methane. Statistical processing of data has been computerized (Obelić and Planinić, 1975). Sample descriptions were prepared with collectors and submitters. The errors quoted correspond to 1σ variation of sample net counting rate and do not include the uncertainty in 14C half-life.

Description: The following radiocarbon dates are a partial list of samples measured since January 1978. The chemical, counting and calculation procedures are the same as indicated in R, v 20, p 000-000.

Description: The response of a heated circular cylinder to impulsive and sinusoidal variations in the velocity of flow past it has been simulated by numerical integration of the governing equations. The fluid has been treated as viscous and incompressible and as having constant properties. The range of Reynolds number investigated was 1 ≪ R ≪ 40. Since vortex shedding normally does not occur in this range, the flows were treated as symmetrical. The thermal and flow transients are presented for the following cases.: (i)impulsive starts from rest to final steady state Reynolds numbers 1, 5, 10, 26·67; (ii)impulsive increases in velocities of 50% magnitude from steady state Reynolds numbers 1, 10 and 26·67; (iii)sinusoidal variation in velocity with amplitude of 10% impressed on a mean flow at Reynolds number 10. Results are also given for the thermal transients associated with instantaneous changes in cylinder temperature at Reynolds numbers 1, 5 and 40. The results obtained for transient and steady state flow parameters are in agreement with those obtained numerically and experimentally by other workers and the results for steady state heat flux from the cylinder are in agreement with experimental values. The new results obtained for heat transfer in unsteady flows provides information which is relevant to the operation of hot-wire anemometers. © 1979, Cambridge University Press

Description: The motion of two immiscible fluids with arbitrary viscosities flowing through a capillary with an almost flat fluid-fluid interface is investigated in the limit of small capillary and Reynolds numbers. A complete description of the dynamics of the fluids is presented. It is shown that the motion of the fluid away from the moving contact line can be completely determined in terms of one material parameter, and how the capillary can be viewed as a device for measuring it. The dynamic behaviour of various contact angles, measured by others, is calculated. It is shown that they all depend on the radius of the capillary; hence, they do not represent properties of only the materials of the system. © 1979, Cambridge University Press

Description: Natural convection flows induced by localized heating of the base of a thermally stratified enclosure are examined. The enclosure is a vertical circular cylinder with height equal to radius. The wall temperature increases linearly with height, and a small heat source is centrally located on the floor. Parameters of the problem are the ambient stratification rate (Γ−1), the Prandtl number (Pr), and a Grashof number (Gr) based on the temperature and the diameter of the heated spot. Over wide ranges of Γ and Gr, vertically layered convection cells are observed in the upper part of the enclosure in both laboratory experiments and numerical calculations. For the case of strong buoyancy and weak stratification, plume-like flows exist immediately above the heat source. Streak photographs are in qualitative accord with the numerical calculations, except for a range of Gr when an azimuthal rotation of the laboratory plume is observed. All flows are otherwise laminar. The theoretical results reveal a √Gr scaling at large Gr for the velocities and heat transfer rates, and a correlation of strongly stratified, viscous flows with the group Gr Pr Γ−1. © 1979, Cambridge University Press

Description: The turbulent velocity fluctuations at eight positions on sections of a plane wake and a boundary layer have been sampled simultaneously and recorded in digital form on magnetic tape for subsequent numerical analysis. Two configurations have been used (lines of equally-spaced sensors in planes normal to the flow, and arrays with three rows) with sensors responsive both to streamwise and cross-stream components of the fluctuations. To the extent that the Taylor approximation of “frozen” flow is valid, the recorded fluctuations may be interpreted as instantaneous values at grid points in the volume swept out by the array. The records have been examined, (a) to find evidence for flow patterns with marked periodicity in one direction, and (b) to select dimensions and orientations for simple eddy flow patterns whose random superposition would lead to correlation functions with a close resemblance to those calculated from the recorded data. In the wake, clear evidence was found for periodic flow patterns that resemble the eddies of a von Kármán street, but, although the spacing of eddy centres in each group was uniform, it varied considerably from one group to another, suggesting that groups are being observed in different stages of development. Two kinds of correlation were calculated from the records, (i) simple mean values of velocity products, and (ii) mean values of the products weighted by the total intensity or Reynolds stress in the effective volume swept by the array of sensors. For both kinds, the correlations are well described by simple inclined roller-type eddies, but the correspondence is greatly improved by weighting in favour of intensity or Reynolds stress. It appears that the eddies contributing most to intensity or Reynolds stress are less variable in form than all the eddies together, and that those contributing most to Reynolds stress are significantly different in shape and in orientation from those contributing most to turbulent energy. © 1979, Cambridge University Press

Description: Solutions to Long's equation for a stably stratified incompressible fluid traversing a mountain range are obtained for various terrain shapes and amplitudes when the horizontal scale is large compared to the vertical wavelength. Nonlinear lower and upper (radiative) boundary conditions are utilized and found to have a strong influence on the wave structure at large amplitudes. The results for symmetric and asymmetric mountain profiles reveal that the wave amplitude and wave drag are significantly enhanced for mountains with gentle windward and steep leeward slopes. These results confirm and explain those obtained by Raymond (1972) using a different solution method. Several results obtained by Smith (1977) from perturbation analysis are also confirmed and extended to large amplitudes. The methods are also applied to investigate the nonlinear nature of the singularity predicted by linear theory for flow over a step. © 1979, Cambridge University Press

Description: Monochromatic waves obliquely incident on a plane beach, and strongly reflected there, are unstable to perturbations by edge waves. Theory suggests the possible width of the resonant edge wave frequency band. Experiments on beaches with absorbers at both ends show that the excited waves have frequencies at the centre of the band, as predicted by Guza & Bowen (1975). Advection by mean longshore currents must be taken into account. If reflectors are placed at the beach ends, the additional boundary conditions apparently lead to resonances scattered across the resonant band. © 1979, Cambridge University Press

Description: A parabolic approximation to the reduced wave equation is investigated for the propagation of periodic surface waves in shoaling water. The approximation is derived from splitting the wave field into transmitted and reflected components. In the case of an area with straight and parallel bottom contour lines, the asymptotic form of the solution for high frequencies is compared with the geometrical optics approximation. Two numerical solution techniques are applied to the propagation of an incident plane wave over a circular shoal. © 1979, Cambridge University Press

Description: The existence of a liquefaction shock wave, a compression shock which converts vapour into liquid, has recently been predicted on physical grounds. The liquefaction shock was experimentally produced as the reflected shock at the closed end of a shock tube. Measurements of pressure, temperature, index of refraction and shock velocity confirm the existence of the shock and its general conformity to classical Rankine-Hugoniot conditions, with a discrepancy ∼ 10°C between measured and predicted liquid temperatures. Photographic observations confirmed the existence of a clear liquid phase and revealed the (unanticipated) presence of small two-phase torus-form rings. These rings are interpreted as vortices and are formed in or near the shockfront (∼ 50 rings/mm2 are visible near the shockfront at any given time). Separate experiments with the incident shock under conditions of partial liquefaction produced a fog behind the shock: measurements of laser-beam attenuation yielded the thickness of the condensation zone and estimates of the droplet size (∼ 10−7 m). © 1979, Cambridge University Press

