ALBERT

Description: The dates presented here were calculated from measurements made at the University Radiocarbon Dating Research Laboratory mostly during 1973–74. The radioactivity of the samples was counted in gas proportional detectors, either silica lined (de Vries et al, 1959) or of pure copper, filled to 2 atmospheres pressure with pure carbon dioxide. The detectors were fixed in, and completely surrounded by, a plastic scintillator anticoincidence shield mounted inside a massive lead shield to protect against environmental radiation (Switsur, Hall and West, 1970). Modern sample gas was obtained from the combustion of ad 1845 to 1855 rings of an oak tree grown near Cambridge and felled in 1950. Background samples were prepared from Welsh anthracite. The contemporary sample was frequently compared with the activity of the NBS oxalic acid international standard. Age calculations were based on the 14C half-life of 5568 years and the uncertainty stated as one standard deviation calculated from the statistical analyses of sample and standards counting rates.

Description: This list includes the second group of age measurements made from September 1972 to July 1974 using the benzene scintillation method. All archaeologic and geologic samples come from Italian territory. Chemical apparatus for benzene synthesis and the liquid scintillation spectrometer are unchanged (Alessio et al, 1970a, 1973). Charcoal and wood samples underwent standard pretreatment by boiling with 5 to 10% HCl; α-labeled samples were given additional leaching with .2N NaOH. The counting rate of approx half the samples was corrected based on the 13C/12C ratio, mass-spectrometrically measured on CO2 obtained in combustion line set up after Broecker et al (1959), according to previously described procedure (Alessio et al, 1969).

Description: This series reports some of the measurements made since the previous list. Methods essentially remain as described in Saskatchewan II (R, 1960, v 2, p 73) with expanded facilities and new electronic equipment since 1973. The laboratory operates commercially, administered by the Saskatchewan Research Council under the direction of A A Rutherford.

Description: UCR I (R, 1974, v 16, p 395–401) previously reported measurements carried out jointly by the UCR and UCLA radiocarbon laboratories between November 1972 and September 1973 and interlaboratory check samples used to calibrate the UCR 1.7L counter. This list reports the measurements of the UCR laboratory from September 1973 to August 1974.

Description: This is the last installment of 14C dates done at the Tata Institute; the lab has now shifted to the Physical Research Laboratory, Navarangpura, Ahmedabad-380 009, India.

Description: The dates presented in this paper comprise results of determinations made at the University Radiocarbon Dating Research Laboratory, mostly during the latter half of 1974. Radioactivity was measured with proportional counters using pure carbon dioxide at 2 atmospheres pressure as filling gas. Effects of cosmic and local environmental radiation on the counters were reduced by surrounding them completely with 1) a plastic scintillator anticoincidence shield, 7.5cm thick, viewed by 2 photomultiplier tubes operating in coincidence mode, the output pulses of which were in anticoincidence with the proportional counters signals, and 2) by a 17.5 ton lead castle.

Description: Measurements have continued with the same proportional counter system, pretreatment procedure, methane preparation and measurement, and calculation, as described previously (R, 1970, v 12, p 298–318). Uncertainties quoted are single standard deviations originating from standard, sample, background counting rates and half-life. No C13/C12 ratios were measured.

Description: The following list of dates contains the majority of measurements made during 1974, ie, since our last list (R, 1974, v 16, p 285–303).

Description: This date list includes most of the archaeologic samples dated in this laboratory since publication of our last date list (R, 1974, v 16, p 219–237), as well as some samples dated previously, which lacked adequate sample information. The BP ages are based on AD 1950, and have been calculated with the half-life value of 5568 yr. All samples were counted at least twice for periods of not less than 1000 min each. Errors quoted for each sample are derived from the measurement of the sample, the background, and several counts of our mid-19th century Oak sample, but do not include the half-life error. All samples were pretreated with 3N HCl and some, where noted, were given additional pretreatment with 2% NaOH for the removal of possible humic acid contaminants.

Description: The Water Resources Division of the US Geological Survey has operated a low-level tritium laboratory since the late 1950's. In 1970, 14C-measuring facilities were added to that laboratory to provide analyses of ground water and other carbonates, primarily for research and field projects of the Division.

Description: This date list is composed of the ages of tests of fossil populations of the foraminiferal species, Amphistegina gibbosa, and algal nodules collected from submerged banks in the N Gulf of Mexico. A Shipek grab sampler was used to collect the Amphistegina gibbosa and a few of the algal nodule samples. Algal nodules from the West Flower Garden Bank were obtained from cores at various intervals as indicated in Sec III.

Description: This list includes most of the samples measured from June 1972 to December 1973 and some other results as yet unpublished.

Description: All samples described in this date list have been dated from November 1973 to January 1975. Only the benzene liquid scintillation installation was used during this time. For the combustion of soil and fossil bone samples containing a high content of sulfur (ie, in the form of pyrite), a new CO2 extraction and cleaning system was built. The gases released by the combustion are dried in ice and dry ice traps, passed through hot copper oxide and bubbled through KOH solution. Following the combustion, the K2CO3 precipitate is acidified in the same vessel where it formed and the released CO2 is again dried in a dry ice trap and by passing it through ascarite. This CO2 gas is quite clean and can be brought to the original system where the gas volume is measured. Further processing is as previously described (Haynes and Haas, 1974).

Description: Most of the 14C measurements reported here were made between October 1973 and October 1974. Equipment, measurement, and treatment of samples are the same as reported previously (R, 1968, v 10, p 36–37; 1970, v 12, p 534).

Description: Procedures of measurements and calculation remain as previously described. All samples are pretreated according to the methods described in R, 1971, v 13, p 103 and p 123 unless specified under the sample descriptions. Unless stated samples are from Ireland.

Description: The following list contains dates of samples measured since our previous list (R, 1973, v 15, p 435–441). As before, age calculations are based on the Libby half-life 5568 ± 30 yr, and reported in years before 1950. The modern standard is 0.950 of the activity of NBS oxalic acid.

Description: The following list of dates is compiled from samples prepared since publication of our last date list (R, 1974, v 16, p 131–141). The counting equipment and operating procedures are the same. Ages are quoted with a 1σ counting error which includes statistical variation of the sample count as well as for background and standard, using ad 1950 as the reference year and 95% NBS oxalic acid for 14C dating as the standard. The half-life value used is 5570 years.

Description: The following list of dates are selected from geologic and archaeologic samples measured in late 1974. The technique employed is liquid scintillation counting of wholly synthesized benzene as described in (R, v 16, p 402–408). Errors are reported as one standard deviation. Sample descriptions and comments were written in collaboration with collectors and submitters.

Description: This list includes the results of measurements made during 1972–73.

Description: The following list of dates are selected from geologic and archaeologic samples measured in late 1973. The laboratory procedures and techniques are the same as indicated in R, 1974, v 16, p 402–408, where sample is synthesized to benzene and counted for 24 hours in either a Beckman LS-100-C or Packard 2311 liquid scintillation spectrometer. Ages are calculated relative to 0.95 x NBS oxalic acid using a 14C half-life of 5568 years. The quoted error is 1σ, which includes only the counting uncertainties of the background, modern standard, and sample. Sample descriptions and comments were written in collaboration with collectors and submitters.

Description: The unsteady laminar compressible boundary-layer flow in the immediate vicinity of a two-dimensional stagnation point due to an incident stream whose velocity varies arbitrarily with time is considered. The governing partial differential equations, involving both time and the independent similarity variable, are transformed into new co-ordinates with finite ranges by means of a transformation which maps an infinite interval into a finite one. The resulting equations are solved by converting them into a matrix equation through the application of implicit finite-difference formulae. Computations have been carried out for two particular unsteady free-stream velocity distributions: (i) a constantly accelerating stream and (ii) a fluctuating stream. The results show that in the former case both the skin-friction and the heat-transfer parameter increase steadily with time after a certain instant, while in the latter they oscillate, thus responding to the fluctuations in the free-stream velocity. © 1975, Cambridge University Press. All rights reserved.

