ALBERT

Description: The following list consists of dates for archaeologic samples mostly measured from July 1976 to December 1977. The dates were obtained by liquid scintillation counting of benzene using the laboratory procedures outlined in previous lists (see, eg, BM-VIII, R, 1976, v 18, p 16). Dates are expressed in radiocarbon years relative to ad 1950 based on the Libby half-life for 14C of 5570 yr, and are corrected for isotopic fractionation (δ13C values are relative to PDB). No corrections have been made for natural 14C variations (although in some instances approximate calibrated dates taken from the tables of R M Clark (1975) have been given in the comments where this aids interpretation of results). The modern reference standard is NBS oxalic acid (SRM 4990). Errors quoted with the dates are based on counting statistics alone and are equivalent to ± 1 standard deviation (± 1σ), Dates in this and the next list (BM-XIV) reported to submitters or published elsewhere before the introduction of the new guidelines for rounding of computed figures have deliberately been left unrounded. From BM-XV onwards all BM dates will be rounded before publication in conformity with the recently recommended procedures (R, 1977, v 19, p 362). Descriptions, comments, and references to publications are based on information supplied by submitters.

Description: The radiocarbon laboratory of the Center of Applied Research and Documentation of Udine (CRAD), became operative early in 1977 and uses a benzene liquid scintillation counting method. Benzene is prepared as outlined by Legers and Tamers (1963), Noakes, Kim, and Akers (1967), Belluomini et al (1978). The procedure of chemical synthesis is detailed in CRAD (1977).

Description: The Radiocarbon Dating Laboratory of The Granada University was established to support the work of archaeologists and geologists. The method of dating is benzene synthesis and liquid scintillation counting developed by a number of investigators (Polach and Stipp, 1967; Tamers, 1969; Pietig and Scharpenseel, 1966) with sample combustion in pure oxygen (Switsur, 1974).

Description: This list reports a portion of the analysis completed on archaeologic and paleo-environmental samples measured in the UCR laboratory between August 1974 and August 1976. Results of measurements made during that period on sample suites which are not as yet completed or lack review by submitters will be reported in a subsequent date list.

Description: The following list consists of dates for archaeologic and geologic samples mostly measured over the period from January 1980 to June 1981. The dates were obtained by liquid scintillation counting of benzene using the laboratory procedures outlined in previous lists (see, eg, BM VIII, R, 1976, v 18, p 16).

Description: During the last seven years, there has been a concerted effort in eastern Australia to obtain 14C ages from detrital shell samples of prograded sand barriers composed of beach ridges and chenier deposits (Cook and Polach, 1973; Cook and Mayo, 1977; Thom, Polach, and Bowman, 1978; Thom et al, 1981). These ages were used to establish the age sequence of deposition and rates of progradation. This date list is the result of work in two areas of the Gulf of Carpentaria, Queensland, Australia, where 57 shell samples were collected for 14C dating. For details of this research, see Rhodes et al (1980).

Description: The following list includes 14C measurements of geologic samples, the majority of which pertain to sea-level variations, and of archaeologic samples mainly from France, West Africa, and South America. Most of the dates were measured between 1972 and 1973 when installations were not modified. The technique used is described in Radiocarbon, 1972, v 14, p 280–320. Dates were calculated using the 14C half-life of 5568 years; modern standard is 0.95 of the NBS oxalic acid. Reported errors are one standard deviation for 2000 minutes measurements.

Description: The SFU Archaeology Department has constructed a small radiocarbon dating facility to serve its own needs and, to the extent that time is available, the needs of other archaeologists and earth scientists. All dates reported here were processed by our laboratory from October 1979 to September 1980. The 14C measurements are made using conventional techniques for liquid scintillation counting of benzene. The samples are burned in a Phonon Mark IV combustion bomb and the resultant CO2 is purified and converted to Li2C2 using a reaction vessel based on the design of Polach, Gower, and Fraser (ms). Acetylene is formed by hydrolysis with distilled H2O which has been aged for a minimum of three months. The acetylene is trimerized to benzene with the Mobil Durabead I catalyst. The conversion efficiency of CO2 to C6H6 is typically 95%. Gas chromatographic analysis of typical samples of the synthesized benzene indicates 99.8% purity with toluene produced in trace amounts.

Description: The following list consists of dates for archaeologic and some geologic samples, mostly measured from January 1978 to December 1979. The dates were obtained by liquid scintillation counting of benzene using the laboratory procedures outlined in previous lists (see, eg, BM-VIII, R, 1976, v 18, p 16). The dates are expressed in radiocarbon years relative to ad 1950 based on the Libby half-life for 14C of 5570 yr, and are corrected for isotopic fractionation (δ13C values are relative to PDB). No corrections have been made for natural 14C variations. The modern reference standard is NBS oxalic acid (SRM 4990). Errors quoted with the dates are based on counting statistics alone and are equivalent to ± 1 standard deviation (± 1σ). Dates in this list reported to submitters or published elsewhere before the introduction of the new guidelines for rounding of computed figures have deliberately been left unrounded. From BM-XV onwards all BM dates will be rounded before publication in conformity with the recently recommended procedures (R, 1977, v 19, p 362). Descriptions, comments, and references to publications are based on information supplied by submitters.

Description: The following list sums up the results of radiocarbon dating of geologic samples obtained mostly during 1978 and 1979. Measurements have continued with the same proportional counters, pretreatment procedures, carbon dioxide purification, measurement and calculation as described previously (Pazdur et al, 1982). Ages are reported as conventional radiocarbon dates in years before ad 1950. No corrections for 13C/12C ratio were made for samples reported in this date list. Infinite dates are based on a 2-sigma criterion (Pazdur and Walanus, 1979). Sample descriptions and comments are based on information provided by the submitters.

Description: The following list contains the measurements of archaeologic samples made during 1978 and 1979 using carbon-dioxide-filled proportional counters. Most of the samples were dated with counter No. 3 (L3) filled to 1 or 2 atm pressure (Mościcki and Zastawny, 1977). Our counter No. 1 (L1) previously described (Mościcki and Zastawny, 1976) has been remounted and is now operating at 2 atm pressure of carbon dioxide. Samples measured with this counter have date numbers starting with Gd-1000. Parameters of proportional counters are listed in Table 1. Our transistorized electronics is being gradually replaced by more compact integrated-circuit electronics in CAMAC system (Bluszcz and Walanus, 1980). Counts from proportional counter and guard counters are recorded in 5 channels and punched every 100 minutes. Typical measurement of any sample, including background and oxalic acid samples, consists of a series of 20 to 25 partial measurements. Partial results obtained in such series are analyzed on ODRA 1325 computer at the Computing Centre of the Silesian Technical University according to code C14C written in ALGOL (Pazdur and Walanus, 1979). Age calculations are based on 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. Ages are reported as conventional radiocarbon dates in years before ad 1950. Corrections for isotopic fractionation in nature are made only for some samples with indicated values of δ13C Errors quoted (±1σ) include estimated overall standard deviations of count rates of the unknown sample, contemporary standard, and background (Pazdur and Walanus, 1979).

Description: Most of the 14C measurements reported here were made between October 1980 and October 1981. Equipment, measurement, and treatment of samples are as reported previously (R, 1968, v 10, p 36–37; 1976, v 18, p 290; 1980, v 22, p 1045).

Description: The stability to three-dimensional disturbances of three classical steady vortex configurations in an incompressible inviscid fluid is studied in the limit of small vortex cross-sectional area and long axial disturbance wavelength. The configurations examined are the single infinite vortex row, the Karman vortex street of staggered vortices and the symmetricvortex street. It is shown that the single row is most unstable to a two-dimensional disturbance, while the Karman vortex street is most unstable to a three-dimensional disturbance over a significant range of street spacing ratios. The symmetric vortex street is found to be most unstable to three-dimensional or two-dimensional symmetric disturbances depending on the spacing ratio of the street. Short remarks are made concerning the relevance of the calculations to the observed instabilities in free shear layer, wake and boundary-layer type flows. © 1982, Cambridge University Press. All rights reserved.

Description: A formalism that accounts for inertial and diffusive effects in the dynamics of a dilute gas-particle suspension is introduced. The treatment is purely deterministic away from a very thin Brownian diffusion sublayer, while, within the sublayer, inertial effects are small, permitting a near-equilibrium expansion in powers of the Stokes number (particle relaxation time divided by flow characteristic residence time). This expansion provides phenomenological expressions for theparticle velocity including two terms: the standard Brownian diffusion, and an additional inertial drift velocity which is closely related to the pressure diffusion term of the Chapman-Enskog expansion. As an example, the general formalism is applied in detail to the case of Stokes flow about a sphere, and sketched for the similar case of a cylinder. Two competing mechanisms are seen to affect the total rate of particle capture by the sphere: (i) the stagnation-point region is considerably enriched in particles owing to the high compressibility of the particle phase, which leads to locally enhanced deposition; (ii) centrifugal forces tend to deplete the Brownian diffusion sublayer of particles, reducing diffusion rates away from the stagnation point to the surface. The first effect is seen to dominate over the second except in a very narrow zone of small Stokes numbers. Our method bridges the gap between Levich's solution for the ‘pure-diffusion’ limit and Michael's treatment in the ‘pure-inertia’ limit. © 1982, Cambridge University Press. All rights reserved.