Description: The horseshoe vortex formed around the base of a cylinder by a separating laminar boundary layer has been investigated experimentally. Smoke flow visualization shows that both steady and unsteady vortex systems exist. Pressure distributions beneath both types of vortex system have been measured and the variation of the horseshoe vortex position on the plane of symmetry upstream of the cylinder has been determined. Unsteady horseshoe vortex systems are shown to have a complex oscillatory behaviour and the nature of this oscillatory behaviour is described. Using smoke flow visualization techniques some measurements have been made of the velocity distributions within horseshoe vortex systems. © 1979, Cambridge University Press

Description: Results from a series of pipe-flow experiments using a range of water-soluble drag-reducing polymers are presented. Degradation has been investigated by means of multiple passes of the solutions through a pipe. A theory predicting drag reduction in pipe flow has been devised which agrees with the experimental results. Changes in polymer molecular weight due to degradation are taken into account. The analysis is then applied to a turbulent boundary layer with polymer injection. © 1979, Cambridge University Press

Description: A simple analysis shows that with a disturbance present the potential jump in a steady flow in a canal is expressed in terms of (1) the effective volume (displaced volume and added mass/density of fluid) and (2) the depth Froude number for either a submerged body or a body with thin waterplane area. For a ship moving in a canal, the expression for potential jump contains a contribution from the line integral term along the intersection between the ship hull and the free surface. When a pressure distribution is given on the free surface, the potential jump can be expressed explicitly in terms of the depth Froude number and the total pressure force, regardless of the shape of the pressure distribution. From the present relations, the added mass of a ship in steady motion in a canal is computed from the potential jump computed previously by the author for various Froude numbers. This added mass plays an essential role in the equation of motion initially when a sudden external force is applied to a steady moving ship. The present analysis is complimentary to that of Newman (1976) and the extension of that to the three-dimensional case. As practical applications of the potential jump, which has had a limited interest, we proposed approximate formulas for speed correction and sinkage of a ship in a towing tank experiment. Also proposed is an approximate formula for the speed correction in a wind tunnel experiment. The present approximate formula is compared with “exact” numerical results obtained by the localized finite element method for both towing tank and wind tunnel experiments. The present speed correction formula is also compared with existing approximate formulas for a wind tunnel experiment. The present formulas compare favourably with the exact numerical results. © 1979, Cambridge University Press

Description: Flows in thin-walled, collapsible tubes are of fundamental importance to various physiologic phenomena and clinical devices. A one-dimensional, unsteady theory is developed for flows generated either by externally applied pressures or by body forces. Part 1 deals with small-amplitude, linearized flows, part 2 with large amplitude, nonlinear flows. Experimental results for a tube collapsing under external pressure are given in part 3, together with theoretical interpretations and comparative results of numerical simulations. Several new and unanticipated phenomena are revealed. These are in part associated with the highly nonlinear “equation of state” (transmural pressure versus area) for a partially collapsed tube, and in part with whether the flow speed is sub- or supercritical relative to the speed of area waves. For instance, a flow produced by a spatially uniform external pressure applied to a limited region becomes choked at a flow-limiting throat at which point the fluid speed reaches the local wave speed. This throat forms at the edge of the pressurized region. The critical velocity can be exceeded with the application of certain types of spatially graded external pressures. © 1979, Cambridge University Press

Description: Experiments have been performed to determine the basic mechanism of heating in resonance tubes of square section with constant area excited by underexpanded jet flows. The jet flow between the nozzle exit and the tube inlet plays a key role in the performance of a resonance tube. A detailed and systematic investigation of the unsteady complex shock structure in this part of the flow region has led to a better understanding of the fundamental mechanisms associated with the gas heating in such tubes. A study of the effects of tube location in relation to free-jet shock location (without the presence of the resonance tube) has shed further light on the underlying mechanism of sustained oscillations of the flow in a resonance tube. © 1979, Cambridge University Press

Description: The linearized problem of water-wave reflexion by a thin barrier of arbitrary permeability is considered with the restriction that the flow be two-dimensional. The formulation includes the special case of transmission through one or more gaps in an otherwise impermeable barrier. The general problem is reduced to a set of integral equations using standard techniques. These equations are then solved using a special decomposition of the finite depth source potential which allows accurate solutions to be obtained economically. A representative range of solutions is obtained numerically for both finite and infinite depth problems. © 1979, Cambridge University Press

Description: The problem of the strong velocity disturbances remaining after the laminarization of an electroconductive fluid flow in a transverse magnetic field was investigated experimentally. The turbulence intensities, two-point correlations, and energy spectra of the velocity pulsations were measured using two-electrode probes and hot-film sensors. The two hypotheses with regard to a physical explanation of the persistence of the disturbances were examined, and it was concluded that these disturbances are generated mainly at the entry of the flow into the magnetic-field region. An almost undisturbed laminarized flow was obtained by eliminating the entry effects. © 1979, Cambridge University Press

Description: A new integro-differential equation is derived for steady free-surface waves. Numerical solutions of this equation for periodic gravity-capillary waves on a fluid of infinite depth are presented. For the two limiting cases of gravity waves and capillary waves, our results are in excellent agreement with previous calculations. For gravity-capillary waves, detailed calculations are performed near the wave-number at which the classical second-order perturbation solution breaks down. Our calculations yield two solutions in this region, which in the limit of small amplitudes agree with the results obtained by Wilton in 1915; one solution has the small amplitude behaviour of a gravity wave and the other that of a capillary wave, but the numerical results show that at large amplitudes both waves have the characteristics of capillary waves. The calculations also show that the wavenumber range in which two solutions exist increases with increasing wave height. © 1979, Cambridge University Press

Description: This paper is concerned with laboratory measurements of turbulence in a mixed layer and through a density interface, in the absence of a mean flow. The present results confirm the conclusion of Hopfinger & Toly (1976) that the turbulence in a mixed layer is not significantly affected by the slow entrainment of fluid across the bounding density interface. In a homogeneous fluid the turbulence intensity is found to be surprisingly non-uniform, even two grid mesh distances away from the grid. Velocity measurements have also been taken through a density interface (at the entraining boundary of a mixed layer) and the turbulence here varies in a manner that bears some resemblance to the theory of Hunt & Graham (1978). These velocity measurements were taken with a laser-Doppler anemometer and they were made possible by a novel experimental technique which eliminates the refractive index variations which normally occur in a turbulent, density-stratified liquid flow. © 1979, Cambridge University Press