Description: The response of turbulent boundary layers to sudden changes in surface roughness under adverse-pressure-gradient conditions has been studied experimentally. The roughness used was in the ‘d’ type array of Perry, Schofield & Joubert (1969). Two cases of a rough-to-smooth change in surface roughness were considered in the same arbitrary adverse pressure gradient. The two cases differed in the distance of the surface discontinuity from the leading edge and gave two sets of flow conditions for the establishment and growth of the internal layer which develops downstream from a change in surface roughness. These conditions were in turn different from those in the zero-pressure-gradient experiments of Antonia & Luxton. The results suggest that the growth of the new internal layer depends solely on the new conditions at the wall and scales with the local roughness length of that wall. Mean velocity profiles in the region after the step change in roughness were accurately described by Coles’ law of the wall-law of the wake combination, which contrasts with the zero-pressure-gradient results of Antonia & Luxton. The skin-friction coefficient after the step change in roughness did not overshoot the equilibrium distribution but made a slow adjustment downstream of the step. Comparisons of mean profiles indicate that similar defect profile shapes are produced in layers with arbitrary adverse pressure gradients at positions where the values of Clauser's equilibrium parameter β (= δ*τ−10dp/dx) are similar, provided that the pressure-gradient history and local values of the pressure gradient are also similar. © 1975, Cambridge University Press. All rights reserved.

Description: In wind-tunnel tests on bluff bodies the Reynolds number is often limited to values that are very much smaller than those of the flows being simulated. In such cases the experiments may have no practical significance whatsoever since both the fluctuating and the steady aerodynamic phenomena can vary considerably with Reynolds number. This difficulty was encountered in an investigation of supercritical incompressible flow over cylinders, and an attempt at artificially increasing the Reynolds number by means of surface roughness was made. In order to evaluate this simulation technique, the influence of various grades of surface roughness on the aerodynamic forces acting on cylinders of different diameters was studied over a wide range of Reynolds numbers in two very different wind tunnels. The results allow very positive conclusions to be drawn. © 1975, Cambridge University Press. All rights reserved.

Description: The evolution of the power spectrum of surface gravity waves is described by means of an energy transport equation. A slowly varying, prescribed ocean current and wind source are assumed to account for spatial inhomogeneities in the surface wave spectrum. These inhomogeneities lead to a new nonlinear wave-wave interaction mechanism. © 1975, Cambridge University Press. All rights reserved.

Description: The linearized initial-value problem for a two-dimensional, unbounded, exponentially stratified, plane Couette flow is considered. The solution is used to evaluate the evolution of wave-packet perturbations to the mean flow for all Richardson numbers J 〉 ¼, demonstrating that a consistent wave-packet approach to wave propagation in these flows is possible for all J 〉 ¼. It is found that the vertical influence of a wave-packet perturbation is limited to a distance of order (J − ¼)½/k0, where k0 is the magnitude of the initial central wave vector. These results are used to clarify the J ≳ ¼ conclusions of an earlier treatment by Booker & Bretherton. © 1975, Cambridge University Press. All rights reserved.

Description: A body is started from rest and moves on an arbitrary path in an inviscid isothermal compressible atmosphere. The phase configuration of the internal waves and the gravity-modified acoustic waves which are generated by the body is studied using small amplitude wave theory. When the body moves at supersonic speeds and the background density gradient approaches zero, it is shown how the wave solutions approach the pure acoustic wave solutions of Lilley et al. (1953). © 1975, Cambridge University Press. All rights reserved.

Description: Measurements of the pressure drop and flow rate were obtained for dilute solutions of polyethylene oxide flowing through beds of packed beads. When the velocity was sufficiently high, the pressure drop was above that for a Newtonian fluid of equal viscosity, often considerably above, and this viscoelastic effect was explored by varying the concentration and molecular weight of the polymer, by testing solutions over a wide range of flow rates, and by using several bead sizes. The non-Newtonian behaviour was most pronounced at moderate flow rates; at the highest velocities, the data were pseudo-Newtonian in character, i.e. the pressure drop still exceeded that for a Newtonian fluid, but was linearly related to the velocity. For some solutions, the large deviation from Newtonian values occurred over such a short range of flow rates that there was an interval in which the pressure drop decreased with velocity. It was not possible, therefore, to obtain steady-state measurements in this regime and a gap appears in the data curve of pressure vs. velocity. The pressure drop was monitored in steps along the test section, so that it was possible to detect molecular degradation of the solutions as they flowed through the porous media. In general, degradation was not extensive and the solutions became stably degraded by the midpoint of the test section. Degradation increased with velocity and, quite surprisingly, became more severe as the bead size increased. A visual examination of the flow field revealed that the streamline pattern for the polymer solutions was the same as that for water. The large non-Newtonian effects were therefore due to changes in the stress field, and in an effort to understand these effects, an analysis was carried out which examined how the stresses generated by each component of the deformation, i.e. by shear and pure strain, influence the pressure drop. This analysis, combined with a study of onset data, indicates that onset and the sudden large departures from Newtonian values are probably due to an interaction between extensional and shearing deformation, and that the reduced viscoelastic effect of higher flow rates may be due to the dominance of extensional stresses. © 1975, Cambridge University Press. All rights reserved.

Description: Shock discontinuities for which the upstream state is vapour and the downstream state is liquid are considered. The possibility of such shock waves is associated with a large number of molecular degrees of freedom: it is necessary that the ideal-gas specific heat cv ≥ 24R at the critical temperature, a condition which is met by several common fluids. Shock properties are found from a corresponding-states thermodynamic model and from several calculations based on data for particular fluids. Condensation shock waves satisfy the usual stability conditions and should be found in laboratory experiments. © 1975, Cambridge University Press. All rights reserved.

Description: The 50th Euromech Colloquium, on wind-tunnel simulation of the atmospheric boundary layer, was held in Berlin from 23–25 September 1974. Thirty-eight participants from eleven countries were present. Papers were presented describing and analysing different methods of simulation of neutral, stable and unstable atmospheric conditions in various types of wind tunnel. Numerous applications of wind-tunnel simulations were described or mentioned in the papers and the discussion sessions. Some conclusions about the validity, the techniques, the limitations and future developments of wind-tunnel simulations were reached in discussion. Tables are presented in appendix A listing the institutes in Europe and the U.S.A. of actual or invited participants where wind tunnels are used for simulation work; also listed are the characteristics of the wind tunnels and relevant measurements of the simulated atmospheric boundary layers, to enable comparisons to be made between different techniques. © 1975, Cambridge University Press. All rights reserved.

Description: A Galerkin method is proposed for a class of boundary-layer flow problems. In this method, the assumed solution is composed of an auxiliary function and a series solution. The representing functions used in the series solution are orthonormal eigenfunctions, closely related to that of the boundary-layer equation, and are independent of the initial condition, as well as the boundary conditions. The reduced system of stiff, first-order, nonlinear, ordinary differential equations then has diagonal dominance for the first part of the flow region. The proposed method has been tested on two representative flows. Numerical experiments show that highly accurate results can be obtained for the entire boundary-layer flow region, if the auxiliary function satisfying the initial and boundary conditions is chosen to satisfy the first compatibility condition of the upstream flow region. In fact the computation is rather simple, and the numerical integration of the reduced initial-value problem can be carried out up to separation with a fairly large step. © 1975, Cambridge University Press. All rights reserved.

Description: Any straight continental shelf of monotonic depth profile is shown to have as its entire complement of barotropic trapped modes (i) an infinite discrete set of ‘continental-shelf waves’, (ii) a single ‘Kelvin wave’, and (iii) an infinite discrete set of ‘edge waves’. The decomposition of energy density and fluxes into modal constituents is discussed. © 1975, Cambridge University Press. All rights reserved.

Description: It is shown that, in two-dimensional non-divergent flow in a bounded region, roughly 70% of triad interactions exchange more energy with longer wavelengths than with shorter wavelengths whilst roughly 40% exchange more enstrophy with longer wavelengths than with shorter wavelengths. © 1975, Cambridge University Press. All rights reserved.

