The effects of peripheral-layer viscosity on the flow characteristics of a bio-fluid due to peristaltic transport has been investigated. It is shown that, for a given pressure drop, the flow flux increases and the frictional force decreases as the viscosity of the peripheral-layer fluid decreases. However, for zero pressure drop, the flux does not depend upon this viscosity while the friction force decreases as it decreases.

The analysis has been applied and compared with observed data.

This paper examines the theory of the interaction of sound with a slit-perforated screen in the presence of a uniform, subsonic tangential mean flow on both sides of the screen. The sound induces vortex shedding from sharp edges of the screen. The coupling of this vorticity with the mean flow leads to a significant modification in the predicted acoustic properties as compared with those predicted by the classical treatments of Rayleigh (1897) and Lamb (1932). In particular a considerable portion of the incident acoustic energy can be lost during the interaction, and is convected away in the mean flow in the form of localized vortical disturbances. The analytical results provide theoretical support for the use of perforated plates to inhibit the onset of cavity resonances in, for example, cross-flow heat exchangers.

This paper is part of a series treating the flow in a variable-area, rectangular duct which is rotating about an axis that is perpendicular to the duct's centre-line and parallel to one pair of walls (sides). The speed of rotation is assumed to be sufficiently large that viscous effects are confined to boundary layers and free shear layers and that inertial effects are much smaller than viscous effects everywhere. Earlier papers present inertialess solutions for a prototype with parallel sides everywhere, parallel top and bottom upstream of a cross-section, and straight, symmetrically diverging top and bottom downstream of the same cross-section. The present paper presents inertial perturbations to the inertialess solutions for the prototype when the slope of the diverging top and bottom is small. This paper begins to bridge the gap between papers treating inertialess flows in ducts with arbitrary geometries and papers treating flows with significant inertial effects in ducts with restricted geometries.

The angular momentum A per unit horizontal distance of a train of periodic, progressive surface waves is a well-defined quantity, independent of the horizontal position of the origin of moment.

The Lagrangian-mean angular momentum $\overline{A}_L$ consists of two parts, arising from the orbital motion and from the Stokes drift respectively. Together these contribute a positive sum, nearly proportional to the energy density (when the origin is taken in the mean surface level). If moments are taken about some point P not at the mean surface level, the angular momentum will differ by an amount proportional to the elevation of P. There is just one elevation for which the Lagrangian-mean angular momentum about P vanishes. This elevation is called the level of action. For infinitesimal waves in deep water the level of action is at a height above the mean surface equal to ½k, that is ¼π times the wavelength.

Just as for ordinary fluid velocities, the Lagrangian-mean angular momentum $\overline{A}_L$ differs from the Eulerian-mean $\overline{A}_L$, the latter being zero to second order. The difference between $\overline{A}_L$ and $\overline{A}_E$ is associated with the displacement of the lateral boundaries of any given mass of fluid.

For waves of finite amplitude, an initially rectangular mass of fluid becomes ultimately quite distorted by the Stokes drift. Nevertheless it is possible to define a long-time average l.t.$\overline{A}$ and to calculate its numerical value accurately in waves of finite amplitude. In low waves, l.t.$\overline{A}$ is equal to $\overline{A}_L$. Defining the level of action ya in the general case as l.t.$\overline{A}/I$, where I is the linear momentum, we find that ya rises from 0·5k−1 for infinitesimal waves to about 0·6k−1 for steep waves. Thus ya is about the same as the height yx of the wave crests above the mean level in limiting waves, a fact which may account for why steep irrotational waves can support whitecaps in a quasi-steady state. The same argument suggests that Gerstner waves (in which the particle orbits are theoretically circular) could not support whitecaps.

Large-Reynolds-number analysis is given for separated flows that have the characteristic feature of being confined in the transverse direction. Two principal limits of the governing equation are obtained depending on whether the streamwise length scale is of order one or of the order of the Reynolds number. The corresponding two types of separated flows are discussed. A method of calculation is given for the second type of flow. It employs an expansion in the eigenfunctions of the Poiseuille flow development and the problem is reduced to solving nonlinear first-order ordinary differential equations that have a tendency to decouple rapidly. The method is tested by a detailed comparison of the results of the present calculation with finite-difference solutions of the Navier–Stokes equations for a channel with sudden expansion. Applicability to other configurations is illustrated by solving the problem of the flow in a channel with a base.