Description: A nonlinear solution is constructed representing the steady flow field generated in viscous incompressible fluid in a spherical envelope by a constant point force F0 acting at the centre O of the envelope. Our analysis shows that when F0, = O(3ν2ρ), where v is the coefficient of kinematic viscosity and ρ the density of the fluid, the linear solution, which is symmetric about a plane through O perpendicular to the force, represents a reasonable approximation to the velocity field. As F0 increases the velocity field develops an asymmetry and the centre of the eddy, that exists in a meridian section, is displaced towards the direction of the force and is closer to the boundary. Also as F0 increases, on the axis of symmetry, the fluid speed per unit force decreases behind the force and increases ahead of it and percentage-wise the increase is larger further from O. © 1979, Cambridge University Press

Description: This paper applies the test field model developed by Kraichnan to the study of an isotropic, passive scalar contaminant convected by decaying isotropic turbulence. Test field model predictions of scalar and velocity dissipation spectra at large Reynolds and Péclet numbers are shown to be in excellent agreement with atmospheric data, after intrinsic scale constants in the model are adjusted to give valid inertial range coefficients. Theoretical values for the inertial range coefficients are obtained for large and small Prandtl numbers. Simulation results for velocity and scalar energy, dissipation and transfer spectra and second- and third-order velocity, scalar and velocity–scalar correlations at moderate Reynolds and Péclet numbers are shown to agree moderately well with heated grid turbulence data. Simulation results are presented for the normalized decay rates of the scalar and velocity dissipation rates and for the ratio of the velocity to scalar decay time scales; these quantities are employed in second-order modelling. In the self-similar decay mode the simulations yield unity levels of the normalized decay rates and of the ratio of decay time scales over the moderate range of Reynolds and Prandtl numbers investigated. These results are compared with data from heated grid turbulence experiments and are discussed in the light of asymptotic decay of concomitant scalar and velocity fields. © 1979, Cambridge University Press

Description: Detailed measurements in the wakes behind two-dimensional square section blocks (height h) mounted in thick rough wall boundary layers (height δ) are presented for cases in which h/δ ≪ 1. The data provides some insight into the relaxing flow downstream of reattachment, confirming the conclusion of Bradshaw & Wong (1972) that reattaching flows are surprisingly complicated and involve considerable distortion of the separated shear layer. In particular, the measurements show that eddy length scales are considerably reduced and, since the flow eventually relaxes to a boundary layer similar to that upstream, turbulence models based on eddy viscosity concepts cannot, in principle, be expected to be satisfactory. Using the present data this is demonstrated by a more detailed comparison with the theoretical predictions of Counihan, Hunt & Jackson (1974) than has been previously possible. It is shown that, whilst their theory does not predict the behaviour of the turbulent stresses, it does give reasonable agreement with the mean velocity perturbations at least in the near wake −10 〈 x/h 〈 30. Except in the near wall region, where the roughness provides the dominant length scale, it is argued that the rate at which the perturbation flow decays is governed largely by the amount by which the separated shear layer is distorted prior to reattachment, which in turn is determined by, say, a turbulence Reynolds number of the body, (hU/v0)h, or, in other words, by the characteristics of the upstream flow at, say, the body height. © 1979, Cambridge University Press

Description: In an effort to determine the characteristics of the various types of convection that can occur in a fluid-saturated porous medium heated from below, a Galerkin approach is used to investigate three-dimensional convection in a cube and two-dimensional convection in a square cross-section. Strictly two-dimensional, single-cell flow in a square cross-section is steady for Rayleigh numbers R between 4π2 and a critical value which lies between 300 and 320; it is unsteady at higher values of R. Double-cell, two-dimensional flow in a square cross-section becomes unsteady when R exceeds a value between 650 and 700, and triple-cell motion is unsteady for R larger than a value between 800 and 1000. Considerable caution must be exercised in attributing physical reality to these flows. Strictly two-dimensional, steady, multicellular convection may not be realizable in a three-dimensional geometry because of instability to perturbations in the orthogonal dimension. For example, even though single-cell, two-dimensional convection in a square cross-section is steady at R = 200, it cannot exist in either an infinitely long square cylinder or in a cube. It could exist, however, in a cylinder whose length is smaller than 0.38 times the dimension of its square cross-section. Three-dimensional convection in a cube becomes unsteady when R exceeds a value between 300 and 320, similar to the unicellular two-dimensional flow in a square cross-section. Nusselt numbers Nu, generally accurate to 1%, are given for the strictly two-dimensional flows up to R = 1000 and for three-dimensional convection in cubes up to R = 500. Single-cell, two-dimensional, steady convection in a square cross-section transports the most heat for R 〈 97; this mode of convection is also stable in square cylinders of arbitrary length including the cube for R 〈 97. Steady three-dimensional convection in cubes transports more heat for 97 ≲ R ≲ 300 than do any of the realizable two-dimensional modes. At R ≳ 300 the unsteady modes of convection in both square cylinders and cubes involve wide variations in Nu. © 1979, Cambridge University Press

Description: The dispersion relations for infinitesimal internal gravity waves (A) and axisymmetric waves in swirling streams (B) are considered. In both cases the mainstream may be sheared and density stratified in the transverse (vertical in case A, radial in case B) direction. The following results are proved for either case: If the maximum speed Wmax (or minimum speed Wmin) (in a meridian plane in case B) of the mainstream occurs at an interior point in the fluid, then the phase speed of any mode takes all values from the Wmax (or Wmin) to +∞ (−∞) as the overall Richardson number λ2 varies from 0 to ∞. If Wmax (Wmin) is attained at a boundary point with finite rate of strain, there is a positive non-zero critical Richardson number below which one or both branches of the dispersion relation terminate. These results employ variational methods and correct erroneous results concerning problem B stated in Chandrasekhar's treatise on hydrodynamic stability. Furthermore, bounds are given on the group velocity for both branches of the dispersion relation. From these bounds it is shown that in the absence of reversals of the mainstream (Wmin 〉 0) upstream propagation of wave energy is impossible whenever upstream propagation of constant phase surfaces is impossible. © 1979, Cambridge University Press

Description: Local wall shear rates in steady flow in the entry region of a curved tube have been measured by the electrochemical limiting current method. A semi-circular rigid tube of circular cross-section with radius ratio 1/7 has been employed for a range of Dean number between 139 and 2868. The circumferential and axial distributions of the wall shear rates have been measured at 20° circumferential increments at five different sections of the entry region. The experimental wall shear distributions show a valley in the circumferential wall shear profile and a region of non-monotonic variation of the average wall shear rates with downstream distance, both of which are prominent features of the entry flow in a curved tube. The existence of the valley suggests a vortex structure with several pairs of vortices in a developing curved tube flow in contrast with one pair in a fully developed flow. The circumferential distribution of wall shear also suggest that a potential vortex flow is formed in the upstream core. The wall shear is lowest at the innermost part of the bend and reaches a maximum in the mid-circumference region. The wall shear is significantly enhanced by secondary flows, as much as eight times greater in the curved tube entry flow than in fully developed Poiseuille flow in the range of Dean number between 139 and 2868. The cross-over in shear maximum from the inner part of the bend to the outer part occurs at about 1·9 cross-section radii from the inlet and seems to decrease with Dean number. © 1979, Cambridge University Press