Description: The temporal evolution of a resonant triad of wave components in a parallel shear flow has been investigated at second order in the wave amplitudes by Craik (1971) and Usher & Craik (1974). The present work extends these analyses to include terms of third order and thereby develops the resonance theory to the same order of approximation as the non-resonant third-order theory of Stuart (1960, 1962). Asymptotic analysis for large Reynolds numbers reveals that the magnitudes of the third-order interaction coefficients, like certain of those at second order, are remarkably large. The implications of this are discussed with particular reference to the roles of resonance and of three-dimensionality in nonlinear instability and to the range of validity of the perturbation analysis. © 1975, Cambridge University Press. All rights reserved.

Description: Sir Geoffrey Ingram Taylor, O.M., F.R.S., who died on 27 June 1975 at the age of 89, was one of the great men of our subject. He was a likeable happy man with an uncomplicated character and a razor-sharp mind for which scientific investigation was a natural activity. He was engaged in research throughout the whole of his life – not only the ‘working'part of it – and the fruits of his enquiries are described in over 200 papers published between 1909 and 1974. Nearly all these papers have been republished by Cambridge University Press in the four volumes of G. I. Taylor: Scientific Papers, three of which are on the mechanics of fluids and one on the mechanics of solids. These four volumes are his legacy to us, and will be a store-house of information and a source of illumination for many years to come.

Description: This paper deals with nonlinear streaming effects in an oscillating fluid in a curved pipe. The secondary steady velocity field in the cross-sectional plane of the pipe is studied in detail. Our experimental results are compared with the theory of Lyne (1970; that part of his theory which is valid for Reynolds numbers Rs ≪ 1) and the theory of Zalosh & Nelson (1973). On the basis of these comparisons we conclude that the theories are in practice valid for higher Reynolds numbers Rs than was formally expected. © 1975, Cambridge University Press. All rights reserved.

Description: The effect of a small surface-tension coefficient on the classical theory of free-streamline separation from a sharp trailing edge is studied. The classical solution fails in a small region surrounding the edge, where it predicts singular behaviour, and an inner solution, satisfying linear boundary conditions, is required to obtain a uniformly valid first approximation. The solution valid near the edge removes the curvature and pressure-gradient singularities of the classical solution and predicts a standing capillary wave along the free streamline. © 1975, Cambridge University Press. All rights reserved.

Description: A model is proposed which attempts to explain the complete ‘burst cycle’. This model views the wall streak as a sub-boundary layer, within the conventionally defined boundary layer, and the lift-up stage of bursting either as an upwelling motion of this sub-boundary layer which is similar to a local, convected separation or, equivalently, as the consequence of a vortex roll-up. ‘Sweeps’ are thought to represent the passage of a previous burst from further upstream. They appear either to impress on the wall streak the temporary adverse pressure gradient required to bring about its lifting or, alternatively, to provide the outer vortex which rolls up with the vortex associated with the wall streak. The model is also used to explain how the interactions between a burst and a sweep bring about (i) breakup, as well as (ii) new wall streaks further downstream. Arguments are presented to demonstrate that the three kinds of oscillatory growth reported by Kim, Kline & Reynolds (1971) may be associated with just one type of flow structure: the stretched and lifted vortex described by Kline et al. (1967). © 1975, Cambridge University Press. All rights reserved.

Description: Following the ideas suggested by Landahl (1967, 1975), some model calculations of the fluctuating velocity field in the wall region of a turbulent boundary layer have been carried out. It was assumed that the turbulent stresses are generated intermittently on small scales in time and space owing to bursting-type motions. The Reynolds-stress distribution during bursting periods and the mean velocity profile were assumed to be known, and the linear large-scale response to a random system of bursts was computed using an idealized model for the joint probability distribution in time and space of the occurrence of bursts. Computed energy spectra of the streamwise velocity fluctuations display scales in the spanwise and streamwise directions and time which are in good agreement with measurements by Morrison, Bullock & Kronauer (1971). However, the wavenumber band-widths of the computed spectra are narrower than those of the measured ones. This discrepancy is probably due to the crudeness of the model employed for the Reynolds stress during bursting. © 1975, Cambridge University Press. All rights reserved.

Description: This paper discusses critically observations of mixing processes across density interfaces in laboratory experiments and inferences that have been made and can be made from these observations. Fluxes of heat or salt and entrainment velocities have been found to depend on negative powers of an overall Richardson number Ri* based on the buoyancy jump across the interface, the depth of the homogeneous layer and the intensity of the turbulence near the source. When the Reynolds and Péclet numbers are large, the fluxes or entrainment velocities appear to be proportional to the minus one and minus three-halves powers of Ri* for flows with and without mean shear respectively, and this difference has caused speculation about the accuracy of the experimental data and about the reasons for the two laws if the difference is real. In the present discussion, we accept the accuracy of the two laws and attribute the higher entrainment rate for shear flows to the decrease of r.m.s. velocities near the interface with increasing Ri* in the case of zero shear. A plausible argument yields the unifying result that the entrainment rates in both cases are proportional to Ri−1, where Ri is a Richardson number based on the buoyancy jump and velocities and lengths characteristic of the turbulence near the interface. It is suggested that the [formula omitted] behaviour inferred by Turner is based on an erroneous interpretation of experimental data. In the course of the discussion, it is shown that the drag coefficient in flow of a stratified fluid over a rough surface is independent of the Richardson number (or density jump across the interface or inversion) and depends only on the ratio of the roughness length to the depth of the homogeneous layer. This has obvious implications for problems of parameterizing the momentum flux near the ground in the atmosphere. © 1975, Cambridge University Press. All rights reserved.

Description: The probability density function and the first three statistical moments of the velocity, acceleration and dynamic pressure are obtained for a Gaussian, stationary, homogeneous, random gravity-wave field in deep water, using infinitesimal wave solutions. It is shown that the velocity, acceleration and pressure are non-Gaussian. While the horizontal accelerations and vertical velocity component are of zero mean and unskewed, the dynamic pressure, vertical acceleration and horizontal velocity components are skewed and have non-zero mean. © 1975, Cambridge University Press. All rights reserved.

Description: New experiments with a gas-filled resonance tube have shown that not only heating, but also cooling of the tube wall is possible and that these phenomena are not restricted to oscillation amplitudes that generate shocks. The present paper concentrates on amplitudes outside the shock region. For this case, an extended acoustic theory is worked out. The results show cooling in the section of the tube with maximum velocity amplitude (and thus dissipation) and marked heating in the region of the velocity nodes. A strong dependence of these effects on the Prandtl number is noted. The results are in good agreement with experiments. Although the theory is not valid for proper resonance conditions, it nevertheless sheds some light on what happens when nonlinear effects dominate. Closely related to the limit of validity of the thermoacoustic theory is the question of transition from laminar to turbulent flow in the viscous boundary layer (Stokes layer). This problem has also been investigated; the results are given in a separate paper (Merkli & Thomann 1975). In the present article laminar flow is assumed. © 1975, Cambridge University Press. All rights reserved.

Description: The purpose of this paper is to consider the effect of one-dimensional random depth variation on the propagation of planetary waves in a homogeneous layer of fluid having a free upper surface. We begin by determining the dispersion relation for the coherent part of the wave using the vorticity equation for the transport stream function and a previously described perturbation method. Then, from the resulting first-order expressions for the wavenumber, we obtain the phase speeds for the two possible planetary-wave solutions. These are compared with the corresponding phase speeds of planetary waves over a smoothly varying topography; the validity limits of the approximations are discussed. For the most physically realizable situation, of random depth correlation lengths much shorter than a typical wavelength, we find that the phase speed of the shorter (longer) wave component is less (greater) over a randomly varying topography than over a smoothly varying topography. In the case of the shorter waves, greatest relative changes in phase speed occur when the associated fluid motions are at right angles to the ‘strike’ of the roughness elements, while for both long and short waves there is no relative change in phase speed if fluid motions are parallel to the roughness contours. Moreover, both types of waves are shown to lose energy in the direction of energy propagation as a result of scattering. Numerical values are then obtained using hydrographic charts of the western North Pacific, and show that the randomness may significantly decrease the phase speed of the shorter planetary-wave component. Finally, we give a brief descriptive explanation of the results based on the effect of the topography on the wave restoring mechanism. © 1975, Cambridge University Press. All rights reserved.