The behaviour of dilute polymer solutions in sink flow, viz., radial flow toward a point, was investigated experimentally and theoretically. Solutions of polyethylene oxide, in the drag-reducing concentration range, were pushed through a 60° conical channel at Reynolds numbers of order 102. Preliminary studies revealed a range of flow conditions in which the flow was free of secondary motion yet non-Newtonian effects were significant. Measurements of pressure differential between two radial positions yielded the non-Newtonian normal stress developed in the radial direction; the magnitude was the same order as the Newtonian stress, i.e., as the dynamic pressure ½ρV2.

Several fluid models were analysed to determine the stress generated by each in sink flow. It was found that a solution of Rouse–Zimm flexible macromolecules produces a stress which is three orders of magnitude below the observed level, and that macro-molecules with finite extension fall short by two orders. A suspension of elongated particles, of the type analysed by Batchelor, was also considered, but application to the present case was difficult because of the small scale required by the theory. Consequently, the theory was extended to include particles the size of the flow field, and an order-of-magnitude analysis revealed that for such particles to produce the desired stress, the aspect ratio must be $O(10^{\frac{7}{2}})$, and the cross dimension is likely O(0·1)μm. Electron micrographs of freeze-dried samples of the polymer solutions showed the solute in the form of an irregular network of apparently undissolved strands, with diameters in the O(0·1)μm range.

A simple dye in water method has been used to visualize the growth of a two-dimensional starting flow vortex formed at a wedge-like sharp edge. Several cases were tested corresponding to different wedge angles and to different values of the time exponent in the velocity–time power law describing the starting flow. Photographic sequences showing the time-wise primary vortex growth are presented from which various secondary-flow details are identified. For the larger wedge angles these include a strong secondary vortex and in some cases a small separation bubble-like flow region immediately adjacent to the wedge apex. For a thin-wedge model the formation of what might be interpreted as small rotation centres along the outer turns of the primary-vortex shear layer is observed but these are not seen as a manifestation of an instability phenomenon in the fluid. Measurements of the trajectories of the primary-vortex centre are compared with the predictions of an inviscid similarity theory of the vortex growth. Although the appropriate Reynolds number in the present experiments was relatively low, comparison between theory and experiments is regarded as reasonable with differences being attributed to viscous effects absent in the similarity theory, and also to apparatus wall effects.

When solving for three-dimensional laminar and turbulent boundary layers on smooth bodies of revolution at incidence, one has to contend with a difficulty near the nose where the usual formulations of the governing equations are singular. A transformation of the co-ordinate system is described which removes this singularity and enables the solution to be carried smoothly around the nose. A further difficulty arises if the body is slender and it is also shown how this may be overcome. As part of our continuing studies of this problem for both laminar and turbulent flows, we compute the laminar boundary layers on the line of symmetry for thin bodies taking the prolate spheroid as a paradigm. We show that if the angle of incidence α is less than 41°, separation never occurs at the nose no matter how thin the body. In contrast, the value of α which provokes separation at the leading edge of a two-dimensional airfoil tends to zero with the thickness ratio of the airfoil.

Heat-transfer rates from a non-equilibrium hypersonic air flow to flat plates at zero and 12° incidence have been measured in a free piston shock tunnel at stagnation enthalpy levels up to 51 MJ kg−1. Nozzle flow conditions resulted in test section velocities up to 8·1 km 8−1 and in an experimental regime in which the free stream was chemically frozen and the flat-plate boundary layer was laminar. Estimates of the gas-phase and surface-reaction Damkohler numbers have been made and the heat-transfer results are discussed in this context. At the highest test-section densities non-equilibrium endothermic gas phase reactions involving oxygen atoms in the boundary layer are suggested as a possible mechanism for the observed low heattransfer rates.