Description: The mean-free-path approach to kinetic theory, initiated by Maxwell, and largely abandoned after the Chapman–Enskog success with Boltzmann's equation, is revised and considerably extended in order to find expressions for the heat flux vector q and pressure tensor p, valid (it is hoped) for all Knudsen numbers, K. These expressions (equations (2.24) and (2.26)) are integrals taken over the whole volume of the fluid plus surface integrals taken over the solid boundaries. The one phenomenological element is the mean free path λ, which takes different values according to whether it is mass, momentum or energy that is transported by the molecules. The need for such an approach is evidenced by the existence of critical values of K, above which the Chapman–Enskog expansion in powers of K, truncated after a finite number of terms, fails to yield a solution. For example with the Burnett equations, which are correct to O(K2), the critical K in a shock wave is only 0·2 based upon the upstream λ. As a first check on our general theory, we have found the O(K2) expansions for q and p from integral equations and found, at least for a Maxwellian gas, almost exact agreement with all 19 coefficients (8 are identically zero) appearing in the second-order terms of Burnett's equations. In a later paper the theory will be tested at high K numbers by applying it to the propagation of very high frequency waves, for which experimental results and alternative theories are available. © 1979, Cambridge University Press

Description: Definitions of energy density, energy flux and momentum flux for capillary-gravity waves are derived by integration of the equations of motion and also by Whitham's averaged Lagrangian method. We then confirm recent results due to Hogan (1979) both in the general case and in the case of pure capillary waves. Comparison with the Lagrangian results also allows us to give general definitions of “wave action density” and “wave action flux”. © 1979, Cambridge University Press

Description: The flow of a homogeneous viscous liquid towards a sink in the interior of a rotating basin with a free surface, a horizontal bottom and a vertical side wall is considered. The conditions assumed are such that an Ekman layer occurs at the bottom beyond a small distance from the sink. A first-order correction to the Ekman model accounting for the influence of the inertial terms in the equations of motion is given for a special case. It is shown theoretically and experimentally that eccentric withdrawal from a circular basin causes a vortex at the sink and a counter-rotating gyre attached to the far wall. © 1979, Cambridge University Press

Description: Our analysis of 18th and 19th century cannon firings shows that knowledge of sphere drag can be substantially extended into the region of 0·3 ≤ M∞ ≤ 2·0 and Re∞d up to 107. Bashforth's chronographic measurements (1868) are of a quality comparable to modern measurements. The data of Mayevski (chronograph, 1868), Hutton (ballistic pendulum, 1787–1791), and Didion (ballistic pendulum, 1839–1840) are of lesser accuracy but in agreement with Bashforth's. These cannon data are combined with modern data to provide the most extensive curves available of CD vs. Re∞d in this region. Interesting features of these curves for M∞ ≤ 1·0 are briefly described. © 1979, Cambridge University Press

Description: A grid-generated turbulence is subjected to a pure plane strain and the principal axes of the Reynolds stress tensor become those of the strain. This “oriented” homogeneous turbulence is then submitted to a new strain the principal axes of which have a different orientation. We show that in such a situation it is possible to observe a transfer of energy from the fluctuating motion to the mean one. Such transfer is necessarily associated with a forced decay of the anisotropy of the motion. A detailed analysis of the reorientation of the principal axes of the Reynolds stress tensor in the frame of those of the second strain gives an explanation of the evolution of the principal axes of the Reynolds stress tensor in a shear flow. © 1979, Cambridge University Press

Description: Oscillations of impinging flows, which date back to the jet-edge phenomenon (Sondhaus 1854), have been observed for a wide variety of impingement configurations. However, alteration of the structure of the shear layer due to insertion of an impingement edge (or surface) and the mechanics of impingement of vortical structures upon an edge have remained largely uninvestigated. In this study, the impingement of a shear layer upon a cavity edge (or corner) is examined in detail. Water is used as a working fluid and laser anemometry and hydrogen bubble flow visualization are used to characterize the flow dynamics. Reynolds numbers (based on momentum thickness at separation) of 106 and 324 are employed. Without the edge, the shear layer produces the same sort of non-stationary (variable) velocity autocorrelations observed by Dimotakis & Brown (1976). When the edge is inserted, the organization of the flow is dramatically enhanced as evidenced by a decrease in variability of autocorrelations and appearance of well-defined peaks in the corresponding spectra. This enhanced organization is not locally confined to the region of the edge but extends along the entire length of the shear layer, thereby reinforcing the concept of disturbance feedback. Comparison of spectra with and without insertion of the edge reveals a remarkable similarity to those of a non-impinging shear layer with and without application of sound at a discrete frequency (Browand 1966; Miksad 1972); with enhanced organization at the fundamental frequency, simultaneous enhancement occurs also at the sub- and higher-harmonics. Visualization of the vortical structures in the vicinity of the impingement edge shows that an impinging structure may experience one of three possible events: complete clipping, whereby the structure is swept down into the cavity; partial clipping, which results in severing of the vortex; or escape, involving deformation of the vortex while it is swept (intact) downstream past the edge. In general, no one of these events persisted continuously over a long period, but tended to occur alternately, meaning that “jitter” of an impinging structure occurs. Plots of paths of these structures versus time showed that the convective speed of the vortex was locally influenced a distance of about four momentum thicknesses upstream of impingement, which is less than the estimated diameter of an impinging vortical structure. Furthermore, this upstream influence of the edge is also evident in the distributions of transverse velocity. Laser measurements indicate that the presence of the edge substantially increases the local value of transverse velocity fluctuation in the region immediately upstream of the edge. © 1979, Cambridge University Press

Description: Hoverming motions, by which an animal (or a helicopter) in stationary fluid generates a downflow to support its weight, entail energy costs that include the induced power (power supplied to that downflow). The simplest classical model for induced power is the actuator-disk model. This paper shows how a relatively insignificant modification can be made to that model to make it aerodynamically self-consistent. The modified simple model of the downflow may be evaluated in fluid that either is unbounded or is bounded below by horizontal ground. Comparison of the calculated induced powers in the two cases (even though made in this paper not for the true axisymmetric flow patterns but for the corresponding two-dimensional flow patterns) appears to give a more satisfactory analysis than was previously available of the observed reduction of induced power associated with proximity to the ground. © 1979, Cambridge University Press