Description: Certain tertiary resonant interactions of gravity waves which have been found previously can be obtained more easily by using a simple extension of Whitham's formalism. The contribution of these interactions to the total energy transfer in an inhomogeneous random field of gravity waves is calculated. It is found to be small for open-ocean waves, but to be of some importance for shallow-water waves, where topography or mean shear currents may produce strong inhomogeneities. The nonlinear splitting of the group velocity is found to be unimportant in wave fields with sufficiently smooth spectra. © 1975, Cambridge University Press. All rights reserved.

Description: This paper is a theoretical investigation of the stable laminar decay of a fully established channel or pipe flow following a sudden blockage such as would be caused by the rapid closure of a valve or imposition of an end wall or gate. The development of the subsequent velocity and pressure fields is examined from the instant the initial pressure wave passes until the final decay of all motion. Three time scales of hydrodynamic interest are identified and the relevant solutions are obtained. The time scales are as follows: (i) a very short time characteristic of the passage of the pressure wave during which the velocity field adjusts inviscidly to the new boundary conditions imposed by the presence of the end wall, (ii) a short diffusion time during which the displacement interaction generated by the diffusion of the primary Rayleigh layer induces a substantial secondary motion with distinct side-wall boundary layers and an inviscid core and (iii) a long diffusion time during which the boundary layers fill the entire channel or pipe and the residual motion then dies out. The secondary flow for short diffusion times is of special interest in that it is an example of an unsteady boundary layer where the external pressure gradient and inviscid outer flow are unknown and determined by the integrated time history of the combined mass flow displacement generated by the primary- and secondary-flow boundary layers. The paper closes with some preliminary comments and experimental observations on decelerating pipe flows. © 1975, Cambridge University Press. All rights reserved.

Description: A low frequency asymptotic theory is proposed for the shielding of noise by jets of arbitrary cross-section. The results of the theory provide a qualitative explanation for the appearance of the quiet and noisy planes of a slot jet. The arguments in favour of this explanation are derived from a model problem in which a pulsating mass source is convecting along the axis of an infinitely long column of fluid of arbitrary cross-section. The jet velocity is represented by a uniform velocity profile (i.e. slug flow). The method of matched asymptotic expansions is applied to derive expressions for the acoustic pressure and the radiative power of the source. The solution for the elliptic jet indicates that the radiative power in the horizontal plane (containing the major axis) is less than that in the vertical plane (containing the minor axis). This difference in power varies with source Strouhal number and jet MacH number. The effects of jet temperature are also included in the analysis. The theoretical results are in good qualitative agreement with experimental findings for slot nozzles. The theory indicates that the noise shielding offered by jets is negligible at low frequencies and low MacH numbers. © 1975, Cambridge University Press. All rights reserved.

Description: The stability of flow of a viscous incompressible fluid contained between a stationary outer sphere and rotating inner sphere is studied theoretically and experimentally. Previous theoretical results concerning the basic laminar flow (part 1) are compared with experimental results. Small and large Reynolds number results are compared with Stokes-flow and boundary-layer solutions. The effect of the radius ratio of the two spheres is demonstrated. A linearized theory of stability for the laminar flow is formulated in terms of toroidal and poloidal potentials; the differential equations governing these potentials are integrated numerically. It is found that the flow is subcritically unstable and that the observed instability occurs at a Reynolds number close to the critical value of the energy stability theory. Observations of other flow transitions, at higher values of the Reynolds number, are also described. The character of the stability of the spherical annulus flow is found to be strongly dependent on the radius ratio. © 1975, Cambridge University Press. All rights reserved.

Description: In this paper we compute the motion and the shape of the free surface on a liquid in a trench heated from its side. The analysis is based on Joseph's Lagrangian theory of domain perturbations, which is developed in general and through simple examples, chosen so as to make the comparison of the Lagrangian method with Stokes's Eulerian theory very clear. The perturbation problems are resolved analytically by application of biorthogonality conditions to a powerful set of biharmonic eigenfunctions. © 1975, Cambridge University Press. All rights reserved.

Description: A viscous incompressible stably stratified fluid with a buoyancy frequency which varies slowly with altitude is considered. A simple harmonic localized disturbance generates an internal wave in which the energy propagates along curved paths. Small amplitude similarity solutions are obtained for two-dimensional and axisymmetric waves. It is found that under certain conditions the wave amplitude can increase with height. The two-dimensional theory compares quite well with experimental measurements. © 1975, Cambridge University Press. All rights reserved.

Description: A model for collective movement and pattern formation in layered suspensions of negatively geotactic micro-organisms is presented. The motility of the organism is described by an average upward swimming speed U and a diffusivity tensor D. It is shown that the equilibrium suspension is unstable to infinitesimal perturbations when either the layer depth or the mean concentration of the organisms exceeds a critical value. For deep layers the maximum growth rate determines a preferred pattern size explicitly in terms of U and D. The results are compared with observations of patterns formed by the ciliated protozoan Tetrahymena pyriformis. © 1975, Cambridge University Press. All rights reserved.

Description: It is known that head seas cannot travel without deformation along a horizontal cylinder of full constant cross-section. Calculations are given which indicate that the waves are refracted away from the axis of the cylinder. Similar refraction effects are found for waves generated by a pulsating source on the cylinder, and also for the Kelvin wave pattern generated by a long ship of nearly constant cross-sectiop moving with constant speed in the axial direction. © 1975, Cambridge University Press. All rights reserved.

Description: Euromech 52, on drag reduction in turbulent flows due to additives, was held from 27-30 August 1974in Stockholm, Sweden, under the chairmanship of M. T. Landahl, and was intended to bring together specialists in the various aspects of the drag-reduction phenomenon to discuss current experimental and theoretical work, and to identify promising directions for future research. There were forty-seven participants from eleven countries and twenty-two papers were presented, with ample time for discussion. These papers, which are briefly summarized in this report, could be grouped roughly under the headings of §§ 2-6 below. © 1975, Cambridge University Press. All rights reserved.

Description: The velocity correlation function of a Brownian particle in a viscous compressible fluid is studied in the limit of very small compressibility. The main effect of compressibility is an initial rapid change of the particle mass from a real inertial mass to a virtual mass. © 1975, Cambridge University Press. All rights reserved.

Description: The motion of a slender axisymmetric rod-like particle is investigated theoretically for translation through a quiescent second-order fluid and for rotation in a simple shear flow of the same material. The analysis consists of an asymptotic expansion about the limit of rheologically slow flow, coupled with an application of a generalized form of the reciprocal theorem of Lorentz to calculate the force and torque on the particle. It is shown that an arbitrarily oriented particle with fore-aft symmetry translates, to a first approximation, at the same rate as in an equivalent Newtonian fluid, but that the motion of particles with no fore-aft symmetry may be modified at the same level of approximation. In addition, it is found that freely translating particles with fore-aft symmetry exhibit a single stable orientation with the axis of revolution vertical. In simple shear flow at small and moderate shear rates, the non-Newtonian nature of the suspending fluid causes a drift through Jeffery orbits to the equilibrium orbit C = 0 in which the particle rotates about its axis of revolution. At larger shear rates, the particle aligns itself in the direction of flow and ceases to rotate. Comparison with the available experimental data indicates that the measured rate of orbit drift may be used to determine the second normal stress difference parameter of the second-order fluid model. Finally, in an appendix, some preliminary observations are reported of the motion of slender rod-like particles falling through a quiescent viscoelastic fluid. © 1975, Cambridge University Press. All rights reserved.

Description: It is argued on the basis of exact solutions for uniform vortices in straining fields that vortices of finite cross-section in a row will disintegrate if the spacing is too small. The results are applied to the organized vortex structures observed in turbulent mixing layers. An explanation is provided for the disappearance of these structures as they move downstream and it is deduced that the ratio of average spacing to width should be about 3·5, the width being defined by the maximum slope of the mean velocity. It is shown in an appendix that walls have negligible effect. © 1975, Cambridge University Press. All rights reserved.