A Galerkin method is used to calculate the finite amplitude, steady, axisymmetric convective motions of an infinite Prandtl number, Boussinesq fluid in a spherical shell. Convection is driven by a temperature difference imposed across the stress-free, isothermal boundaries of the shell. The radial gravitational field is spherically symmetric and the local acceleration of gravity is directly proportional to radial position in the shell. Only the case of a shell whose outer radius is twice its inner radius is considered. Two distinct classes of axisymmetric steady states are possible. The temperature and radial velocity fields of solutions we refer to as ‘even’ are symmetric about an equatorial plane, while the latitudinal velocity is antisymmetric about this plane; solutions we refer to as ‘general’ do not possess any symmetry properties about the equatorial plane. The characteristics of these solutions, i.e. the isotherms, streamlines, spherically averaged temperature profiles, Nusselt numbers, etc., are given for Rayleigh numbers Ra as high as about 10 times critical for the even solutions and 3 times critical for the general solutions. Linear stability analyses of the nonlinear steady states show that the general solutions are the preferred form of axisymmetric convection when Ra is less than about 4 times critical. Furthermore, while the preferred motion at the onset of convection is non-axisymmetric, axisymmetric convection is stable when Ra exceeds about 1·3 times the critical value.

An experimental study of wind-generated capillary waves has been carried out in a laboratory wind-wave tunnel. In this tunnel it was possible to generate a stationary homogeneous wave field and to vary the wind over a range of speeds. A technique which makes use of a Preston tube has been used to measure the shear stress at the air-water boundary. Measurements of surface elevation and wave slope spectra in the capillary range of frequencies were obtained. Equations describing the wave spectra equilibrium range under the action of wind shear, surface tension and viscosity are derived. For frequencies beyond 15 hertz the measured spectra are in satisfactory agreement with the derived equations. Comparisons with other existing data have also been made.

A theoretical account is given of experiments performed by Saffman & Taylor (1958) in which a fluid drives a liquid out of a long straight channel of very small thickness formed between two parallel sheets sealed at the edges. The penetrating fluid forms a long finger, whose sides are parallel to the edges of the channel, and which has a rounded tip, which advances with unaltered shape at a constant speed U. The theory correctly predicts the shape of the finger as a function of the ratio λ = (asymptotic width of finger)/(width of channel) and gives the relation between λ and U, which is in good agreement with experiment. In particular it shows that, as U increases from zero to infinity, λ steadily decreases from 1 to 0·5.

Analytical and numerical analyses have been made of the physical behaviour of a collapsing bubble in a liquid. The mathematical formulation takes into account the effects of compressibility of the liquid, non-equilibrium condensation of the vapour, heat conduction and the temperature discontinuity at the phase interface. Numerical solutions for the collapse of the bubble are obtained beyond the time when the bubble reaches its minimum radius up to the stage when a pressure wave forms and propagates outward into the liquid. The numerical results indicate that evaporation and condensation strongly influence the dynamical behaviour of the bubble.

In addition, the propagation of the stress wave, both in a solid and a liquid, due to the collapse of the bubble has been observed by means of the dynamic photoelasticity. It is clearly demonstrated that the stress wave in a photoelastic specimen is caused by impact of the pressure wave radiated from the bubble.

The classical problem of water waves on an incompressible irrotational flow is considered. By introducing an appropriate non-dimensionalization, we derive four Korteweg–de Vries equations: two expressed in Cartesian co-ordinates and two in plane polars. The equations are: the classical (plane) KdV equation, the two-dimensional ‘nearly-plane’ equation, the concentric equation and a new ‘nearly-concentric’ equation. On the basis of the underlying water-wave equations, it is seen that two simple transformations exist between these KdV equations.

By constructing appropriate asymptotic regions defined in terms of the relevant small parameters, we show how various initial value problems give rise to certain solutions of the KdV equations. In particular, the generation of the similarity solutions is examined in detail and it is found that these solutions must eventually match to a solution of the full water-wave equations in a neighbourhood of the origin.

Calculated numerical results are presented for laminar buoyancy-induced flows driven by thermal transport to or from a vertical isothermal surface in cold pure and saline water wherein a density extremum arises. The present calculations specifically explore the consequences of temperature conditions wherein the buoyancy force reverses across the thermal region owing to the presence of a density extremum within the region. Such conditions commonly occur in terrestrial waters and in technological processes utilizing cold water. The linear approximation of density dependence on temperature, used in conventional analysis, is here replaced by a very accurate non-linear density equation of state for both pure and saline water. This permits an accurate treatment of such flows for bounding temperatures up to 20 °C at ambient salinity and pressure levels from 0 to 40 p.p.t. and 1 to 1000 bars, respectively. The results may be applied to the melting or slow freezing of a vertical ice surface in pure water as well as to a heated or cooled vertical isothermal surface in pure or saline water. For example, buoyancy force reversals arise for a vertical ice surface at 0 °C melting in fresh water between 4 °C and 8 °C at atmospheric pressure. Temperature conditions for which buoyancy force reversals occur are of special interest because of the resulting anomalous flow behaviour and low surface heat-transfer rates. The transition from conditions with no buoyancy-force reversal to those resulting in a large buoyancy-force reversal is accompanied by as much as 50% decrease in surface heat transfer. This produces a corresponding trend in the melt rate of a vertical ice surface in pure water. Sufficiently strong buoyancy force reversals are found to cause local flow reversal either at the edge of the flow layer or near the surface. Conditions are determined for which flow reversals occur at each of these locations. These local flow reversals are the precursors of convective inversion, that is, of the reversal of the net flow direction with changing ambient medium temperature. Limits on conditions for convective inversion are determined. Calculated transport is compared with previous experimental results, with good agreement throughout the several regions of such complicated flows. The calculations indicate that such flows are relatively very weak. However, their form may lead to early laminar instability.