Description: Arguments are presented to show that the concept of gradient diffusion is inapplicable to mixing in turbulent shear layers. A new model is proposed for treating molecular mixing and chemical reaction in such flows at high Reynolds number. It is based upon the experimental observations that revealed the presence of coherent structures and that showed that fluid elements from the two streams are distributed unmixed throughout the layer by large-scale in viscid motions. The model incorporates features of the strained flame model and makes use of the Kolmogorov cascade in scales. Several model predictions differ markedly from those of diffusion models and suggest experiments for testing the two approaches.† Present address: Dept of Aeronautics, University of Washington, Seattle, WA 98195. © 1982, Cambridge University Press. All rights reserved.

Description: Observations of inertial waves generated by uniform horizontal flow over ridges and truncated axisymmetric obstacles in a homogeneous fluid rotating about a vertical axis are discussed and compared with linear theory. The dependence of the flow on obstacle shape, Ro, H, E and e is investigated. Here Ro = U/2ΩL is the Rossby number, H = Ro(D/L), E = v/2ΩL2 is the Ekman number, and e = h/L is the non-dimensional height of the obstacle, where U is the basic velocity Ω is the angular frequency, L is a streamwise length, D is the depth of the fluid, h is the height of theobstacle, and v is the kinematic viscosity. Previous linear analysis of this problem has been for the limit H fixed, Ro→ 0, referred to here as the small-Ro limit. However, it is shown that certain linear terms neglected in the small-Ro limit can be important for finite Ro, and are included in the analysis given here. The observed flow is then well described by linear theory for H/ e 1, particularly in the case of two-dimensional flow over a ridge. However, for H/e 1 the flow field is dominated by a vertical columnar motion, which is not adequately described by the analysi. © 1982, Cambridge University Press. All rights reserved.

Description: The robustness of localized states that transport energy and mass is assessed by a numerical study of the Euler equation in two space dimensions. The localized states are the translating ‘F-states’ discovered by Deem & Zabusky. These piecewise-constant dipolar (i.e. oppositely-signed or) vorticity regions are steady translating solutions of theEuler equations. A new adaptive contour-dynamical algorithm with curvature-controlled node insertion and removal is used. The evolution of one F-state, subject to a symmetric-plus-asymmetric perturbation is examined and stable (i.e. non-divergent) fluctuations are observed. For scattering interactions, coaxial head-on (or on) and head-tail (or on) arrangements are studied. The temporal variation of contour curvature and perimeter after F-states separate indicate that internal degrees of freedom have been excited. For weak interactions we observe phase shifts and the near recurrence to initial states. When two similar, equal-circulation but unequal-area F-states have a head-on interaction a new asymmetric state is created by contour ‘exchange’. There is strong evidence that this is near to a F-state. For strong interactions we observe phase shifts, ‘breaking’ (filament formation) and, for head-tail interactions, merger of like-signed vorticity regions. © 1982, Cambridge University Press. All rights reserved.

Description: The onset of double-diffusive convection is discussed for a layer of fluid in which the vertical salinity gradient varies with depth and for which the thermal and saline Rayleigh numbers R and Rs are large. These conditions are similar to those that exist in a solar pond prior to the onset of any instability. It is shown that when convection occurs it takes the form of an overstable mode and is essentially confined to a narrow region of vertical extent Rs- 1/4 x depth of the fluid layer, centred at the critical depth where the salt gradient is smallest. The leading terms in asymptotic expansions of the ratio R/Rs, the frequency of oscillation p and the horizontal wavenumber a are determined for Rs 1. The results predicted by the theory are shown to be in good agreement with numerical results and with observations of solar ponds. © 1982, Cambridge University Press. All rights reserved.

Description: Truncated modal equations are used to study the time evolution of thermal convection. In the Boussinesq approximation these nonlinear equations are obtained by expanding the fluctuating velocity and temperature fields in a finite set of planforms of the horizontal coordinates. Here we report on numerical studies dealing with two or three modes with triad interactions. We have found rich time dependence in these cases: periodic and aperiodic solutions can be obtained, along with various steady solutions. Three-mode solutions reproduce the qualitative appearance of spoke-pattern convection as observed in experiments at high Prandtl numbers. Though the values of the periods of the time-dependent solutions do not agree with those of the experiments, their variation with Rayleigh number compares favourably. Except at the highest Rayleigh number we have considered (107), the theoretical Nusselt numbers agree well with experiment.† N values from II, table 1.‡ P-estimates from Rossby (1969) and Krishnamurti (1973). © 1982, Cambridge University Press. All rights reserved.

Description: The fluid motion, temperature distribution and the mass-transfer problem of a binary gas mixture in a rapidly rotating centrifuge are investigated. The model centrifuge considered consists of a pair of concentric circular cylinders bounded on the top and bottom by horizontal end plates; the apparatus rotates rapidly about the axis of the cylinders. During steady operation a binary gas mixture containing species A and B is injected into and withdrawn from the centrifuge through axisymmetric slots located on the sidewalls. Solutions for the velocity, temperature and mass-fraction fields within the centrifuge are obtained for mechanically or thermally driven centrifuges. For the mass-transfer problem, a detailed analysis of the fluid-mechanical boundary layers is required, and, in particular, mass fluxes within the boundary layers are obtained for a wide range of source-sink geometries. Solutions to the mass-transfer problem are obtained for moderately and strongly forced flows in the container; the dependence of the separation (or enrichment) factor on centrifuge configuration, rotational speed and fraction of the volumetric flow rate extracted at the product port (the cut) are predicted. © 1982, Cambridge University Press. All rights reserved.

Description: The stability of weakly compressible boundary-layer flow over a spring-mounted piston is examined theoretically by modelling the mean boundary layer at low Strouhal numbers by means of a step-function velocity profile. This constitutes a prototype problem for the treatment of the interaction of unsteady boundary-layer flow with a compliant surface, and the present discussion complements a recent analysis due to Ffowcs Williams and Purshouse by incorporating the influence of flow separation at the edges of the piston. This is effected analytically by application of the unsteady Kutta condition at both the leading and trailing edges of the piston. At high Reynolds numbers and in the case of light fluid loading itis predicted that the separated flow can cause piston flutter. Stability criteria are derived for a rectangular piston of large aspect ratio. © 1982, Cambridge University Press. All rights reserved.

Description: Joint Institute for Laboratory Astrophysics, and Department of Astrophysical, Planetary and Atmospheric Sciences, University of Colorado, Boulder, CO 80309.A two-layer configuration of thermohaline convection is studied, with the principal aim of explaining the observed indeendence of the buoyancy-flux ratio on the stability parameter when the latter is large. Temperature is destabilizing and salinity is stabilizing, so diffusive interfaces separate the convecting layers. Theconvection is treated in the single-mode approximation, with a prescribed horizontal planform and wavenumber. Surveys ofnumerical solutions are presented for a selection of Rayleigh numbers R, stability parameters γ and horizontal wavenumbers a. The solutions yield a buoyancy flux ratio Xthat is insensitive to γ, in accord with laboratory experiments. However X increases with increasing R, in contradiction to laboratory observations. © 1982, Cambridge University Press. All rights reserved.

Description: The central features of linear and nonlinear disturbance growth in the unstable shear layer, mechanisms of impingement of the resultant vortices on the edge, induced force on the wedge, and upstream influence in the form of induced velocity fluctuations at separation are examined by simultaneous visualization, velocity, and force-measurement techniques.The nature of the vortex-wedge interaction, and the associated force on the wedge, are directly related to the induced velocity at the upstream separation edge, thereby providing the essential ‘feedback’ for the self-sustained oscillation. Velocity fluctuations at the upper and lower sides of the separation edge tend to be n out of phase, a condition that is maintained along the outer boundaries of the downstream shear layer. Moreover, the phase between velocity fluctuations at separation and impingement satisfies the relation 2nΠ, where n is an integer.The shear layer downstream of the separation edge initially forms an asymmetric wake, which evolves into large-scale vortices, all of which have a circulation appropriate to the high-speed side. The disturbance amplification associated with the high-speed side dominates from the separation edge onwards, precluding development of instabilities associated with the low-speed side.Regardless of the initial amplitude of the disturbance induced at the separation edge, the same saturation amplitude is attained in the downstream (nonlinear) region of the shear layer, underscoring the fact that variations in force amplitude at the wedge are dominated by the type of vortex-edge interaction mechanism. The sensitivity of this interaction to small offsets between the vortex centre and the leading edge entails that jumps in frequency of oscillation are also associated with jumps in the force amplitude. © 1982, Cambridge University Press. All rights reserved.

Description: Velocity moments have been calculated for the rapid distortion of axisymmetric turbulence in a uniform mean shear. The moments are compared with data on steady pipe flows and two-dimensional channel flows, and the turbulence structure of these flows is summarized in terms of effective distortion strain. The centre-line structure is taken to be characteristic of the undistorted state which from the data is more nearly axisymmetric rather than isotropic. A closer comparison is found than that by Townsend (1970), and in particular the differences in stress ratios T/pu21 T/pq2 found between different experiments can be accounted for with the hypothesis of initially axisymmetric turbulence. Profiles for the effective strain are derived from the experiments and are shown to have the same form and to indicate the existence of a relaxation timescale for the large eddies, comparable to the energy decay timescale. An equation for the effective distortion strain is formulated that can be incorporated into a turbulence model. © 1982, Cambridge University Press. All rights reserved.

Description: This note is to show that in the presence of surface tension small progressive waves can always exist in water having aninertial surface composed of uniformly distributed floating particles, in contrast to the known result in the absence ofsurface tension that precludes propagation under a surface that is too heavy. © 1982, Cambridge University Press. All rights reserved.