Description: The linear stability of a slowly varying flow, the flow in a diverging straight-walled channel, is studied using a modification of the ‘WKB’ or ‘ray’ method. It is shown that ‘quasi-parallel’ theory, the usual method for handling such flows, gives the formally correct lowest-order growth rate; however, this growth rate can be substantially in error if its magnitude is comparable to that of the rate of change of the basic state. The method used clearly demonstrates the dependence of the growth rate, wavenumber, neutral curves, etc., on the cross-stream variable and on the flow quantity under consideration. When applied to the divergent channel, the method yields a much wider ‘unstable’ region and a much lower ‘critical’ Reynolds number (depending on the flow quantity used) than those predicted by quasi-parallel theory. The determination of the downstream development of waves of constant frequency shows that waves of all frequencies eventually decay. © 1975, Cambridge University Press. All rights reserved.

Description: The stability of a compressible non-dissipative swirling flow to adiabatic infinitesimal disturbances of arbitrary orientation is considered. The resulting sufficient condition for stability is the general form of the effective Richardson criterion for swirling flows, first obtained, for axisymmetric modes only, by Howard. In addition, upper bounds to the growth rate of unstable modes are obtained and some extensions of the semicircle theorem to azimuthal disturbances are stated. © 1975, Cambridge University Press. All rights reserved.

Description: The method of characteristics is used to calculate the supersonic flow past a wedge of small angle with non-equilibrium effects. The wave decay and development distances are presented in a concise similarity form which permits accurate extrapolation to very weak waves. The numerical solutions are compared with shock-tube flows of CO2 and N2O. © 1975, Cambridge University Press. All rights reserved.

Description: This paper describes the development of a new technique for removing surface-active contaminants from water so that it may be used for surface-clean experiments in fluid mechanics. The removal of contamination from concentrated aqueous solutions of non-surface-active materials is also possible, allowing considerable variation of density and viscosity in these experiments. Instead of using the conventional distillation processes necessary for most work involving surface chemical phenomena, surface-active substances are removed by adsorption onto a dense current of small nitrogen gas bubbles rising in a long vertical column of the water. The efficiency of the technique was found to increase to a great extent when common salt was dissolved in the water, up to concentrations around 40 g/l, and experiments are described which allow the identification of several physical processes which aid the operation of the method. The adequate performance of the cleaning technique in the removal both of an ionic surface-active material and also of Gentian Violet dye is demonstrated. The method should permit the design of surface-clean experiments using much larger volumes of water than are possible when the water has to be distilled using conventional surface chemical techniques. A simple apparatus for the measurement of surface tension is also described. © 1975, Cambridge University Press. All rights reserved.

Description: Steady liquid flow in a variable-area rectangular duct rotating rapidly about an axis perpendicular to its centre-line is treated. This problem is significant because the idea of driving a liquid through a rotating system has been largely overlooked by rotating-fluid dynamicists and because it closely resembles the flow inside the impellers of centrifugal pumps and hydraulic turbines. For a prototype formed by joining a semi-infinite constant-area duct and a semi-infinite duct with straight diverging walls, the flow in the diverging duct is carried entirely by large, O(E1/3) velocities in a boundary layer of thickness O(E1/3) adjacent to one of the (side) walls parallel to the axis of rotation, where E is the (small) Ekman number. With a vertical axis of rotation this high-velocity boundary layer is adjacent to the side wall on the right when facing in the flow direction. For a diverging or converging duct placed between two semi-infinite constant-area ducts, large, O(E1/3) velocities occur in side-wall boundary layers on both sides of the variable-area duct and on the left and right sides of the upstream and downstream constant-area ducts respectively. The existence of high-velocity side layers in rapidly rotating rectangular ducts should be relatively easy to prove experimentally and actual measurements of their velocity profiles would provide a good test of the present theory. © 1975, Cambridge University Press. All rights reserved.

Description: Computations of the steady viscous flow past a fixed spherical gas bubble are reported for Reynolds numbers in the range 0·1 ≤ R ≤ 200. Good agreement with Moore's (1963) asymptotic theory for the drag coefficient is obtained for R ≤ 40 and with the well-known small-R theory for R ≤ ½. The method of series truncation is used to reduce the problem to a nonlinear two-point boundary-value problem, which is then solved by an accurate and efficient finite-difference procedure. © 1975, Cambridge University Press. All rights reserved.

Description: The method of characteristics is used to calculate the flow ahead of an impulsively started piston moving at constant velocity. Particular attention is paid to the development of weak shock waves which are either fully or partly dispersed at very large distances from the piston. It is found that the global features of the flows may be represented in similarity form, and the graphs obtained allow extrapolation to very weak waves. © 1975, Cambridge University Press. All rights reserved.

Description: In this paper we apply the techniques of higher-order boundary-layer theory to study the steady streaming induced in the neighbourhood of a cylinder which vibrates harmonically, perpendicular to its generators, in an unbounded fluid. The theoretical predictions are compared with the results of experiments performed at high streaming Reynolds numbers. Improved agreement between theory and experiment is achieved although unresolved discrepancies remain. © 1975, Cambridge University Press. All rights reserved.

Description: At high jet velocity the aerodynamic interaction between a capillary jet and the surrounding medium leads to an enhanced growth rate of axisymmetric disturbances. The available theories which account for this effect fail to agree with experimental observations. The difference is attributed, in part, to the relaxation of the velocity profile in jets formed by fully developed laminar pipe flow. The profile relaxation has a destabilizing effect just as does the aerodynamic interaction. In the absence of velocity-profile relaxation it is shown that the available theories overestimate the aerodynamic effect. A consideration of the viscosity of the ambient fluid yields a semi-empirical modification to the theory which shows good agreement with experimental values. © 1975, Cambridge University Press. All rights reserved.

Description: Electrically and thermally conducting inviscid fluid rotating about a vertical axis is confined between two horizontal plates maintained a t different temperatures, the upper plate being the cooler. The fluid is permeated by a horizontal magnetic field that corotates with the fluid. In an earlier paper (Roberts & Stewartson 1974) the fluid is supposed to be in a state of near-marginal instability to convective overturning and the nonlinear evolution of single rolls is discussed. Inertial terms are neglected. However, if q 〈 2 and λ 〈 2/3½, where q and λ may be defined by equation (2.3) below, the principle of the exchange of stabilities holds and there is also a degeneracy in the linear stability problem. There are now two distinct unstable rolls equally possible and their nonlinear interaction leads to a violation of the governing equations. This difficulty has already been noted by Taylor (1963) and it is resolved in this paper by adding a geostrophic motion (the Taylor shear) parallel to the magnetic field and by restoring the inertial terms in the governing equations. We consider particularly instabilities in which one roll predominates and find that, if λ is sufficiently small, each of the rolls that can occur is stable with respect to the other, i.e. an initially weak roll of the other type dies out relative to it. This means that we can expect the fluid motion to consist of single rolls at large times. On the other hand when λ is near 2/3½ both rolls are unstable with respect to the other. The Taylor shear does not then die out and the two rolls become comparable in magnitude and modify each other's structure. At intermediate values of λ one of the rolls is stable in this way and the other unstable. The study is motivated by a desire to understand better the dynamical means by which a large mass of conducting fluid can create its own magnetism. It is argued that these instabilities suggest the existence of a mechanism of self-adjustment preventing λ from either increasing or decreasing indefinitely and noted that, very roughly, λ is of order unity in the earth's core. © 1975, Cambridge University Press. All rights reserved.

Description: Systematic measurements of drift currents below and of airflows above an air-water interface have been made under various wind conditions. The current near but not immediately below the water surface is found to follow a Kármán-Prandtl (logarithmic) velocity distribution. The current immediately below the water surface varies linearly with depth. The transitions of the current boundary layer to various regimes appear to lag behind, or to occur a t a higher wind velocity than, those of the airflow. The fraction of the wind stress supported by the wave drag seems to vary with the wind and wave conditions: a large fraction is obtained at low wind velocities with shorter waves and a small fraction is obtained a t high wind velocities with longer waves. At the air-water interface, the wind-induced current is found to be proportional to the friction velocity of the wind. The Stokes mass transport, related to wave characteristics, is only a small component of the surface drift in laboratory tanks. However, in terms of the fraction of the wind velocity, the mass transport increases, while the wind drift decreases, as the fetch increases. The ratio between the total surface drift and the wind velocity decreases gradually as the fetch increases and approaches a constant value of about 3·5% at very long fetches. © 1975, Cambridge University Press. All rights reserved.