Description: In the early theoretical study of aquatic animal propulsion either the two-dimensional theory or the large aspect-ratio theory has been generally used. Only recently has the unsteady lifting-surface theory with the continuous loading approach been applied to the study of this problem by Chopra & Kambe (1977). Since it is well known that the continuous loading approach is difficult to extend to general configurations, a new quasi-continuous loading method, applicable to general configurations and yet accurate enough for practical applications, is developed in this paper. The method is an extension of the steady version of Lan (1974) and is particularly suitable for predicting the unsteady lead-edge suction during harmonic motion. The method is applied to the calculation of the propulsive efficiency and thrust for some swept and rectangular planforms by varying the phase angles between the pitching and heaving motions. It is found that with the pitching axis passing through the trailing edge of the root chord and the reduced frequency k equal to 0·75 the rectangular planform is quite sensitive in performance to the phase angles and may produce drag instead of thrust. These characteristics are not shared by the swept planforms simulating the lunate tails. In addition, when the pitching leads the heaving motion by 90°, the phase angle for nearly maximum efficiency, the planform inclination caused by pitching contributes to the propulsive thrust over a large portion of the swept planform, while, for the rectangular planform, only drag is produced from the planform normal force at k = 0·75. It is also found that the maximum thrust is not produced with maximum efficiency for all planforms considered. The theory is then applied to the study of dragonfly aerodynamics. It is shown that the aerodynamically interacting tandem wings of the dragonfly can produce high thrust with high efficiency if the pitching is in advance of the flapping and the hindwing leads the forewing with some optimum phase angle. The responsible mechanism allows the hindwing to extract wake energy from the forewing. © 1979, Cambridge University Press

Description: A stability analysis for high wavenumber perturbations of a Stokes wave of wave-number k1 and slope ε is presented. Except for a correction term the governing equation is shown to be of Hill's type. The analysis predicts instability at wave-numbers k2 = 1/4(m + 1)2 k1. The two lowest and strongest instabilities are the Benjamin-Feir instability at m = 1, and the quartet resonance at m = 2. Both are incorrectly treated by the present method. For m ≥ 3 the analysis should be asymptotically (ε → 0) correct, yielding instability O(εm) due to m-fold Bragg-scattering. The non-resonant perturbations behave as predicted by WKBJ theory. The instability is too weak for experimental detection; numerical tests should be possible, but are not available at present. © 1979, Cambridge University Press

Description: A study is made of the flow and the shape of the free surface of a non-Newtonian fluid contained in a flat-bottomed cylindrical vessel performing torsional oscillations of small amplitude. For the case where the fluid depth is small compared with the vessel radius, the solution is shown to have a simple radial dependence except in a boundary-layer region near the side wall. It is shown that under certain circumstances the mean steady second-order components of both free surface curvature and radial–axial flow may be in the reverse direction to those for a Newtonian fluid. It is found that flow reversal may occur at any frequency of oscillation, but that surface curvature reversal cannot occur at low frequencies. © 1979, Cambridge University Press

Description: This paper studies the effect of alternating or rotating magnetic fields on containers of conducting fluid. The magnetic Reynolds number is assumed small. The frequency of alternation or rotation is rapid so the magnetic field is confined to a thin layer on the surface of the container. A boundary-layer analysis is used to find the rate of vorticity generation due to the Lorentz force. When the container is an infinitely long cylinder of uniform cross-section, alternating fields normal to the generators or fields rotating about an axis parallel to the generators generate vorticity at a constant rate. For containers of any other shape the rate of vorticity generation includes both constant and oscillatory terms. A perturbation analysis is used to study the flow induced in a slightly distorted circular cylinder by a rotating field. Complex flows develop in the viscous-magnetic boundary layer which may be unstable. © 1979, Cambridge University Press. All rights reserved.

Description: The unsteady flow past a circular disk is studied with hot-wire and microphone probes positioned in planes normal to the axis of symmetry at 3 and 9 disk diameters down-stream. Both the fluctuating velocity and pressure signals are shown to be continuously dominated by large-scale coherent motions enveloping the wake flow as a whole. This suggests narrowband two-point space correlations as an experimental tool for describing spatial coherence and phase characteristics of the basically random signals. The specific symmetry imposed by the axisymmetric boundary conditions of the disk enables a decomposition of the large-scale flow phenomena into relatively simple elementary structures or modes. The resulting azimuthal constituents are quantified in terms of their respective magnitudes and individual power spectra. The capability of the approach to uncover characteristic features of turbulence as far as its large-scale domain is concerned is demonstrated by a comparison of the present results with certain remarkably different features found in earlier jet flow investigations: the m = 1 and m = 2 modes are found to clearly dominate in wakes whereas the m = 0 and m = 1 modes were dominant in jets in a relevant range of Strouhal numbers. These large-scale coherent structures are more than just an interesting flow phenomenon; they must have a tremendou back-reaction on rigid flow boundaries (particularly if these allow a vibrational response) and may give rise to specific feedback mechanisms. The analysing technique proposed for studying large-scale flow phenomena injets and wakes removes part of the randomness in the turbulent signals without artificially exciting or forcing them in one way or another. No conditional sampling of the naturally occurring fluctuations is required, either. The method may be applicable to other than strictly axisymmetric flow configurations, too. © 1979, Cambridge University Press. All rights reserved.

Description: The asymptotic properties of Burgers turbulence at extremely large Reynolds numbers and times are investigated by analysing the exact solution of the Burgers equation, which takes the form of a series of triangular shocks in this situation. The initial probability distribution for the velocity u is assumed to decrease exponentially as u → ∞. The probability distribution functions for the strength and the advance velocity of shocks and the distance between two shocks are obtained and the velocity correlation and the energy spectrum function are derived from these distribution functions. It is proved that the asymptotic properties of turbulence change qualitatively according as the value of the integral scale of the velocity correlation function J, which is invariant in time, is zero, finite or infinite. The turbulent energy per unit length is shown to decay in time t as t−1 (with possible logarithmic corrections) or [formula ommited] according as J = 0 or J ≠ 0. © 1979, Cambridge University Press

Description: Strong external disturbances were introduced into a mixing layer in order to test the formation of the quasi two-dimensional coherent eddies and their survival under less than ideal conditions. Velocity and temperature correlation measurements, flow visualization, and the simultaneous use of a large number of sensors suggest that these eddies are very stable in the range of Reynolds numbers considered and they persevere in spite of the external buffeting imposed. Some measurements were carried out in a mixing layer between two parallel streams and some in a mixing layer entraining quiescent surrounding fluid. In both cases the large eddies could be described. as vortex rolls spanning the test section; these rolls may be contorted and sometimes skewed, but they are basically two-dimensional. © 1979, Cambridge University Press

Description: By establishing that the length scale governing the detachment of a shock wave from a wedge is the distance from the leading edge to the sonic line, and by considering the view of observers with different length scales, it is predicted that the detachment distance increases gradually with wedge angle for relaxing flow and more rapidly in a perfect gas. Both of these features are confirmed by experiments in the free-piston shock tunnel. The influence of other length scales is discussed. The phenomenon is related to a relaxation effect in which a subsonic layer grows from the translational-rotational shock as the wedge inclination is increased beyond the frozen sonic point. © 1979, Cambridge University Press. All rights reserved.