Description: An analytical theory is developed for the stability properties of planar fronts of premixed laminar flames freely propagating downwards in a uniform reacting mixture. The coupling between the hydrodynamics and the diffusion process is described for an arbitrary expansion of the gas across the flame. Viscous effects are included with an arbitrary Prandtl number. The flame structure is described for a large value of the reduced activation energy and for a Lewis number close to unity. The flame thickness is assumed to be small compared with the wavelength of the wrinkles of the front, this wavelength being also the characteristic lengthscale of the perturbations of the flow field outside the flame. A two-scale method is then used to solve the problem. The results show that the acceleration of gravity associated with the diffusion mechanisms inside the front can counterbalance the hydrodynamical instability when the laminar-flame velocity is low enough. The theory provides predictions concerning the instability threshold. In particular, the dimensions of the cells are predicted to be large compared with the flame thickness, and thus the basic assumption of the theory is verified. Furthermore, the quantitative predictions are in good agreement with the existing experimental data. © 1982, Cambridge University Press. All rights reserved.

Description: An algorithm is formulated for computing perturbation-series solutions for standing waves on the interface between two semi-infinite fluids of different but uniform densities. Using a computer, the series solutions are computed to fifth order for a general value of r, the ratio of the density of the upper fluid to that of the lower fluid (0 ≤r ≤ 1), and to 21st order for five specific values of this ratio: r = 0, 10-3, 01, 0.5, 1.0. The series for the period, the energy, and the interface profile of the waves are summed using Padé approximants. The maximum wave height for each of the above five density ratios is estimated from the locations of the poles of the Padé approximants for the wave period and the wave energy. At maximum height the interface appears to be vertical at a point on the interface that is very near the crest for r = 10-3 and approaches the midpoint between the crest and the trough as r approaches 1.0. © 1982, Cambridge University Press. All rights reserved.

Description: Steady three-dimensional symmetric wave patterns for finite-amplitude gravity waves on deep water are calculated from the full unapproximated water-wave equations as well as from an approximate equation due to Zakharov. These solutions are obtained as bifurcations from plane Stokes waves. The results are in good agreement with the experimental observations of Su. © 1982, Cambridge University Press. All rights reserved.

Description: The mean-velocity profiles and entrainment rates in the similarity region of a two-dimensional jet are generated by a simple superposition of Rankine vortices arranged to represent a vortex street. The spacings between the vortex centres, their two-dimensional offsets from the centreline, as well as the core radii and circulation strengths, are all governed by similarity relationships and based upon experimental data.Major details of the mean flow field such as the axial and lateral mean-velocity components and the magnitude of the Reynolds stress are properly determined by the model. The sign of the Reynolds stress is, however, not properly predicted. © 1982, Cambridge University Press. All rights reserved.

Description: Solutions for interfacial waves of permanent form in the presence of a current were obtained for small-to-moderate wave amplitudes. A weakly nonlinear approximation was used to give simple analytical solutions to second order in wave height. Numerical methods were used to obtain solutions for larger wave amplitudes; details are reported for a number of selected cases. A special class of finite-amplitude solutions, closely related to the well-known Stokes surface waves, were identified. Factors limiting the existence of steady solutions are examined. © 1982, Cambridge University Press. All rights reserved.

Description: The motion of free surfaces in incompressible, irrotational, inviscid layered flows is studied by evolution equations for the position of the free surfaces and appropriate dipole (vortex) and source strengths. The resulting Fredholm integral equations of the second kind may be solved efficiently in both storage and work by iteration in both two and three dimensions. Applications to breaking water waves over finite-bottom topography and interacting triads of surface and interfacial waves are given. © 1982, Cambridge University Press. All rights reserved.

Description: Visual examination of simultaneous temperature traces from a rake of cold wires placed across a turbulent boundary layerhad enabled the identification of coherent temperature fronts. An X-wire/cold-wire arrangement was used simultaneously with the rake to provide measurements of the velocity fluctuations u (longitudinal) and v (normal) and the temperature fluctuation 6. Conditional averages of u, v, ᶿ and products uv, uᶿ, vᶿ were obtained by application of conditional techniques based on the detection of the temperature fronts using information obtained at only one point in space. These averages, obtained at various positions across the layer, have been compared with those obtained when the rake was used to detect the fronts. The comparison has indicated that none of the one-point detection techniques is in good quantitative agreement with the rake detection technique, the largest correspondence between the rake technique and any of the other one-point techniques being only 51 %. With the exception of the hole technique used in conjunction with the quadrant decomposition analysis, conditional averages obtained from one-point techniques are in reasonable qualitative agreement with those deduced using the rake. © 1982, Cambridge University Press. All rights reserved.

Description: Measurements have been made of the Couette flow in the annular space between concentric cylinders with a radius ratio of 1.5, the outer cylinder being held stationary and the inner one rotated at speeds to give Taylor numbers in the range 1.0 × 104−2.3 × l06 times the critical value for first instability of the steady viscous flow. Mean velocities have been measured both with Pitot tubes and with linearized hot-wire anemometers, and turbulent intensities and stresses, frequency spectra and space-time correlations have been obtained using single hot-wire anemometers of X-form and linear arrays of eight single-wire anemometers. For Taylor-number ratios to the critical number less than 3 × l05, the most prominent feature of the flow is a system of toroidal eddies, encircling the inner cylinder and uniformly spaced in the axial direction with nearly the separation of the Taylor vortices of the viscous instability. They are superimposed on a background of irregular motion and, except within the thin wall layers, the toroidal eddies contribute more to the total intensity. With increase of rotation speed, the toroidal eddies lose their regularity, and they cannot be clearly distinguished at Taylor-number ratios beyond 5 × l05.The change of flow type from quasi-regular toroidal to fully irregular turbulent takes place over an extensive range of Taylor-number ratio centred near 3 × l05, and it may be linked with changes in the thin wall layers that separate the flow boundaries from the central region of nearly constant circulation. For ratios over 5 × l05, an appreciable part of the wall layers is comparatively unaffected by flow curvature and has a logarithmic distribution of mean velocity similar to that found in channel flows. It is suggested that the motion in the wall layers changes from a set of Gortler vortices characteristic of curved-wall flow to the more irregular motion found on plane walls, causing the toroidal eddies to break into sections of length ranging from a considerable fraction of the flow perimeter to nearly the separation of the cylinders. Changes in the frequency spectra of the radial and azimuthal velocit'y fluctuations are consistent with such a change.

Description: Weapons Systems Research Laboratory, Defence Research Centre, Salisbury, South Australia It is shown experimentally that, in steady flow, transition to Mach reflection occurs at the von Neumann condition in the strong shock range (Mach numbers from 2-8 to 5). This criterion applies with both increasing and decreasing shock angle, so that the hysteresis effect predicted by Hornung, Oertel & Sandeman (1979) could not be observed. However, evidence of the effect is shown to be displayed in an unsteady experiment of Henderson & Lozzi (1979). © 1982, Cambridge University Press. All rights reserved.

Description: Exact solutions are used to contrast the behaviour of vertical dye streaks and of point discharge in the deep ocean. After a few inertial periods the growth of the contaminant cloud in both cases can be modelled by a diffusion equation withslowly varying coefficients. However, the apparent long-term diffusivity for the dye streak can be as much as three times as large as the horizontal diffusivity for the point discharge, depending upon the precise time of release. This anomalously large rate of spreading for the dye streak can persist for several weeks until sufficient time has elapsed for vertical diffusion over the vertical lengthscale of the dominant inertial-frequency waves. © 1982, Cambridge University Press. All rights reserved.

Description: Velocity measurements in the plane of symmetry of a turbulent spot are reported. The number of data points taken at various streamwise locations was adequate to map the ensemble-averaged flow field in a spot at a given instance. These results are compared with velocities taken in laboratory coordinates (i.e. at a given station with variable time), whereupon it is shown that the flow field in the spot depends either on the distance from its origin or on the time elapsed from its initiation. The two variables are related so that the flow may be transformed into either a time- or a space-independent problem. The dependence of the spot on the Reynolds number and on the surrounding laminar boundary layer isestablished. The effects of these parameters on the shape of the ensemble-averaged spot, its size, characteristic celerities, and relative rate of entrainment, are discussed.The present results indicate that a similarity approach based on ensemble-averaged data is severely limited. It might be used to predict the overall scales and flow field but much more sophisticated data-processing techniques are required to describe the structure of the spot. © 1982, Cambridge University Press. All rights reserved.

Description: Energy-stability theory is employed to study the finite-amplitude stability of a viscous incompressible fluid occupying the space between a pair of concentric cylinders when the inner-cylinder angular velocity varies linearly with time. For the case with a fixed outer cylinder and increasing inner-cylinder speed, we find an enhancement of stability, consistent with a linear-theory result due to Eagles. When the inner-cylinder speed decreases, we find an initially decreased stability bound, indicating the possibility of hysteresis, while, if the inner cylinder is allowed to reverse direction and linearly increase in speed, we find significant stability enhancement. © 1982, Cambridge University Press. All rights reserved.