Description: The rate of entrainment of ambient fluid across a turbulent interface has been defined as the mean rate of increase of turbulent fluid in the flow direction. Experiments to measure this quantity by conditional sampling in a two-dimen- sional wall jet are described. Further, estimates of this entrainment rate were made for the turbulent boundary layer, two-dimensional wake, two-dimensional jet and round jet and the results are discussed. © 1975, Cambridge University Press. All rights reserved.

Description: Gans' criterion is shown to be valid for all inviscid non-diffusive flows where the radial velocity is everywhere zero and the physical variables are functions of the radial distance only. That is, a modified form of the Miles-Howard theorem holds for a large class of helical gas flows. © 1975, Cambridge University Press. All rights reserved.

Description: A potential flow model of two-dimensional vortex shedding behind an inclined plate is developed. The free shear layers which emanate from the sides of the plate are represented by discrete vortices through the use of the appropriate complex-velocity potential, the Kutta condition and the Joukowsky transformation between a circle and the plate cross-section. The analysis is then applied to predict the kinematic and dynamic characteristics of the flow for various angles of attack. The results compare favourably with the available experimental data as far as the form of vortex shedding and the Strouhal number are concerned. The calculated normal-force coefficients are 20−25% yo larger than those measured by Fage & Johansen (1927). © 1975, Cambridge University Press. All rights reserved.

Description: The internal-wave system is calculated for a body oscillating transversely, and translating uniformly, through an infinite stratified fluid of constant Brunt-Väisälä frequency. A linearized, time-dependent analysis is used, in which the vertical displacement of a fluid element is the basic dependent variable. Axisym-metric slender-body theory for a homogeneous fluid is used to determine the time-dependent source and dipole distributions required to represent the motion of the body for excitation of the internal waves. The equations are solved by Fourier-transform techniques; and the internal-wave amplitude is evaluated in the far field by the method of stationary phase. The surfaces of constant phase are found to change character as the ratio of the oscillation frequency ω of the body to the Brunt-Väisälä frequency N varies through unity. Along preferred directions, the amplitude of the internal waves is found to decay inversely with distance to the [formula omitted] power, whereas, for uniform translation, the amplitude of the internal waves falls off inversely with distance from the body. An asymptotic expression for the amplitude in preferred directions is calculated for several values of the ratio ω/N. © 1975, Cambridge University Press. All rights reserved.

Description: This paper presents a summary of the results of an extensive experimental investigation of the problem considered by Tatsumi (1952a, b) and more recently by Huang & Chen (1974a, b). The results, like the analyses, show that the linear instability is confined to the non-similar inlet region of the pipe. © 1975, Cambridge University Press. All rights reserved.

Description: The Laplace–Young equation is solved for axisymmetric menisci, analytically in terms of elliptic integrals for all possible types of pendular rings and liquid bridges when the effect of gravity is negligible, numerically for selected other cases in order to assess gravity's effect. Meniscus shapes, mean curvatures, areas and enclosed volumes are reported, as are capillary forces. It is shown that capillary attraction may become capillary repulsion when wetting is imperfect. The special configurations of vanishing capillary force and of zero mean curvature are treated. The range of utility of the convenient ‘circle approximation’ is evaluated. © 1975, Cambridge University Press. All rights reserved.

Description: The incompressible laminar flow in the neighbourhood of the trailing edge of an aerofoil undergoing sinusoidal oscillations of high frequency and low amplitude in a uniform stream is described in the limit as the Reynolds number R tends to infinity. The aerofoil is replaced by a flat plate on the assumption that leadingedge stall does not take place. It is shown that, for oscillations of non-dimensional frequency [formula omitted] and amplitude [formula omitted], a rational description of the flow at the trailing edge is based on a subdivision of the boundary layer above the plate into five distinct regions. Asymptotic analytic solutions are found in four of these, whilst in the fifth a linearized solution yields an estimate for the viscous correction to the circulation determined by the Kutta condition. © 1975, Cambridge University Press. All rights reserved.

Description: The similarity equations for rotationally symmetric flow above an infinite counter–rotating disk are investigated both numerically and analytically. Numerical solutions are found when α, the ratio of the disk's angular speed to that of the rigidly rotating fluid far from it, is greater than −0.68795. It is deduced that there exists a critical value αcr, of α above which finite solutions are possible. The value of α and the limiting structure as α → αcr are found using the method of matched asymptotic expansions. The flow structure is found to consist of a thin viscous wall region above which lies a thick inviscid layer and yet another viscous transition layer. Furthermore, this structure is not unique: there can be any number of thick inviscid layers, each separated from the next by a viscous transition layer, before the outer boundary conditions on the solution are satisfied. However, comparison with the numerical solutions indicates that a single inviscid layer is preferred. © 1975, Cambridge University Press. All rights reserved.

Description: A sharp wedge expansion flap was tested in the von Kámán Institute Long-shot tunnel at Mach 16 and data on the wall pressure and heat transfer were obtained. Pitot pressure measurements in the boundary layer just ahead of the expansion flap were also made. The surface data are compared with predictions from a characteristics solution for the boundary-layer expansion and from a simple heat-transfer theory. © 1975, Cambridge University Press. All rights reserved.

Description: A few statistical properties of fine-scale velocity and temperature fluctuations have been measured on the axis of symmetry of a heated turbulent round jet. The probability density of ∂θ/∂x, the streamwise derivative of the temperature fluctuation, is strongly negatively skewed, indicating a lack of isotropy for the fine-scale temperature structure. An estimate of the correlation between the velocity and temperature dissipation fields has been obtained by assuming that the dissipation of velocity and dissipation of temperature can be approximated by (∂θ/∂x)2, where u is the streamwise velocity fluctuation, and (∂θ/∂x)2r respectively. The correlation between the quantities (∂θ/∂x)2r and (∂θ/∂x)2r averages over a volume of linear dimension r, is fairly high and depends on the choice of r. An analysis shows that this correlation plays a vital role in the prediction of high-order structure functions of u and θ. The assumed lognormality of the probability density of (∂θ/∂x)2r and (∂θ/∂x)2r and of their joint density is found to be reasonable over a range of r corresponding to the inertial subrange. © 1975, Cambridge University Press. All rights reserved.

Description: Observations made in a well-developed, thermally stratified, horizontal, flat- plate boundary layer are used to study the effects of buoyancy on the mean flow and turbulence structure. These are represented in a similarity framework obtained from the concept of local equilibrium in a fully developed turbulent flow. Mean velocity and temperature profiles in both the inner and outer layers are strongly dependent on the thermal stratification, the former suggesting an increase in the thickness of the viscous sublayer with increasing stability. The coefficients of skin friction and heat transfer, on the other hand, decrease with increasing stability. Normalized turbulent intensities, fluxes and their correlation coefficients also vary with buoyancy. In stable conditions, turbulence becomes rapidly suppressed with increasing stability as more and more energy has to be expended in over- coming buoyancy forces. The buoyancy effects are found to be more dominant in the stress budget than in the turbulent energy budget. The horizontal heat flux is much greater than the vertical heat flux and their ratio increases with stability. The ratio of the eddy diffusivities of heat and momentum, on the other hand, decreases with increasing stability. The spectra of velocity and temperature fluctuations indicate no buoyancy subrange, but the wavenumber corresponding to peak energy is found to increase with increasing stability. © 1975, Cambridge University Press. All rights reserved.

Description: Detailed experimental data are presented on the transition between regular and Mach reflexion. Data have been obtained for steady, pseudo-steady and un-steady flows, and include a study of the continuous and discontinuous transitions predicted by previous researchers. It is found that the criterion often used to calculate the transition condition is wrong in every case that we have investigated. In its place we propose an alternative criterion which has the property that the system remains always in mechanical equilibrium during transition. © 1975, Cambridge University Press. All rights reserved.