Description: The initial development of turbulence in the shear layer of a circular jet is observed to show disturbances of increasing scale at discrete frequencies in an approximate 4:2:1 sequence. These are completely confined within the laminar shear layer and convect at 0·59 of the jet velocity. Such relatively regular behaviour was not observed once the disturbances became larger in transverse dimension than the laminar shear layer. In the development of the subsequent turbulent shear layer it was found that the fluctuating turbulent shear did not scale with local mean shear, but rather scaled more closely with the minus half power of distance from the apparent origin of the laminar shear layer emanating from the nozzle. The scale of the shear fluctuations departed from growth in proportion to shear layer thickness, remaining almost constant. In these aspects it appears that the turbulent shear layer is not well described by a similar growth with axial distance. The shear fluctuations convected at a speed closer to the local mean velocity than do velocity fluctuations and showed a relatively more patchy distribution with a distinct rotational sense and no reversal of skewness across the layer. Velocity fluctuations showed phase lags approaching [formula ommited] relative to shear fluctuations suggesting that dominant velocity disturbances are those associated with entrainment behind concentrations of rotation. © 1979, Cambridge University Press. All rights reserved.

Description: A theoretical framework is given, upon which to examine the dispersion relation of random gravity waves. First a weakly nonlinear theory is developed to the third-order for a statistically stationary and homogeneous field of random gravity waves. Both the spectrum of forced waves and the nonlinear dispersion relation are expressed in terms of the spectrum of free waves under the assumption of the Gaussian process for the first-order surface displacement. Next a method is proposed by which to separate each of the spectra of free and forced waves from the measured spectrum. This gives practical and powerful means of investigating the statistical structure of wind waves. © 1979, Cambridge University Press. All rights reserved.

Description: The mixing of rain with otherwise calm near-surface water is investigated experimentally, using both uniform drops and crude drop-size distributions. The results are interpreted in terms of mixed-layer depths and the upward entrainment of quiescent water. Large drops, even in quite small numbers, are shown to play a very important role in the mixing process. Entrainment coefficients vary as the inverse of a suitably defined bulk Richardson number, and behave similarly in both fresh and salt receiving water. © 1979, Cambridge University Press. All rights reserved.

Description: The flow of an incompressible fluid contained between two infinitely long circular cylinders is considered when the inner cylinder performs small harmonic oscillations about the centre of the larger (fixed) cylinder. Numerical solutions are presented for the Navier–Stokes equations governing the steady-streaming component of the motion. Special attention is then paid to this flow when the Reynolds number of the steady streaming is large, and when the radius of the outer cylinder is much larger than that of the inner. Results obtained show an improved correlation with experimental results and indicate strongly that the finiteness of the domain is the major cause of the discrepancies between experiment and previous theoretical studies. © 1979, Cambridge University Press. All rights reserved.

Description: A statistical theory is developed for the structure and propagation velocity of premixed flames in turbulent flows with scales large compared with the laminar flame thickness. The analysis, free of usual closure assumptions, involves a regular perturbation for small values of the ratio of laminar flame thickness to turbulence scale, termed the scale ratio ε, and a singular perturbation for large values of the non-dimensional activation temperature β. Any effects of the flame on the flow are considered to be given. In this initial study, molecular coefficients for diffusion of heat and reactants are set equal. The results identify convective-diffusive and reactive-diffusive zones in the flame and predict thickening of the flame by turbulence through streamwise displacement of the reactive-diffusive zone. Profiles for intensities of temperature fluctuations and for streamwise turbulent transport are obtained. A fundamental quantity occurring in the analysis is the longitudinal displacement of the reactive-diffusive zone in an Eulerian frame by turbulent fluctuations, and to first order in the scale ratio this equals the longitudinal displacement of fluid elements in an Eulerian frame by turbulent fluctuations, herein termed simply the Eulerian displacement. To first order in the scale ratio it is found that, if the Eulerian displacement experiences the same type of statistical non-stationarity as the corresponding Lagrangian displacement, then the diffusion approximation is valid for streamwise turbulent transport but the turbulent flame thickens as time increases, while if the Eulerian displacement is statistically stationary then the diffusion approximation necessitates a negative coefficient of diffusion in part of the flame but the flame thickness remains constant. By carrying the analysis to second order in the scale ratio it is shown that the turbulent-flame speed exceeds the laminar-flame speed by an amount proportional to the mean square of the transverse gradient of the Eulerian displacement. This result can be understood from the mechanistic viewpoint of a wrinkled laminar flame in terms of the increase in flame area produced by turbulence. Thus the theory provides a precise statistical quantification of the model of the wrinkled laminar flame for describing structures of turbulent flames. © 1979, Cambridge University Press. All rights reserved.

Description: We consider the evolution of packets of water waves that travel predominantly in one direction, but in which the wave amplitudes are modulated slowly in both horizontal directions. Two separate models are discussed, depending on whether or not the waves are long in comparison with the fluid depth. These models are two-dimensional generalizations of the Korteweg-de Vries equation (for long waves) and the cubic nonlinear Schrödinger equation (for short waves). In either case, we find that the two-dimensional evolution of the wave packets depends fundamentally on the dimensionless surface tension and fluid depth. In particular, for the long waves, one-dimensional (KdV) solitons become unstable with respect to even longer transverse perturbations when the surface-tension parameter becomes large enough, i.e. in very thin sheets of water. Two-dimensional long waves (‘lumps’) that decay algebraically in all horizontal directions and interact like solitons exist only when the one-dimensional solitons are found to be unstable. The most dramatic consequence of surface tension and depth, however, occurs for capillary-type waves in sufficiently deep water. Here a packet of waves that are everywhere small (but not infinitesimal) and modulated in both horizontal dimensions can ‘focus’ in a finite time, producing a region in which the wave amplitudes are finite. This nonlinear instability should be stronger and more apparent than the linear instabilities examined to date; it should be readily observable. Another feature of the evolution of short wave packets in two dimensions is that all one-dimensional solitons are unstable with respect to long transverse perturbations. Finally, we identify some exact similarity solutions to the evolution equations. © 1979, Cambridge University Press. All rights reserved.

Description: The equations for the rotation of non-axisymmetric ellipsoids in a simple shear flow at low Reynolds numbers are derived in terms of Euler angles. Numerical solutions of this third-order system of equations show a doubly periodic structure to the rotation, with a change in the general nature of the solutions when a certain planar rotation of the particle becomes unstable. Some analytic progress can be made for nearly spherical ellipsoids and for nearly axisymmetric ellipsoids. The near spheres show the same qualitative behaviour as the general ellipsoids. Quite small deviations from axial symmetry are found to produce large changes in the rotation. © 1979, Cambridge University Press. All rights reserved.