Description: The transition of a laminar two-dimensional wake is studied experimentally to establish the role of amplitude and phase modulations in the spectral-broadening and energy-redistribution process. Multiple instability modes f0 and f1 are triggered by acoustic excitation. The spectrum of the fluctuating velocity field formed by the growing and interacting instabilities shows the development of a complicated sideband structure reminiscent of amplitude- and phase-modulated waves. Digital complex demodulation techniques are used to obtain quantitative measurements of local instantaneous amplitude and phase modulations. Measurements of the modulation time traces, their modulation indices, the lag between phase and amplitude modulations, and the power spectra of the modulations are presented. Our results show that both phase and amplitude modulation play a role in the transition process. The dominant modulation frequency of both amplitude and phase is that of the difference mode fv =f1- f0 produced by the interaction of the two excited instabilities. Phase modulation becomes progressively more important as transition proceeds downstream, and seems to play the dominant role in the spectral-broadening and energy-redistribution process. Measurements of the bicoherency spectrum indicate that sideband structures, and accompanying modulations, are produced by nonlinear interactions between the low-frequency difference mode and higher-frequency instability modes. Some limited measurements indicate that finite-amplitude induced nonlinear dispersion effects (k,a2) may provide a physical mechanism by which amplitude modulations generated by nonlinear interactions can induce simultaneous phase modulations. © 1982, Cambridge University Press. All rights reserved.

Description: The problem of determining both the steady and unsteady axially symmetrical motion of a viscous incompressible fluid outside a fixed sphere when the fluid at large distances rotates as a solid body is considered. It is assumed that the Reynolds number for the motion is so large that the boundary-layer equations may be assumed to hold. The steady-state boundary-layer equations are solved using backward-forward differencing and the terminal solutions at the equator and the pole of the sphere are generated as part of the numerical procedure. To check that this steady-state solution can be approached from an unsteady situation, the case of a sphere that is initially rotating with the same constant angular velocity as the fluid and is then impulsively brought to rest is investigated. In this case the motion is governed by a coupled set of three nonlinear time-dependent partial differential equations, which are solved by employing the semi-analytical method of series truncation to reduce the number of independent variables by one and then solving by numerical methods a finite set of partial differential equations in one space variable and time. The physical properties of the flow are calculated as functions of the time and compared with the known solution at small times and the steady-state solution. © 1982, Cambridge University Press. All rights reserved.

Description: Inviscid transonic shear flow in a rectangular channel is considered; opposite walls are parallel except in the region of interest, where one pair of opposing walls form a nozzle-like constriction. The flow exhibits the essential features found in an axial-flow rotor of zero stagger angle, where the relative velocity is transonic, the constricted passage being similar to the channel formed between two adjacent blades. Analytical solutions, valid to second order, are presented for the case where the ratio of the order of the change in velocity caused by the variation in flow area to the order of the change in velocity across the channel due to the shear is unity. The case where this ratio is small compared with one is discussed, as is the problem formulation for a flow with a shock wave in the passage. © 1982, Cambridge University Press. All rights reserved.

Description: The analysis by Busse (1975) of preferred patterns of convection in spherical shells is extended to include the case of odd degrees I of spherical harmonics. In the general part of the paper only the property of spherical symmetry of the basic state is used. The results are thus applicable to all bifurcation problems with spherical symmetry. Except in the case 1=1 a pattern degeneracy of the linear problem exists, which is partly removed by the solvability conditions that are generated when nonlinear terms are taken into account as perturbations. In each of the cases I considered so far, at least I physically different solutions have been found. The preferred solution among I existing ones is determined for I 〉 2 by a stability analysis. In the case I = 3 emphasized in this paper the axisymmetric solution is found to be always unstable, and the solution of tetrahedronal symmetry appears to be generally preferred. The latter result is rigorously established in the special case of a thin layer with nearly insulating boundaries treated in the second part of the paper. © 1982, Cambridge University Press. All rights reserved.

Description: Spatial growth of mechanically generated water waves under the action of wind has been measured in a laboratory wind-wave flume both for pure water and for water containing a surfactant (sodium lauryl sulphate, concentration 2.6 x 10-2%). In the latter case, no wind waves develop on the surface of the mechanically generated waves as well as on the still water surface for wind speeds up to U10 ~ 15 m/s, where U10 is the wind velocity at the height Z = 10 m. Therefore we can study the wind-induced growth of monochromatic waves without the effects of co-existing short wind waves. © 1982, Cambridge University Press. All rights reserved.

Description: Fully developed air flow has been investigated over a Reynolds-number range of 82800-346700 in a duct that simulates two interconnected subchannels of a rod bundle with a pitchldiameter ratio of 1.20. Based on equivalent hydraulic diameter, friction factors were found to be 2% lower than for pipe flow. Detailed measurements were made at a Reynolds number of 200000 of axial velocities, secondary velocities, and the Reynolds stresses. The distribution of axial velocity near the walls (normalized with the local friction velocity) could be expressed by an inner law of the wall for y+ up to 1500. Distributions of the normal Reynolds stresses and the mean turbulence kinetic energy were similar to those observed in a number of pipe and two-dimensional channel flows and could be correlated using the axial-velocity fluct,uations normalized with the local friction velocity. Maximum secondary velocities were about 1.5 % of the bulk axial velocity. The ‘k-ε’ turbulence model and an algebraic vorticity source for generating secondary velocities enabled the computation of axial velocities, secondary velocities, and mean turbulence kinetic energies that are in satisfactory agreement with those measured.

Description: Measurements of the mean-pressure distribution and the Strouhal number on a smooth circular cylinder, circular cylinderswith distributed roughness, and circular cylinders with narrow roughness strips were made over a Reynolds-number range 4.0x 104 to 1.7 x 106 in a uniform flow. A successful high-Reynolds-number (transcritical) simulation for a smooth circular cylinder is obtained using a smooth circular cylinder with roughness strips. High-Reynolds-number simulation can only be obtained by roughness strips and not by distributed roughness. A similarity parameter correlating the pressure distributions on circular cylinders with distributed roughness in the supercritical range is presented. The same parameter can also be applicable to the drag coefficients of spheres with distributed roughness. © 1982, Cambridge University Press. All rights reserved.

Description: When light rotating fluid spreads over heavier fluid in the vicinity of a vertical wall (coast) a boundary jet of width L forms, the leading edge or nose of which propagates with speed 6 along the coast. A certain fraction 8 of the boundarytransport is not carried by the nose but is deflected backwards (detrained) and left behind the propagating nose. Theoretical and experimental results for L, c, and 8 are given for a quasi-equilibrium (constant-c) regime. Over longer time intervals the laboratory observations suggest that the nose slows down and stagnates, whereupon the trailing flow separates from the coast and an intermittent boundary current forms. These processes may be relevant to the mixing of oceanic coastal currents and the maintenance of the mean current. © 1982, Cambridge University Press. All rights reserved.

Description: Displacements of wind waves in the laboratory were measured with a laser displacement gauge, a recently developed, optical, non-intrusive sensor, which avoids the meniscus effects that severely limit the frequency response of conventional thin-wire gauges. The new gauge is a digital device, which has a maximum frequency response of 25 kHz. Its spatial resolution, which depends on the field of view, is typically 0016 cm for a 4 cm field of view. The wind-wave displacements were measured at several fetches for three wind speeds. Wave-variance spectra derived from these measurements indicate the presence of a quasi-equilibrium spectrum in the capillary-wave regime. The quasi-equilibrium spectrum follows an f-7/3 power law that has been predicted on dimensional grounds. The spectral density increases with increasing wind speed from 4 to 10 m/s but is independent of the fetch from 3 to 5 m. In addition, the capillary-wave spectrum is practically unchanged when a relatively long but -low-amplitude mechanical wave is superposed onto the windgenerated waves. © 1982, Cambridge University Press. All rights reserved.

Description: It is demonstrated experimentally that the influence of viscosity on the transition condition in pseudosteady flow is very significant. A mechanism is proposed for this effect, which explains the features of the observed behaviour. In particular, an experimental method of finding the inviscid transition condition, by extrapolation to infinite Reynolds number,gives excellent agreement with the calculated inviscid sonic criterion. It is thought that this provides the explanation for the usual persistence of regular reflection beyond the sonic condition. © 1982, Cambridge University Press. All rights reserved.

Description: The effect of periodic two-dimensional excitation on the development of a turbulent mixing region was studied experimentally. Controlled oscillations of variable amplitude and frequency were applied at the initiation of mixing between two parallel air streams. The frequency of forcing was at least an order of magnitude lower than the initial instability frequency of the flow in order to test its effect far downstream. The effect of the velocity difference between the streams was also investigated in this experiment. A typical Reynolds number based on the velocity difference and the momentum thickness of the shear layer was 104. © 1982, Cambridge University Press. All rights reserved.

Description: We derive a path-integral representation for the effective diffusion function of a passive scalar field. We use it to calculate the long-time effective diffusivity in Gaussian turbulence in the near-Markovian limit. Our results confirm the negative effect of vorticity predicted by previous discussions. They also demonstrate that the helicity of the turbulence when present may be as important an influence as the vorticity. © 1982, Cambridge University Press. All rights reserved.

Description: The shape of a rising bubble, or of a falling drop, in an incompressible viscous fluid is computed numerically, omitting the condition on the tangential traction at the bubble or drop surface. When the bubble is sufficiently distorted, its top is found to be spherical and its bottom is found to be rather flat. Then the radius of its upper surface is in fair agreement with the formula of Davis & Taylor (1950). This distortion occurs when the effect of gravity is large while that of surface tension is small. When the effect of surface tension is large, the bubble is nearly a sphere.The shape is found, together with the flow of the surrounding fluid, by assuming that both are steady and axially symmetric, with the Reynolds number being large. The flow is taken to be a potential flow. The boundary condition on the normal component of normal stress, including the viscous stress, is satisfied, but not that on the tangential component. The problem is converted into an integro-differential set of equations, reduced to a set of algebraic equations by a difference method, and solved by Newton's method together with parameter variation. © 1982, Cambridge University Press. All rights reserved.