Description: Free convection has been studied in gaseous helium at low temperatures in a cylindrical vessel of aspect ratio (diameterlheight) 2·5. Compared with measurements in fluids at room temperature the present arrangement has the advantages of small size, a short time constant and improved accuracy. As the Rayleigh number was varied from 60 to 2 × 109, the Nusselt number rose from 1 to 69, obeying the relation Nu = 0·173Ra0·2800±0·0005 over the upper four decades of Ra. The critical Rayleigh number was 1630, but the conditions of the experiment did not allow reliable measurements at such low values of Ra. The very high sensitivity within a given experiment showed the presence of several ‘discrete transitions’, which were often step like and not merely a change of gradient as reported by other workers. The largest of these, at Ra = 3 · 105, involved a drop in heat flux of some 6% and was somewhat hysteretic. The temperature fluctuations increased markedly as the step was crossed. © 1975, Cambridge University Press. All rights reserved.

Description: Stability characteristics of a single-phase free convection loop are presented. In the experiments, water was placed inside a toroidal glass loop oriented in a vertical plane. The lower half of the loop was heated and the upper half was cooled. At low heat-transfer rates and also a t high heat-transfer rates the free convection flow was observed to be steady. For the intermediate range, however, the flow was found to be highly oscillatory. Stability predictions are also developed. The comparison between theory and experiment yields favourable agreement. Observations of unstable behaviour have been reported previously for single-phase fluids in the vicinity of the thermodynamic critical point. In these situations it has been assumed that the unusual behaviour of the fluid properties in the near-critical region necessarily constitutes the underlying cause of such instabilities. In contrast t o this view, analyses by Keller (1966) and Welander (1967) indicate that instabilities can occur for ordinary fluids as well. Results of the present study confirm this contention, since instabilities were clearly observed for water at atmospheric pressure and moderate temperatures. © 1975, Cambridge University Press. All rights reserved.

Description: In this paper we consider the flow field generated by a uniform electrostatic field in and about a pair of identical liquid drops immersed in a conducting fluid. It is assumed that the undisturbed electric field is parallel to the line joining the centres of the two drops. The flow field is due to the tangential electric stress over the surfaces of the drops and here this stress and the flow field are expressed in terms of bispherical harmonics. When the distance between the centres of the drops is many drop diameters the tangential electric stress and the flow field in and about one drop are unaffected by the presence of the other drop, as expected. When the distance between the centres of the drops is of the order of two drop diameters there is a substantial modification in the tangential electric stress at the surfaces of the drops and in the induced flow field, especially in the region between the planes through the drop centres perpendicular to the undisturbed electric field. © 1975, Cambridge University Press. All rights reserved.

Description: It was suggested by Lau, Fisher & Puchs (1972) that the basic structure of a ‘turbulent’ round jet might consist, essentially, of an axial array of fairly evenly spaced vortices moving downstream in the mixing region of the jet. The present experimental study is an attempt to establish this hypothesis on a sound footing. The problem which was posed was first to find proof of the existence of a fairly regular pattern in the mixing region, and second to extract detailed information on the component parts of this pattern to identify the nature of the structure. Hot-wire signals in the mixing layer are known to possess a predominance of spikes. In the region closer to the high velocity side of the layer, these spikes tend to be downward ones whilst in the opposite region, they are upward. These spikes have been attributed to the entrainment mechanism in the mixing layer and had been thought to be random. A closer study of time-history curves of these hotwire signals suggests that they might not be as random as would appear at first glance. A probability analysis was conducted of the time intervals between the successive downward spikes in the u′ signals, and it was found that indeed the highest probability occurred when the time interval corresponded to a frequency equal to the vortex passing frequency. A time-domain averaging (or eduction) technique was used to try to identify the nature of the flow structure using the spikes to trigger the eduction process. On the basis of these results it would seem that the suggestion of a vortex street is well founded. Furthermore, it appears that, as the individual vortices in the street move downstream, they are continuously transporting fluid masses across the mixing layer, and it is this effect which is producing the Reynolds stresses in the mixing layer, and causing the spikes in the u’ signals in this region. © 1975, Cambridge University Press. All rights reserved.

Description: Measurements have been made concerning the fine structure of the turbulence in the part adjacent to the wall of the wall region of a plane turbulent boundary layer. The objective was to gain further information concerning the larger-scale disturbance mechanism which is mainly responsible for the generation of turbulence. Hot-wire anemomet.ry was used and information on the fine structure was obtained by differentiating and filtering the hot-wire signal.The distributions of the Kolmogorov microscale and of the flatness and skewness factors of the axial fluctuating velocity u and its first and second derivative determined at two Reynolds numbers suggest the existence of Reynolds number similarity. In the region y+ 〈 15 the flatness and skewness factors of u increase with decreasing y+. At approximately y+ = 15 the flatness factor shows a minimum value, while the skewness factor becomes zero. This location agrees with that where the turbulence intensity u′ has a maximum value. In the outer part of the wall region (y+ 〉 100) the flatness and skewness factors approach values obtained in shear-free turbulence at the same turbulence Reynolds number.The fine structure of the turbulence is strongly associated with and dominated by the random, larger-scale, intermittent inrush-ejection cycle. In the viscous sublayer both the fine structure, and the large-scale mechanism of the turbulence are influenced mainly by the inrush phase, while further out in the wall region (y+ 〉 40) they are influenced by both inrush and ejection. As a result, in the viscous sublayer the average burst periods of the high frequency turbulence components and their flatness factors (of ∂u/∂t and of ∂2u/∂t2) attain values twice those in the outer part.The change in the mechanism of the fine structure with distance from the wall is clearly demonstrated by the spectra of non-negative variables, i.e. (∂u/∂t)2 and (∂2u/∂t2)2. The spectra agree with each other and decrease with increasing frequency, following a power law as predicted by Gurvich & Yaglom (1967). The power law applies to almost the whole frequency range, when the highest, viscous, frequency range is excluded. However, the exponent is different for the viscous sublayer and the outer part of the wall region. In the buffer layer the spectra have two distinct power-law regions. In the lower frequency range the exponent is the same as that for the viscous sublayer, while in the higher frequency range it is the same as that for the outer part of the wall region.

Description: A simple approximation is proposed for the problem of the dispersion of marked particles in an incompressible fluid in random motion when the probability distribution of the velocity field is taken as Gaussian, homogeneous, isotropic, stationary and of zero mean. Approximations for the Lagrangian velocity correlation function and the dispersion are given and compared with exact computer calculations of Kraichnan. Agreement is found to be good except for time-independent velocity fields and singular wavenumber spectral functions. © 1975, Cambridge University Press. All rights reserved.

Description: The equilibrium statistical mechanics of inviscid two-dimensional flow are re-examined both for a continuum truncated at a top wavenumber and for a system of discrete vortices. In both cases, there are negative-temperature equilibria for finite flows. But for spatially infinite flows, there are only positive-temperature equilibria, and both the continuum and discrete system exhibit proper, extensive, thermodynamic limits a t all realizable values of the energy and enstrophy density. The negative-temperature behaviours of the continuum and discrete system are semi-quantitatively the same, except for a supercondensation phenomenon in the discrete case a t the smallest realizable values of negative temperature. The supercondensed states have very large energy and in them all vortex cores of the same sign are clumped within an area small eompared with the mean area per vortex. The approach of the continuum system to absolute equilibrium by enstrophy cascade to high wavenumbers and energy cascade to low wavenumbers is examined. It is argued that the enstrophy cascade is closely analogous to distortion of a passive scalar field by straining of large spatial scale. This implies that high intermittency of spatial derivatives of the vorticity field can develop but that there is no associated change in the previously proposed log-corrected k−1 enstrophy spectrum law. On the other hand, intermittency build-up in the downward energy cascade can result in a change of the exponent in the energy spectrum law to a negative value of smaller magnitude than 5/3. Intermittency effects in the non-equilibrium energy cascade seem a more plausible explanation for vortex clumping observed in recent computer experiments than do the spatially smooth condensation phenomena associated with the negative-temperature absolute equilibria. © 1975, Cambridge University Press. All rights reserved.