Description: Temperature-sensitive constant-current wires operating at very low resistance ratios have been tested for temperature fluctuation response. A significant step in the response was found to occur with a centre-frequency of typically 1/6 Hz. The step size was observed to be as large as 30% and grew from zero to its maximum value in about a decade. Analysis shows that this phenomenon is associated with axial conduction of heat to and from the prongs. If it is recognized that prongs have finite thermal inertia then a modification of the boundary conditions to the equations of Betchov (1948) predicts this step, in agreement with the simple asymptotic analysis of Maye (1970). Experiments indicate that a similar phenomenon occurs with velocity-sensitive wires. Axial conduction appears to be the most likely cause. Aeroelastic deflexions and non-uniform cooling caused by bowing of the wire make precise predictions impossible. Here the differences in step size between wires were observed to be as large as 10% (or 20% in mean-square energy), the centre-frequency was usually beyond 10 Hz for the wires tested and the step extended over a much broader frequency range than in the temperature-sensitive case. The effect occurred at all velocities, resistance ratios and wire geometries. An analysis based on non-uniform cooling of the wire filament predicts the correct frequency range and shows that steps of 10% in frequency response are quite plausible. © 1979, Cambridge University Press. All rights reserved.

Description: A model equation is derived for the combined longitudinal and lateral dispersion of a buoyant contaminant in open-channel flow. The central hypotheses are that the water is shallow and that to a first approximation the effluent is vertically well mixed. The model includes allowance for the reduction in turbulent intensity due to weak vertical stratification, a buoyancy-driven secondary flow, and the redistribution of longitudinal momentum by the secondary flow. For a plume the theoretical results for the excess spreading due to buoyancy agree well with Prych's (1970) experimental results. © 1979, Cambridge University Press. All rights reserved.

Description: The flow past a cylinder bounded by parallel planes in a rotating frame is treated in terms of a nonlinear Stewartson layer. It is shown that separation is strongly dependent on the ratio of the Rossby number to the square root of the Ekman number, covering the whole range from fully attached flow to the classical non-rotating separated flow past a cylinder. The results are in agreement with published experimental observations. © 1979, Cambridge University Press. All rights reserved.

Description: Free-flight and wind-tunnel measurements by previous investigators of the flat-plate autorotation phenomenon have been analysed. The variation of the autorotation characteristics with changes in the Reynolds number and the aspect ratio, thickness ratio and moment of inertia of the flat plate have been correlated. The interpretation of the role of the Reynolds number made in a previous investigation is shown to be incorrect. The tip-speed ratio, for the ranges of the dimensionless parameters investigated, is shown to be a function of only the plate aspect ratio, thickness ratio, and also the moment of inertia if the latter is sufficiently small. The lift and drag coefficients, and therefore the free-flight glide angle, are shown to be functions of the tip-speed ratio, the aspect ratio and the Reynolds numbers based on the chord and plate thickness. © 1979, Cambridge University Press. All rights reserved.

Description: The flow of grid-generated turbulence past a circular cylinder is investigated using hot-wire anemometry over a Reynolds number range from 4·25 × 103 to 2·74 × 104 and a range of intensities from 0·025 to 0·062. Measurements of the mean velocity distribution, and r.m.s. intensities and spectral energy densities of the turbulent velocity fluctuations are presented for various radial and circumferential positions relative to the cylinder, and for ratios of the cylinder radius a to the scale of the incident turbulence Lx ranging from 0·05 to 1·42. The influence of upstream conditions on the flow in the cylinder wake and its associated induced velocity fluctuations is discussed. For all measurements, detailed comparison is made with the theoretical predictions of Hunt (1973). We conclude the following. The amplification and reduction of the three components of turbulence (which occur in different senses for the different components) can be explained qualitatively in terms of the distortion by the mean flow of the turbulent vorticity and the ‘blocking’ or ‘source’ effect caused by turbulence impinging on the cylinder surface. The relative importance of the first effect over the second increases as a/Lx increases or the distance from the cylinder surface increases. Over certain ranges of the variables involved, the measurements are in quantitative agreement with the predictions of the asymptotic theory when a/Lx ≪ 1, a/Lx ≫ 1 or |k| a ≫ 1 (where k is the wavenumber). The incident turbulence affects the gross properties of the flow in the cylinder wake, but the associated velocity fluctuations are probably statistically independent of those in the incident flow. The dissipation of turbulent energy is greater in the straining flow near the cylinder than in the approach flow. Some estimates for this effect are proposed. © 1979, Cambridge University Press. All rights reserved.

Description: The asymptotic theory for the laminar, incompressible, separating and reattaching flow past the bluff body is based on an extension of Kirchhoff's (1869) free-streamline solution. The flow field (only the upper half of which is discussed since we consider a symmetric body and flow) consists of two basic parts. The first is the flow on the body scale l*, which is described to leading order by the Kirchhoff solution with smooth inviscid separation, but with an [formula ommited] modification to explain fully the viscous separation (here Re (≫ 1) is the Reynolds number). The influence of this [formula ommited] modification is determined for the circular cylinder. The second part is the large-scale flow, comprising mainly the eddy and the ultimate wake. The eddy has length scale O(Rel*), width O(Re½l*) and is of elliptical shape to keep the eddy pressure almost uniform. The ultimate wake is determined numerically and fixes the eddy length. The (asymptotically small) back pressure from the eddy acts (on the body scale) both in the free stream and in the eddy, and it has a marked effect at moderate Reynolds numbers; combined with the Kirchhoff solution, it predicts the pressure drag on a circular cylinder accurately, to within 10% when Re = 5 and to within 4% when Re = 50. Other predictions, for the eddy length and width, the front pressure and the eddy pressure, also show encouraging agreement with experiments and Navier-Stokes solutions at moderate Reynolds numbers (of about 30), both for the circular cylinder and the normal flat plate. Finally, an analysis in the appendix indicates that, in wind-tunnel experiments, the tunnel walls (even if widely spaced) can exert considerable influence on the eddy properties, eventually forcing an upper bound on the eddy width as Re increases instead of the O(l* Re½) growth appropriate to the unbounded flow situation. © 1979, Cambridge University Press. All rights reserved.

Description: The weakly reactive state leading to the ignition of a steady laminar boundary-layer flow of a combustible mixture over a hot, isothermal, non-permeable, non-catalytic flat plate is studied both numerically and using matched asymptotic analysis in the realistic limit of large activation energy. It is shown that the flow consists of a locally similar diffusive-reactive region next to the plate and a non-similar diffusive-convective region outside it; that the analytic solution obtained reproduces the lower half of the S-shaped ignition-extinction response curve such that ignition is expected to occur when a suitably defined Damköhler number, which increases with the streamwise distance, reaches unity; and that at the point of ignition the heat transfer from the wall vanishes identically. An explicit expression for the minimum distance for ignition to occur is also derived. © 1979, Cambridge University Press. All rights reserved.

Description: The cross-stream migration of a deformable drop in a unidirectional shear flow of a second-order fluid is considered. Expressions for the particle velocity due to the separate effects of deformation and viscoelastic rheology are obtained. The direction and magnitude of migration are calculated for the particular cases of Poiseuille flow and simple shear flow and compared with experimental data. © 1979, Cambridge University Press. All rights reserved.