Description: Experiments on the vortex-shedding frequencies of various rectangular cylinders were conducted in a wind tunnel and in a water tank. The results show how Strouhal number varies with a width-to-height ratio of the cylinders in the range of Reynolds number between 70 and 2 x 104. There is found to exist a certain range of Reynolds number for the cylinders with the width-to-height ratios of 2 and 3 where flow pattern abruptly changes with a sudden discontinuity in Strouhal number. The changes in flow pattern corresponding to the discontinuity of Strouhal number have been confirmed by means of measurements of velocity distribution and flow visualization. These data are compared with those of other investigators. The experimental results have been found to show a good agreement with those of numerical calculations. © 1982, Cambridge University Press. All rights reserved.

Description: The convective circulation driven by a surface buoyancy flux in a dead-end open channel is analysed. On the assumption of similarity profiles for velocity and temperature, the governing partial differential are reduced to two nonlinear ordinary differential equations by integrating over the flow depth. A closed-form solution of the differential equations is presented. The solution is a function of the Grashof number G and the modified Prandtl-Grashof number Pm defined in (21). The velocity and temperature along the channel vary linearly as the distance and as the square of the distance respectively. Analytical expressions for the rate of total heat loss from the channel and the rate of flow in the channel are derived. The analytical results compare well with the available experimental data. © 1982, Cambridge University Press. All rights reserved.

Description: An integral-equation and variational formulation for the radiation of swfaee waves from a submerged cylindrical duct is developed. This formulation, which complements that of Simon (1981a) for the corresponding scattering problem, provides variational representations of the radiation impedance of the duct and (through the Green-function identities established by Simon) of the pressure-amplification factor in the scattering problem. An exact solution of the integral equation is obtained for the limiting case of a narrow duct. © 1982, Cambridge University Press. All rights reserved.

Description: The cylinder end boundaries, whether they be end plates or simple free ends, alter the vortex-shedding mechanism near these boundaries. This effect has in the past usually been overlooked. In a region near an end plate or a free end (ranging from 6 to 15 cylinder diameters in length), the shedding frequency f2 is found to be 10–15% less than the regular Strouhal frequency fs. The latter frequency is observed over the remaining cylinder length. The simultaneous occurrence of two frequencies results in a beat frequency, which is best observed at the junction of the two regions characterized by fs and f2 respectively. A third frequency f3 with fs 〉 f3 〉 f2 is observed over the entire cylinder length when the cylinder is bounded by two end plates less than 20 to 30 cylinder diameters apart. Here the critical Reynolds number for the onset of shedding is shifted to about 60 and the laminar Reynolds-number range is extended from about 150 to about 250. © 1982, Cambridge University Press. All rights reserved.

Description: The transition to turbulence in Bénard convection in a layer of air bounded by rigid conducting walls is studied by numerical solution of the three-dimensional time-dependent Boussinesq equations. The wavy instability of rolls is compared with available experimental and theoretical results. The subsequent transition to chaotic convection is shown to occur for Rayleigh numbers larger than about 9000. The role of symmetry-breaking perturbations in the production of chaos is clarified. © 1982, Cambridge University Press. All rights reserved.

Description: Hot-film measurements of the streamwise velocity component were carried out in a fully developed turbulent water-channel flow for three different Reynolds numbers (13800, 34600 and 48900). The results for the first four statistical moments complement and extend the results from previous studies of turbulent channel flow. The VITA variance technique was employed to detect deterministic events in the stream-wise velocity. It was demonstrated that the VITA technique has a band-pass-filter character. The number of events detected was found to decrease exponentially with the threshold level and the events occupy a wide range of timescales. This makes it impossible to define one unique frequency of occurrence or one unique duration of the events. However, by using this technique information was obtained on the amplitude and timescale distributions of the events. The characteristic features of the conditional averages were found to be related to the skewness and flatness factors. © 1982, Cambridge University Press. All rights reserved.

Description: A numerical study of the laminar flow of an incompressible viscous fluid in rotating ducts of rectangular cross-section is conducted. The full time-dependent nonlinear equations of motion are solved by finite-difference techniques for moderate to relatively rapid rotation rates where both the convective and viscous terms play an important role. At weak to moderate rotation rates, a double-vortex secondary flow appears in the transverse planes of the duct whose structure is relatively independent of the aspect ratio of the duct. For Rossby numbers Ro 〈 100 this secondary flow is shown to lead to substantial distortions of the axial velocity profiles. For more rapid rotations (Ro 〈 1), the secondary flow (in a duct with an aspect ratio of two) is shown to split into an asymmetric configuration of four counter-rotating vortices similar to that which appears in curved ducts. It is demonstrated mathematically that this effect could result from a disparity in the symmetry of the convective and Coriolis terms in the equations of motion. If the rotation rates are increased further, the secondary flow restabilizes to a slightly asymmetric double-vortex configuration and the axial velocity assumes a Taylor-Proudman configuration in the interior of the duct. Comparisons with existing experimental results are quite favourable. © 1982, Cambridge University Press. All rights reserved.

Description: Camber distributions are chosen for airfoils of zero thickness that maximize the angular velocity induced by a sudden decrease in free-stream velocity. Those optimal shapes that are in equilibrium in steady forward flow are also neutrally stable in that position. © 1982, Cambridge University Press. All rights reserved.

Description: A quantitative theory for particle coagulation in continuous particle size distributions is presented and experimentally verified. The analysis, following Friedlander (1960a, b), assumes a local equilibrium in the size distribution maintained by a particle flux through the size distribution. Only particle collisions caused by Brownian motion, fluid shear and differences in settling velocities are considered. For intervals of particle size where only one coagulation mechanism is dominant, dimensional analysis predicts self-similar size distributions that contain only one dimensionless constant for each mechanism. Experiments were designed to test these predictions with clay particles in artificial seawater sheared in the gap between concentric rotating cylinders. Particle-size distributions measured over time were self-similar in shape and agreed with the Brownian- and shear-coagulation prediction in terms of shape and dependence on fluid shear rate and particle volume flux through the size distribution. © 1982, Cambridge University Press. All rights reserved.

Description: Statistical fluid dynamics identifies a functional of the fluid energy spectrum that plays the role of Boltzmann’s entropy for fluids. Through a series of two-dimensional flow simulations we confirm the theoretical predictions for the behaviour of this entropy functional. This includes a demonstration of Loschmidt’s paradox and an examination of the effects of Rossby waves and viscosity on the behaviour of the entropy. © 1982, Cambridge University Press. All rights reserved.

Description: Extensive single- and two-point measurements have been made in a high-Reynolds-number single-stream mixing layer growing to encounter a wind-tunnel floor on its high-velocity side. The measurements include detailed conditionally sampled results, which separate the turbulent and irrotational contributions to the two-point covariances. These measurements show that the true (vorticity-bearing) large-scale structure in the isolated mixing layer, well away from the region influenced by the floor, is three-dimensional without a trace of the two-dimensional orderly structure found in some two-stream mixing-layer experiments. The structure appears to be a combination of the classical mixing jet and double-roller eddy (Grant 1958); the circulation in the latter is confined almost exclusively to the (x, z)-plane. The large spanwise scales in the potential motion are attributed to the effect of pressure disturbances and not to two-dimensionality of the turbulent structure, as claimed by previous workers. The first effect of the wall is to stretch the streamwise and spanwise scales of the large eddies. Near the high-velocity edge [Formula omited] is amplified more than [Formula omited]. The surprising result that the low-wavenumber (large-eddy) contribution to v2 is amplified across the whole layer is associated with the nature of the mixing jets and the alteration of the pressure field by the wall. The change in turbulence structure occurs before any significant change in the mean-velocity profile, and the implications for the calculation of the change in boundary conditions are discussed. The measurements made after the mixing layer reached the wind tunnel floor will be presented in part 2. © 1982, Cambridge University Press. All rights reserved.

Description: Electrochemical measurements of the local wall shear were made along the inner bend of a curved pipe in the entry region,to examine the nature of the secondary-flow boundary-layer collision. Analysis by Stewartson, Cebeci & Chang (1980) predicts a vanishing of the wall shear at the collision point, but without flow reversal. The experimental results are in good agreement with the analytical predictions upstream of the collision point, and its location appears to be predicted accurately. However, downstream of the collision point agreement is poor. © 1982, Cambridge University Press. All rights reserved.

Description: Cut-off frequencies are well known in acoustic ducts to be the thresholds of propagation and evanescence. If at one end of a duct the piston oscillates at very near the cut-off frequency, cross-duct resonance occurs and the linearized theory breaks down. This paper studies the nonlinear response, near a cut-off frequency of a guided wave, as an initial-boundary-value problem. The asymptotic state is shown to be governed by a modified cubic Schrödinger equation. Numerical solutions are then obtained for inputs of finite and long duration. In addition to the characteristics of the input envelope, two quantities control the transient phenomenon: frequency detuning and nonlinearity. Under certain circumstances, energy can be trapped near the piston long after a short-lived input has expired, while for a sustained input there is no sign of a steady state. Dissipation is not considered. © 1982, Cambridge University Press. All rights reserved.