Description: First, the linear stability of the flow between two concentric cylinders when the outer one is a t rest and the inner has angular velocity Ω{1+ ɛcosωt} is considered. In the limit in which ɛ and ω tend to zero it is found that the critical Taylor number a t which instability first occurs is decreased by an amount of order ɛ2 from its unmodulated value, the stabilizing effect a t order ɛ2ω2 being slight. The limit in which ω tends to infinity with ɛ arbitrary is then studied. In this case it is found that the critical Taylor number is decreased by an amount of order ɛ2ω−3 from its unmodulated value. Second, the effect of taking nonlinear terms into account is investigated. It is found that equilibrium perturbations of small but finite amplitude can exist under slightly supercritical conditions in both the high and low frequency limits. Some comparisons with experimental results are made, but these indicate that further theoretical work is needed for a broad band of values of ω. In appendix B it is shown how this can be done by an alternative formulation of the problem. © 1975, Cambridge University Press. All rights reserved.

Description: An attempt is made to explain theoretically two curious phenomena involving the motion of the liquid in a spinning, gyrating, liquid-filled gyroscope. One of the phenomena is the periodic breakdown of the free-surface wave form of the spinning liquid in the gyroscope when it gyrates at angles larger than about 1°. The other is the resonant amplitude growth rate of the liquid-filled gyroscope at these angles, for then the small angle stability theory of Stewartson (1959) fails to make the correct predictions. The analysis exploits the experimental fact that the axis of rotation of liquid in the rotor of a spinning gyrating gyroscope does not remain coincident with the axis of rotation of the rotor when the gyroscope gyrates at amplitudes greater than the above-mentioned 1°. It is shown that this lack of coincidence generates Rossby waves and modifies the inertial wave frequencies that would ordinarily occur in a right circular cylinder. There is no nonlinear interaction between these Rossby and inertial waves; hence the free-surface breakdown remains unexplained. However, the modification of the inertial wave frequencies does seem to account for the curious amplitude growth rate. © 1975, Cambridge University Press. All rights reserved.

Description: The properties of edge waves confined by the interaction of buoyancy and Coriolis forces to the vicinity of a rigid plane boundary in a rotating, stratified, electrically conducting fluid pervaded by a magnetic field are established in some simple cases. The background shear is taken to be zero, the basic Alfvén velocity V and Brunt–Väisälä frequency N are assumed uniform, and all dissipative effects are taken to be vanishingly small. It is shown that waves trapped against the bounding wall can occur only if V is parallel to the wall. When the basic rotation vector Ω is also parallel to the wall, the hydromagnetic edge waves have a higher frequency and smaller spatial extent perpendicular to the wall than their non-hydromagnetic counterparts, but more complex behaviour is found when Ω possesses a component normal to the wall. There are conditions under which edge waves may exist even when the basic density stratification is top-heavy (i.e. when N2 〈 0). © 1975, Cambridge University Press. All rights reserved.

Description: A similarity solution is obtained for a model of the turbulent starting plume comprising a steady plume feeding mass, momentum and buoyancy into a vortex ring. Bulk equations representing the time rate of increase of ring momentum and ring buoyancy, together with equations (dependent on broad features of the ring structure) representing the velocity of propagation and time rate of circulation increase are used to determine the motion of the vortex ring. The similarity solution is found to exist only for diffuse distributions of vorticity and buoyancy within the ring. Further, the ratio of ring velocity to plume velocity, which is assumed to be constant, is found to take a value which agrees with that obtained from experimental observations. © 1975, Cambridge University Press. All rights reserved.

Description: Stability experiments were made on plane Poiseuille flow generated in a long channel of a rectangular cross-section with a width-to-depth ratio of 27·4. By reducing the background turbulence down to a level of 0·05 %, we succeeded in maintaining the flow laminar at Reynolds numbers up to 8000, which is much larger than the critical Reynolds number of the linear theory, about 6000. The downstream development of the sinusoidal disturbance introduced by the vibrating ribbon technique was studied in detail at various frequencies in the range of Reynolds number from 3000 to 7500. This paper presents the experimental results and clarifies the linear stability, the nonlinear subcritical instability and the breakdown leading to the transition. © 1975, Cambridge University Press. All rights reserved.

Description: The properties of reflexion, refraction and absorption of a gravity wave incident upon a shear layer are investigated. It is shown that one must expect these properties to be very different depending upon the parameters (such as the Richardson number Ri, the wavelength normalized by the length scale of the shear and the ratio of the flow speed to the phase speed of the wave) characterizing the interaction of a gravity wave with a shear layer. In particular, it is shown that for all Richardson numbers there is a discontinuity in the net wave-action flux across the critical level, i.e. at a height where the flow speed matches the horizontal phase speed of the wave. When Ri 〉 ¼, this is accompanied by absorption of part of the energy of the incident wave into the mean flow. In addition it is shown that the phenomenon of wave amplification (over-reflexion) can arise provided that the ultimate shear flow speed exceeds the horizontal phase speed of the wave and Ri is less than a certain critical value Ric ≃ 0·1129, in which case the reflected wave extracts energy from the streaming motion. It is also pointed out that wave amplification can lead to instability if the boundary conditions are altered in such a way that the system can behave like an ‘amplifier’. © 1975, Cambridge University Press. All rights reserved.

Description: We examine two-dimensional motion of a stably stratified fluid containing two solutes with different molecular diffusivities in an inclined slot. The two solutes have continuous opposing gradients with the slower-diffusing one more dense at the bottom. It is found that, in the steady state, there exists a slow upward flow along the slope driven by the slight buoyancy difference near the wall, not unlike the solution found by Phillips (1970) for a single solute. The magnitude of the flow is less than that in Phillips’ solution by a factor of approximately (1-λ)/(1-λτ), where λ is the ratio of the density gradient and τ−1 is the ratio of the diffusivity of the faster-diffusing solute to that of the slower-diffusing one. For the time-dependent flow resulting from switching on the diffusivities at t = 0, there may be a dramatic reversal of the flow near the walls depending on the relative magnitude of λ and τ. If λ is somewhat greater than τ, the initial flow is downward, along the slope, reaching a maximum magnitude about one order of magnitude greater than the steady-state value. Then the ‘reverse’ flow gradually diminishes and approaches the steady state rather slowly. For λ ≳ τ, the approach to the steady state is monotonic; there is no ‘reverse’ flow near the wall. The existence of the downward flow, which was observed by Turner & Chen (1974), may lead to double-diffusive instabilities which eventually result in horizontal convecting layers. © 1975, Cambridge University Press. All rights reserved.

Description: The electron-beam fluorescence technique has been employed in measuring simultaneous density and temperature fluctuations in a hypersonic (M ≃ 16), adiabatic wall boundary layer. The paper discusses this technique, as it is applied to the conditions of relatively high density associated with turbulent flows. It presents general considerations concerning the attainable frequency response and spatial resolution of the technique. It describes results from initial measurements in a boundary layer on a wind-tunnel wall. These results show that the r.m.s. of the density, temperature and pressure fluctuations are large, much larger than observed in supersonic boundary layers. © 1975, Cambridge University Press. All rights reserved.

Description: The flow around a cylinder and a sphere rotating freely in a simple shear was studied experimentally for moderate values of the shear Reynolds number Re. For a freely rotating cylinder, the data were found to be consistent with the results obtained numerically by Kossack & Acrivos (1974), at least for Reynolds numbers up to about 10. Rates of rotation of a freely suspended sphere were also obtained over the same range of Reynolds numbers and showed that, with increasing Re, the dimensionless angular velocity does not decrease as fast for a sphere as it does for a cylinder. In both cases, photographs of the streamline patterns around the objects were consistent with this behaviour. Furthermore, it was found in each case that the asymptotic solutions for Re 〈 1 derived by Robertson & Acrivos (1970) for a cylinder and by Lin, Peery & Schowalter (1970) for a sphere are not valid for Reynolds numbers greater than about 0.1, and that the flow remains steady only up to values of Re of about 6. © 1975, Cambridge University Press. All rights reserved.