Description: The propagation of linearized waves on a non-uniform slowly varying potential current is studied by converting the equations of flow into a Schrödinger ordinary differential equation in the complex plane. This equation, which is solved by the WKB method, indicates the existence of current barriers which allow partial energy transmission while reflecting the complementary part. The classical result of total transmission (Longuet-Higgins & Stewart 1961) as well as that of complete reflexion (Peregrine 1976) are recovered as limiting cases by the present, more general approach. © 1979, Cambridge University Press. All rights reserved.

Description: Cairns (1979) has recently shown how the concept of negative wave energy used in plasma physics can be exploited to obtain insights into the linear and nonlinear instability of certain parallel flows. We here analyse the linear stability and nonlinear three-wave resonance in a three-layer flow with step-wise velocity and density profiles. The results are in complete agreement with Cairns' qualitative predictions. In particular, the existence is confirmed of an ‘explosive’ instability in which all three waves of a resonant triad grow simultaneously while total wave energy is conserved. Such nonlinear instabilities, previously undetected in fluid flows, may well be important in the ocean and atmosphere. © 1979, Cambridge University Press. All rights reserved.

Description: The inviscid spatial growth of spiral modes of circular, slowly diverging jets is analysed. A multiple-scales expansion is used to develop a linear stability study for non-axisymmetric disturbances of arbitrary helicity. The numerical evaluation is restricted to axisymmetric modes and to the first two helical modes. It is shown that in the case of comparatively high values of the Strouhal number the modes exhibit a very rapid growth and reach their maximal amplification after a short distance, the axisymmetric instabilities being excited more strongly than their spiral counterparts. Contrary to this, the modes grow comparatively slowly in the case of smaller values of the Strouhal number and exhibit their maximal amplification further downstream. In the latter case the first spiral mode is more unstable than the axisymmetric one. A comparison with experiments seems to support these results. © 1979, Cambridge University Press. All rights reserved.

Description: We present a simple model of a steady barotropic eddy superimposed on a current, with varying Coriolis force, to study the structure of a nonlinear deformed eddy. We also develop the linearized time-dependent formulation of the problem. The resulting solutions are stable perturbations, with scales smaller than the eddy. © 1979, Cambridge University Press. All rights reserved.

Description: It is shown that the pressure and velocity fluctuations of the unsteady motion on a transversely sheared mean flow can be expressed entirely in terms of the derivatives of two potential functions. One of these is a convected quantity (i.e. it is frozen in the flow) that can be specified as a boundary condition and is related to a transverse component of the upstream velocity field. The other can be determined by solving an inhomogeneous wave equation whose source term is also a convected quantity that can be specified as a boundary condition in any given problem. The latter is related to the curl of the upstream vorticity field. The results are used to obtain an explicit representation of the three-dimensional gust-like or hydrodynamic motion on a transversely sheared mean flow. It is thereby shown that this motion is ‘driven’ entirely by the two convected quantities alluded to above. The general theory is used to study the interaction of an unsteady flow with a scmi-infinite plate embedded in a shear layer. The acoustic field produced by this interaction is calculated in the limits of low and high frequency. The results are compared with experimental one-third octave sound pressure level radiation patterns. The agreement is found to be excellent, especially in the low frequency range, where the mean-flow and convective effects are shown to have a strong influence on the directivity of the sound. © 1979, Cambridge University Press. All rights reserved.

Description: The formation of singularities in two-dimensional magnetohydrodynamic flow is investigated by direct numerical simulation. It is shown that two-dimensional magnetohydrodynamic turbulence is not as singular as three-dimensional hydrodynamic turbulence (in the sense that it has a less highly excited small-scale structure) but that it is more singular than two-dimensional hydrodynamic turbulence. © 1979, Cambridge University Press. All rights reserved.

Description: A general linear theory is presented to describe oscillatory flows of gases and liquids in a tube of circular cross-section, including the effects of radial and tangential pressure gradients as well as the temperature. The basic equations are solved by separation of variables. The resulting eigenvalue equation is extensively discussed whereby the splitting of the eigenvalues into ‘bands’ is obtained in a natural way. A systematic analysis of a number of simplified cases leads to analytic approximations for the eigenvalues over an extended domain of parameter variation (frequency, friction) so that a complete survey of all the eigenvalues is established. Then the problem of satisfying simultaneously arbitrary end-conditions for all flow variables with the obtained bands of eigenfunctions is formulated in a way to allow the application of Galerkin's method. Finally the theory is applied to a few examples of ‘end-layers’ and radial resonance, which cannot be treated by previous theories. © 1979, Cambridge University Press. All rights reserved.

Description: Two inequalities are proposed for the purpose of bounding from below the mean shear U′o(z) in turbulent channel flow. The first of these inequalities pertains to the energetics of the boundary layer, and the second pertains to the logarithmic form of the asymptote to Uo. These inequalities imply a maximum value of von Kármán's constant, the numerical value of which lies between the measurements of Laufer (1951) and the value obtained from bulk discharge measurements in a pipe. The formalism, which contains no adjustable parameters, is then applied to the turbulent thermal convection problem, and a lower bound for the mean temperature [formula ommited] is obtained. The minimum value of the latter at large distances from the boundary is in fair agreement with Townsend's (1959) measurements. Although the proposed inequalities have not been deduced from the equations of motion, they provide facts which may be useful in the search for new variational formulations of theturbulent transport problem. © 1979, Cambridge University Press. All rights reserved.

Description: Submerged resonant ducts offer an approach to the design of wave-energy extraction devices consistent with the need for maximum seaworthiness. This paper gives a full account of one type of analysis of these systems, based upon two-dimensional wave hydrodynamics and linearized duct dynamics. The mathematical analyses are given in detail in § 2 while § 1 describes as concisely as possible (i) the assumptions underlying each analysis, (ii) its results and their implications for design, and (iii) any available experimental comparisons. One theoretical prediction, unexpected when it was first made but since confirmed by experiment (Knott & Flower 1979), is that the effective pressure fluctuations to which a resonant duct responds can be substantially greater than those that would be present at the level of the duct mouth if the duct were absent. Other important predictions are concerned with added mass, radiation damping and the conditions for optimum energy extraction, calculated below for a wide variety of mouth design configurations and internal duct geometries. Broad tentative conclusions from the analyses are given at the end of § 1. © 1979, Cambridge University Press. All rights reserved.

Description: This paper examines the energy conversion mechanisms which govern the emission of low frequency sound from an axisymmetric jet pipe of arbitrary nozzle contraction ratio in the case of low Mach number nozzle flow. The incident acoustic energy which escapes from the nozzle is partitioned between two distinct disturbances in the exterior fluid. The first of these is the free-space radiation, whose directivity is equivalent to that produced by monopole and dipole sources. Second, essentially incompressible vortex waves are excited by the shedding of vorticity from the nozzle lip, and may be associated with the large-scale instabilities of the jet. Two linearized theoretical models are discussed. One of these is an exact linear theory in which the boundary of the jet is treated as an unstable vortex sheet. The second assumes that the finite width of the mean shear layer of the real jet cannot be neglected. The analytical results are shown to compare favourably with recent attenuation measurements. © 1979, Cambridge University Press. All rights reserved.