Description: Aspects of the various steady states of Taylor-vortex flow between concentric cylinders have been investigated by means of flow visualization. The experiments have focused principally on the evolution of the primary flow, that is, on the continuum of steady states parametrized by the Reynolds number R, beginning at small R where the primary flow is the only one possible. For any particular aspect ratio I the primary flow develops a well-defined pattern of cells at higher R, but then other steady cellular flows (secondary modes) are also possible. The observations presented demonstrate mutations of the primary flow as Y is varied through critical values: its R-dependent evolution is thereby switched from one to another array of cells realized at higher R. In each of four cases (4–6, 6–8, 8–10 and 10–12 cells), the mutation is shown to involve hysteresis of the primary-flow locus and complicated interactions with secondary modes. Following a description of the apparatus in § 2, a discussion of the experimental method used to observe the often delicate hysteresis effects is given in § 3. The experimental results in § 4 are in broad agreement with abstract mathematical ideas that have been previously shown to bear on the Taylor experiments, but several new and surprising features, such as the coupling between pairs of cells, have been uncovered. © 1982, Cambridge University Press. All rights reserved.

Description: Conditionally sampled hot-wire and ‘cold-wire’ (resistance-thermometer) measurements confirm the general flow picture advanced by Falco (1974, 1977, 1980; see also Smith & Abbott 1978) and by Head & Bandyopadhyay (1981; see also Smith & Abbott) on the basis of smoke observations and more limited hot-wire measurements. The probability density function of turbulent-zone lengths in the intermittent region varies rapidly with Reynolds number, supporting the above authors’ finding that the hairpin-vortex ‘ typical eddies ’ in the viscous superlayer scale on the viscous length v/uT rather than on boundary-layer thickness. However the average turbulent-zone length, deduced as an integral moment of the probability distribution, tends to a constant fraction of the boundary-layer thickness above a momentum-thickness Reynolds number of 5000, which strongly suggests that at high Reynolds numbers the overall shape of the turbulent irrotational interface is controlled by the classical ‘ large eddies ’ and not by the viscosity-dependent small eddies. The intermittency profile is practically independent of Reynolds number. The second-order structural parameter u2/v2 increases strongly with increasing Reynolds number but the triple-product parameters, with the exception of the w-component skewness, vary only slowly with Reynolds number. This behaviour of the intermittency and velocity statistics is most simply explained by supposing that the lengthscale of the large eddies is nearly independent of Reynolds number while their intensity is somewhat lower at low Reynolds number. ‘ Typical eddies ’ evidently contribute to the Reynolds stresses at low Reynolds number, but it is probable that the large eddies carry most of the triple products at any Reynolds number. Our results confirm the usual finding that the mixing length and dissipation length parameter increase, while the wake component of the velocity profile decreases, as Reynolds number decreases. © 1982, Cambridge University Press. All rights reserved.

Description: The general axisymmetric creeping motion of a spherical particle in a stagnation region near a finite surface is modelled by the motion of a sphere of arbitrary size towards a disk for the following conditions: (a) pure translation in quiescent fluid, (6) uniform flow past a fixed sphere-disk configuration, and (c) a neutrally buoyant sphere carried by the fluid towards a disk. The combined analytic and numerical solution procedure is similar to that described in Dagan, Weinbaum & Pfeffer (1982 b) for the motion of a sphere towards an orifice. The drag force acting on the sphere and on the disk under the flow conditions mentioned above is presented. In addition, the fluid velocity field has been obtained for the case of uniform flow past a fixed sphere-disk configuration. These solutions show the formation and coalescence of separated regions of closed streamlines adjacent to the sphere and the disk. © 1982, Cambridge University Press. All rights reserved.

Description: A vertically oscillating grid is used to simulate boundary mixing in the laboratory. The oscillation of the grid creates a turbulent mixing region in its vicinity, and mixing within this region creates a step-like structure in an initial density distribution which varies linearly with depth. If the initial density varies only at the boundary between two homogeneous layers, the same grid turbulence generates additional steps above and below the initial one. The steps, in turn, drive multiple intrusions of mixed fluid away from the boundary and into the non-turbulent interior of the fluid. A compensating return flow carries fluid from the interior into the turbulent mixing region. From the data, the inference is made that the intrusions make a negligible direct contribution to the vertical mass transport. An analytical model of the intrusions, which employs only molecular values of the transport coefficients and also demonstrates negligible vertical mass transport, is consissent with the laboratory observations. Nevertheless, the data indicate that the fluid eventually reaches a homogeneous density by means of the gradual change of the gradient a t a rate which is essentially the same both near the grid and far from it. For an initially uniform density profile this change occurs at all heights simultaneously, and for an initial density step it occurs preferentially near the step. Thus in both cases the interior flow must include slow vertical advection away from the horizontal centre plane. These advective currents can be made part of a consistent dynamic model, the buoyant equivalent of the spindown in a rotating flow, provided that the net effect of the grid mixing includes a decrease in the local slope of the density gradient. This mode of adjustment explains satisfactorily the experimentally observed negligible horizontal density gradients. For the case of an initially uniform density stratification, the shape of the evolving density gradient is not accounted for. In particular, it is not clear why the gradient changes at mid-depth almost simultaneously with variations at top and bottom boundaries. The vertical mass flux is found to be independent of container length, and it increases with grid frequency of oscillation, amplitude of oscillation and with the mean density gradient. © 1982, Cambridge University Press. All rights reserved.

Description: The object of this paper is to derive the added mass and damping coefficients associated with the periodic motions of a floating hemisphere. Two physically distinct cases are considered; namely those of heave and surge, where these nautical terms refer respectively to a vertical or horizontal oscillation of the body. Computations have been done and the values found for the various force coefficients are presented in tabulated form. A brief derivation of the long- and short-wave asymptotics of these coefficients has also been included. © 1982, Cambridge University Press. All rights reserved.

Description: Time-dependent flows such as occur in breaking surface waves are often most conveniently described in parametric form, with the coordinate z and velocity potential X each expressed in terms of a third complex variable w and the time t. In this paper we discuss some interesting flows given in terms of elementary functions of ω and t. Included are the Stokes 120° corner flow, the 45° rotor or rotating wedge, and a decelerated upwelling flow, with an exactly plane surface. Lastly it is shown that a class of cubic flows, which are related to the plane upwelling flow just mentioned, has a free surface that corresponds with remarkable accuracy to the forward face of an overturning, or plunging, breaker. © 1982, Cambridge University Press. All rights reserved.

Description: A quantitative theoretical model is developed to describe the time-dependent draining of an initially uniform-thickness fluid squeeze film between an infinitely flexible membrane-bound fluid cell and a planar rigid surface or between two symmetrically loaded cells subject to impulsive loading. The solution of the coupled nonlinear membrane-fluid-film equations shows that two characteristic times and length scales are required to describe the membrane deformation and draining behaviour of the fluid film. The early-time behaviour is strikingly different from that predicted by elasto hydrodynamic squeeze-film theory (Christensen 1962), where the local elastic deformation of the boundary is not controlled by membrane tension but is proportional to the local film pressure. While fluid trapping occurs in both cases, a bidirectional flow is set up during the early-time period in the membrane squeeze film owing to the establishment of an off-axis pressure maximum near the edge of the near contact area. Fluid is driven radially inward, causing upwelling of the membrane in the central region, and driven radially outward near the edge of the contact area., causing this region to form a narrow fluid gap. After the narrow-edge region has formed, the off-axis pressure maximum gradually disappears and is replaced by a pressure plateau in the interior and a radial outflow at all locations that is similar to the elasto hydrodynamic squeeze film. The present problem is closely related to the fluid films studied by Hartland (1967,1968,1969), Jones & Wilson (1978) and others when a, small spherical particle or fluid droplet rises or settles under gravity towards a uniform-tension fluid-fluid interface. These studies have theoretically and experimentally examined the long-time drainage of the film after the narrow edge region has formed and the fluid-trapping phenomenon is established. The solutions to the initial-value problem described herein show how this asymptotic quasi-steady drainage state is reached. A simple experiment has been constructed to confirm qualitatively the theoretically predicted short-time behaviour. Experimental photographs graphically illustrate the gradual thickening of the lubricating layer near the origin and the formation and draining of the edge region as predicted by the membrane squeeze-film theory. © 1982, Cambridge University Press. All rights reserved.

Description: In an experimental investigation of the transient processes that occur when a single droplet of butane at the superheat limit vaporizes explosively, short-exposure photographs and fast-response pressure measurements have been used to construct a description of the complete explosion process. It is observed that only a single bubble forms within the drop during each explosion, and that the growth proceeds on a microsecond time scale. An interfacial instability driven by rapid evaporation has been observed on the surface of the bubbles. It is suggested that the Landau mechanism of instability, originally described in connection with the instability of laminar flames, also applies to rapid evaporation at the superheat limit. The photographic evidence and the pressure data are used to estimate the evaporative mass flux across the liquid-vapour interface after the onset of instability. The rate of evaporation is shown to be two orders of magnitude greater than would be predicted by conventional bubble-growth theories that do not account for the effects of instability. An estimate of the mean density within the bubbles during the evaporative stage indicates that it is more than one half of the critical density of butane. Additional interesting dynamical effects that are observed include a series of toroidal waves that form on the interface between the butane vapour and the external host liquid in the bubble column apparatus after the bubble has grown large enough to contact the outer edge of the drop, and violent oscillations of the bubble that occur on a millisecond time scale, after evaporation of the liquid butane is complete, that cause the disintegration of the bubble into a cloud of tiny bubbles by Rayleigh-Taylor instability. © 1982, Cambridge University Press. All rights reserved.

Description: The two-phase flow in settling vessels with walls that are inclined to the vertical is investigated. By neglecting inertial effects and the viscosity of the suspension it is shown that the particle concentration remains constant on kinematic-wave fronts. The wave fronts are horizontal and propagate in a quasi-one-dimensional manner, but are imbedded in a two-dimensional or three-dimensional basic flow which, in turn, depends on the waves via the boundary conditions. Concentration discontinuities (interfaces) are described by kinematic-shock theory. The kinematic shocks are shown to be horizontal, with the possible exception of discontinuities that separate the suspension from the sediment. At downward-facing inclined walls conservation of mass enforces the existence of a boundary-layer flow with relatively large velocity. As G/R2→∞ and G/R4→0, where G and R are respectively a sedimentation Grashof number and a sedimentation Reynolds number, the entrainment of suspended particles into the boundary-layer flow of clear liquid is negligibly small. This provides an appropriate boundary condition for the basic flow of the suspension. Thus, in the double limit considered, a kinematic theory suffices to determine the convective flow of the suspension due to the presence of inclined walls. As an example batch sedimentation in vessels with inclined plane or conical walls is investigated. The settling process is terminated after a time that can be considerably smaller than the time required in a vertical vessel under the same conditions. Depending on the initial particle concentration, there are centred kinematic waves that are linked to a continuous increase of the particle concentration in the suspension. In an appendix, the flow in the boundary layer at a downward facing, inclined wall is investigated. With G/R2→∞ and G/R→0 the boundary layer consists of an inviseid particle-free main part, a viscous sublayer at the wall, and a free shear sublayer at the liquid/particle interface. © 1982, Cambridge University Press. All rights reserved.

Description: This paper is an attempt at a mathematical synopsis of the theory of wave motions on glaciers. These comprise surface waves (analogous to water waves) and seasonal waves (more like compression waves). Surface waves have been often treated and are well understood, but seasonal waves, while observed, do not seem to have attracted any theoretical explanation. Additionally, the spectacular phenomenon of glacier surges, while apparently a dynamic phenomenon, has not been satisfactorily explained. The present thesis is that the two wave motions (and probably also surging, though a discussion of this is not developed here) can both be derived from a rational theory based on conservation laws of mass and momentum, provided that the basal kinematic boundary condition involving boundary slip is taken to have a certain reasonable form. It is the opinion of this author that the form of this ‘sliding law’ is the crux of the difference between seasonal and surface waves, and that a further understanding of these motions must be based on a more satisfactory analysis of basal sliding. Since ice is here treated in the context of a slow, shallow, non-Newtonian fluid flow, the theory that emerges is that of non-Newtonian viscous shallow-water theory; rather than balance inertia terms with gravity in the momentum equation, we balance the shear-stress gradient. The resulting set of equationsis, in essence, a first-order nonlinear hyperbolic (kinematic) wave equation, and susceptible to various kinds of analysis. We show how both surface and seasonal waves are naturally described by such a model when the basal boundary condition is appropriately specified. Shocks can naturally occur, and we identify the (small) diffusive parameters that are present, and give the shock structure: in so doing, we gain a useful understanding of the effects of surface slope and longitudinal stress in these waves. © 1982, Cambridge University Press. All rights reserved.

Description: A linearized stability analysis is carried out for the breakup of small-diameter liquid filaments of dilute polymer solutions into droplets. Oldroyd's 8-constant model expressed in a corotational reference frame is used as the rheological equation of state. The crucial idea in this theory is the recognition that the liquid may be subject to an unrelaxed axial tension due to its prior history. If the tension is zero, the present analysis predicts that jets of shear-thinning liquids are less stable than comparable jets of Newtonian liquids; this is in agreement with previous analyses. However, when the axial tension is not zero, and provided the stress relaxation time constant is sufficiently large, the new theory predicts that the axial elastic tension can be a significant stabilizing influence. With reasonable values for the tension and stress relaxation time the theory explains the great stability observed for jets of some shear-thinning, dilute polymer solutions. The theory explains why drops produced from jets of such liquids are larger than drops from corresponding Newtonian liquids. The theory also appears capable of explaining the sudden appearance of irregularly spaced bulges on jets after long distances of travel with little amplification of disturbances. © 1982, Cambridge University Press. All rights reserved.

Description: Attention is confined to roll-cell development and roll-cell interaction appropriate to one horizontal dimension larger than either the other horizontal dimension or the depth. At simple eigenvalues Mc, the roll-cell amplitude and transport fields can be obtained. Near those aspect ratios corresponding to double eigenvalues Mc, where two roll-cell states of linear theory areequally likely, the nonlinear theory predicts sequences of transitions from one steady convective state to another as the Marangoni number is increased. Direct comparisons are made of the results here with those of the previous paper for Marangoni convection in circular cylinders. Time-periodic convection is possible in certain cases. © 1982, Cambridge University Press. All rights reserved.

Description: This paper analyses the problem of a flow past an oscillating body moving with constant velocity, below and parallel to a free surface. Special attention is given to frequencies of oscillation in the neighbourhood of the critical frequency ωc = 0×25 g/U, where the classical linearized solution yields infinitely large wave amplitude. As a result both the lift and drag forces acting on the oscillating body at the resonant frequency are singular. It is demonstrated in the paper how this resonance is eliminated by considering higher-order free-surface effects, in particular the interaction between the first- and third-order terms. The resulting generalized solution yields finite wave amplitudes at the resonant frequency which are 0(ε½) and O(εlog½) for 2 and 3 dimensions respectively. Here ε is a measure of the singularity strength. It is also shown that inclusion of third-order terms causes a shift in the wavenumber and group velocity which eliminates the singularity in the lift and drag expressions at the resonant frequency. These results are illustrated by computing the lift and drag experienced by a submerged oscillating horizontal doublet in a uniform flow. © 1982, Cambridge University Press. All rights reserved.

Description: An experimental investigation has been carried out into the nature of the transport of airborne material in the near aerodynamic wakes of bluff bodies with simple shapes. The main attention was focused on the essential differences existing between axi-symmetric flows (as about disks) and two-dimensional flows (as about rectangular long thin flat plates). Measurements were made for such bodies of the near-wake residence time of injected small particles, along with other and more familiar near-wake properties such as the vortex-shedding frequency and base pressure. It was concluded for disks that the transport of material into and out of the near-wake region is dominated by turbulent diffusion, and is strongly influenced by free-stream turbulence, especially for free-stream turbulence whose length scale is substantially smaller than the disk diameter. For rectangular flat plates, transport is dominated by the periodic shedding of vortices, and to only a secondary extent by turbulent motions, and is not strongly influenced by free-stream turbulence. © 1982, Cambridge University Press. All rights reserved.

Description: A technique is developed to model the multiple scattering of surface waves in an array of axisymmetric wave-energy devices. The matrix equation which results is inverted to yield the exciting forces, the added-damping and added-mass matrices, the optimal power absorption and the optimal device responses. The matrix method is also used on the previously unstudied problem of an unconstrained array. Finite-size effects of devices are shown to be important in producing phase-shifts, which shift the unconstrained frequency response, but leave the optimal energy absorption virtually unchanged. © 1982, Cambridge University Press. All rights reserved.

Description: We consider liquid in a circular cylinder that undergoes nonlinear Marangoni instability. The upper free surface of the liquid is taken to have large-enough surface tension that surface deflections are neglected. The side walls are adiabatic and impenetrable, and for mathematical simplicity the liquid is allowed to slip on the side walls. The linearized stability theory for heating from below gives the critical Marangoni number Mc as a function of cylinder dimensions, surface-cooling condition and Rayleigh number. The steady nonlinear convective states near Mc are calculated using an asymptotic theory, and the stability of these states is examined. At simple eigenvalues Mc the finite-amplitude states are determined. We find th at the Prandtl number of the liquid influences the stability of axisymmetric states, distinguishing upflow at the centre from downflow. Near those aspect ratios corresponding to double eigenvalues Mc, where two convective states of linear theory are equally likely, the nonlinear theory predicts sequences of transitions from one steady convective state to another as the Marangoni number is increased. These transitions are determined and discussed in detail. Time-periodic convection is possible in certain cases. © 1982, Cambridge University Press. All rights reserved.

Description: This paper describes an experimental study of the effects of surface roughness on the flow between two concentric cylinders, one of which rotates. The surface roughness has some effects on the coefficient of viscous frictional torque CM in the transient and in the fully developed turbulent region. In the fully developed rough turbulent flow, the value of CM depends on both the Reynolds number Ra and the relative roughness rm/k in the case where the outer cylinder rotates, but CM depends only on rm/k in the case where the inner cylinder rotates. The effect of the surface roughness of the inner cylinder is greater than that of the outer one for both cases. © 1982, Cambridge University Press. All rights reserved.

Description: We have investigated a sequence of dynamical systems corresponding to spherical truncations of the incompressible three-dimensional Navier-Stokes equations in Fourier space. For lower-order truncated systems up to the spherical truncation of wavenumber radius 4, it is concluded that the inviscid Navier-Stokes system will develop mixing (and a fortiori ergodicity) on the constant energy-helicity surface, and also isotropy of the covariance spectral tensor. This conclusion is, however, drawn not directly from the mixing definition but from the observation that one cannot evolve the trajectory numerically much beyond several characteristic correlation times of the smallest eddy owing to the accumulation of round-off errors. The limited evolution time is a manifestation of trajectory instability (exponential orbit separation) which underlies not only mixing, but also the stronger dynamical characterization of positive Kolmogorov entropy (K-system). © 1982, Cambridge University Press. All rights reserved.

Description: To evaluate the usefulness of digital image analysis in extracting quantitative information from flow pictures we have studied a 16 mm ciné film of a turbulent mixing layer. A sequence of 373 frames is digitized and analysed to isolate and measure the concentration eddies that constitute the large structure and to follow their individual evolution in time. As a result, statistics are given on the life history of the eddies, the structure of the amalgamation process and the amount of entrainment, as measured by area change, due to amalgamation as compared to the total. It is found that most of the entrainment occurs during the normal life of eddies and not during pairing. Mixing intermittency is computed from the observed shape of the eddies and seen to compare well with previous measurements. The significance of these results in modelling the mixing layer is discussed briefly and some comments are given on the general usefulness of the techniques presented. © 1982, Cambridge University Press. All rights reserved.

Description: The outer cylinder was kept stationary whilst the inner rotated. Weak circulatory motion (‘embryo cells ’) was observed in all the fluids investigated at Taylor numbers Ta less than the critical Taylor number Tac. These cells grew with increasing Ta, then burst into vigorous Taylor vortices at Ta = Tac. In solutions of rigid elongated molecules having concentrations above a minimum concentration, an axial oscillation (overstability?) of the embryo cells was observed. The oscillation did not occur in solutions of flexible folded molecules nor in the solvent. The oscillation was observed over a range Ta0 ≨ Ta ≨ Tac. For concentrations above the minimum Ta0/Tac decreased with increasing concentration. Other phenomena of the flow were also studied. It was found for solvent and solutions that the torque on the outer cylinder increased relatively less rapidly with the speed of rotation of the inner cylinder when Ta/Tac 〈 1·08 than it did when 1 〈 Ta/Tac ≨1·08. In this latter range there was a torque reduction in the flow of the solutions relative to that in the flow of solvent. At sufficiently high speeds of rotation circumferential waves occurred in the fully developed Taylor cells (at Ta = Taw) and it was found that when R1/R2 = 0· then Taw/Tac = 1·5 for the solvent, whereas for the solutions Taw/Tac≧ 1·5. When R1/R2 = 0·90 then Taw/Tac = 1×25, and for the solutions Taw/Tac 〉 l·25. No experiment was done at Ta 〉 Taw. The normal-stress coefficients of the solution have been evaluated from the results. © 1982, Cambridge University Press. All rights reserved.

Description: The discrete-vortex model is applied to simulate the separation bubble over a two-dimensional blunt flat plate with finite thickness and right-angled corners, which is aligned parallel to a uniform approaching stream. This flow situation is chosen because, unlike most previous applications of the model, the separation bubble is supposed to be strongly affected by a nearby solid surface. The major objective of this paper is to examine to what extent the discrete-vortex model is effective for such a flow. A simple procedure is employed to represent the effect of viscosity near the solid surface; in particular, the no-slip condition on the solid surface. A reduction in the circulation of elemental vortices is introduced as a function of their ages in order to represent the three-dimensional deformation of vortex filaments. An experiment was also performed for comparison purposes. The calculation yielded reasonable predictions of the time-mean and r.m.s. values of the velocity and the surface-pressure fluctuations, together with correlations between their fluctuating components, over most of the separation bubble. The interrelation between instantaneous spatial variations of the surface-pressure and velocity fluctuations were also obtained. A comparison between the calculated and measured results suggests that, in the real flow, the three-dimensional deformation of vortex filaments will become more and more dominant as the reattachment point is approached. © 1982, Cambridge University Press. All rights reserved.

Description: The influence of leading-edge separation vortices on the Weis-Fogh (1973) lift-generation mechanism for insect hovering is investigated. The analysis employs a vortex-shedding model (Edwards 1954; Cheng 1954) and represents an extension of Lighthill's (1973, 1975) analysis of an inviscid model without separated vortices. Results of the study compare reasonably well with observations on a laboratory model at high Reynolds number (Maxworthy 1979), confirming that vortex separation significantly enhances the initial circulation on each of the wings. Unlike the un-separated-model solution, this circulation was found to depend on the history of the wing motion and to increase with a large opening angle. © 1982, Cambridge University Press. All rights reserved.

Description: Based on somewhat simplified profiles of turbulent eddy diffusivity and mean velocity in turbulent flow, an expression is derived for the convection current in a pipe where electrification occurs at the wall. The expression is in explicit analytic form, and applies for all turbulent Reynolds numbers and all fluid conductivities, from conditions where the Debye length is small compared with the diffusion sublayer (typical aqueous solutions) to conditions where the Debye length is large compared with the sublayer (typical liquid hydrocarbons). © 1982, Cambridge University Press. All rights reserved.

Description: A numerical method for calculating the interaction of steep (nonlinear) ocean waves with large fixed or floating structures of arbitrary shape is described. The interaction is treated as a transient problem with known initial conditions corresponding to still water in the vicinity of the structure and a prescribed incident waveform approaching it. The development of the flow, together with the associated fluid forces and structural motions, are obtained by a time-stepping procedure in which the flow at each time step is calculated by an integral-equation method based on Green's theorem. A few results are presented for two reference situations and these serve to illustrate the effects of nonlinearities in the incident waves. © 1982, Cambridge University Press. All rights reserved.

Description: For a non-uniform discharge of contaminant in a shear flow the initial adveetion velocity and the amount of shear across the contaminant cloud depend upon the discharge shape across the flow. Here it is shown how the continuing influence of the discharge non-uniformity can be incorporated into a delay-diffusion description of the dispersion process (Smith 1981). An important improvement over the variable coefficient diffusion equation derived by Gill & Sankarasubramanian (1971) is that the solutions have the physically correct superposition property. © 1982, Cambridge University Press. All rights reserved.

Description: The steady oblique interaction of two solitary waves on the surface of water of constant depth is considered. One wave is taken to be of arbitrary (large) amplitude and the other is small with a (non-dimensional) amplitude measured by the parameter ε. A solution is sought as an asymptotic expansion, based on ε, that assumes that in some region the solution is the sum of the two waves plus interaction terms. It is shown that this expansion is not uniformly valid close to a critical angle. This angle varies from zero (parallel waves) up to about 63×5°, as the amplitude of the larger wave increases from infinitesimally small to the largest-possible solitary wave. In the limit of two small waves, the details agree precisely with the results obtained by Miles (1977a). When the angle between the two waves is close to the critical angle, for a given large wave, an alternative asymptotic expansion is required. In this strong-interaction case, the dominant term is just the large wave but with a phase shift that is an arbitrary function of the characteristic variable associated with the small wave. This function is determined by matching to an appropriate far field, and it turns out to be proportional to the logarithm of a hypergeometric function (which itself can be expressed in terms of the associated Legendre function Pv−μ). The phase shift is then well-defined (finite, real) provided the angle is not very close to the critical value. When this occurs the phase shift can be infinite at a specific angle (which corresponds to the case ǀμǀ = v 〉 0), and even closer to the critical angle (ǀμǀ 〈 v) the phase shift is undefined (no longer real). A real solution for the wave profile is still possible if negative amplitudes are allowed, but the resulting solution is unacceptable since the surface is then not undisturbed at infinity. It is shown that the criterion ǀμǀ 〈 v matches exactly (for two small waves) with Mile's criterion for the non-existence of a regular reflection. For the strong interaction (and ǀμǀ ≨ v) it is argued that the small wave cannot penetrate the large wave unchanged. The large wave suffers significant distortion (bending) in the interaction, but the small wave, if it penetrates at all, must have an amplitude o(ε). This is the main aspect of the problem which cannot be completely determined using the present methods. The difficulty can be traced to the large solitary wave which is not known in closed form: only the exponential behaviour in the ‘tail’ is used explicitly in this work. © 1982, Cambridge University Press. All rights reserved.

Description: Measurements of air and solid velocities were made in an air-solid two-phase flow in a horizontal pipe by the use of a laser-Doppler velocimeter (LDV). The pipe was 30 mm inner diameter, and two kinds of plastic particles, 0·2 and 3·4 mm in diameter, were conveyed in addition to fine particles (ammonium chloride) for air-flow detection. The air velocities averaged over the pipe cross section ranged from 6 to 20 m/s and the solid-to-air mass-flow ratio was up to 6. Simultaneous measurements of both air and 0·2 mm particle velocities were found possible by setting threshold values against the pedestal and Doppler components of the photomultiplier signal. As the loading ratio increased and the air velocity decreased, mean-velocity distributions of both phases increased asymmetrical tendency. In the presence of 0·2 mm particles, a flattening of the velocity profile was remarkable. The effects of the solid particles on air-flow turbulence varied greatly with particle size. That is, 3·4 mm particles increased the turbulence markedly, while 0·2 mm ones reduced it. The probability-density function of the air flow deviated from the normal distribution (Gaussian) in the presence of particles. Finally, the frequency spectra of air-flow turbulence were obtained in the presence of 0–2 mm particles by using a fast Fourier transform (FFT). As a result, it was found that the higher-frequency components increased with increasing loading ratio. © 1982, Cambridge University Press. All rights reserved.

Description: Measurements are presented, of the pressure fluctuations acting on a stationary square-section cylinder, with the front face normal to the flow, and one forced to oscillate, transverse to a flow, at amplitudes up to 25 % of the length of a side. The range of reduced velocities investigated, 4−13, includes the vortex lock-in regime. At lock-in the amplification of the coefficient of fluctuating lift is found to be much less than that found for a circular cylinder. The variation of the phase angle, between lift and displacement, is also different from that measured on a circular cylinder, and vortex-induced oscillations are possible only at the high-reduced-velocity end of the lock-in range. At reduced velocities sufficiently far below lock-in the natural vortex-shedding mode is suppressed and vortices are found to form over the side faces at the body frequency. Intermittent reattachment occurs over the side faces and, for an amplitude of oscillation equal to 10 % of the length of a side face, the time-mean drag coefficient can be reduced to 60 % of its fixed-cylinder value. © 1982, Cambridge University Press. All rights reserved.