Measurements of turbulent flow through a constricted tube with a contoured 75% constriction have been performed with a laser-Doppler anemometer. One motivation for these studies was the problem of flow through arterial stenoses and consequently a range of relatively low Reynolds numbers (5000–15000) was employed. Velocity profiles, r.m.s. turbulence velocities, and energy spectra were recorded along with determinations of the wall pressure variation and length of recirculation region. Results show extremely high levels of turbulence and considerable turmoil within the so-called recirculation region. A method for determining the reattachment point in an intensely turbulent flow is given which should offer improvement over flow visualization techniques. Similarity in turbulence energy spectra measured at various radial positions is found at several axial locations, but does not occur in the region immediately downstream of separation. The downstream recovery of the turbulence velocity to upstream values takes place slowly. A secondary motivation of providing experimental data useful in evaluating turbulence models for computational fluid dynamics led to extensive measurements of radial and axial r.m.s. turbulence velocity components at a Reynolds number of 15000.

Water waves that propagate over a non-rigid bed are attenuated as a result of energy dissipation within the bed. This paper describes the analysis, from the basis of small-amplitude wave theory, of the coupled interaction between the bed, which responds in both an elastic and viscous manner, and an overlying layer of inviscid fluid. A dispersion relation is derived, from which rates of wave attenuation and sea bed deflexions are calculated.

The results are relevant wherever the sea bed, in its response to water waves, is non-rigid, as is often the case in coastal waters. Depending on the elasticity and viscosity of the sea bed, the wave attenuation can be of the same or of a larger order of magnitude than that due to bottom friction or percolation in a permeable bed. Where waves propagate over a soft viscous bed, for example as is the case at certain mud flats off the south-west coast of India, exceptionally high rates of attenuation are possible whereby waves are almost completely damped within several wavelengths.

The fluid is incompressible, inviscid and non-diffusive. It has a uniform Brunt–Väisälä frequency, N, and is of constant depth, D. A body or wing moves horizontally through the fluid at velocity U in a straight line, exerting a vertical force during a given time interval. The force is constant, or oscillatory with frequency σ. The vertical average of the strain rate in a thin surface layer is calculated for a network of points behind the body.

The linearized analysis is first applied with tank walls, then modified for remote walls and a vertical force of long duration.

For moderately high velocity and forcing frequency (U/ND = 5, σ/N≅ 4−16) the recurring internal wave pattern just behind the body is well established in one cycle of the oscillatory force. A tank width one or two times the depth gives good agreement between tank and no-wall calculations for the chosen examples.

For a stationary wing (U/ND = 0) in a cubic tank with forcing frequency one-half the natural frequency (σ/N = ½) the strain rates after one cycle are 103 times greater than for the moving wing case. After five cycles the magnitudes are twenty times larger than after one cycle. Presumably these large increases are due to the continuous and efficient feeding of energy into a small fluid volume which occurs for the stationary wing. No-wall calculations for many cycles give amplitudes roughly one-half those for five cycles in the tank, showing the effect of escaping energy.

The relation of these developments to stationary phase analysis and preferred directions is discussed.

Measurements of wall pressure fluctuations under a turbulent boundary layer were made on the fuselage of a sailplane. This flow offers a noise-free environment with a low free stream turbulence level. The axisymmetric boundary layer undergoes natural transition and develops in a zero pressure gradient region. Spectra of the wall pressure were found to decrease at low frequency in agreement with calculations based upon a turbulence–mean shear interaction mechanism. Velocity fluctuations at several positions within and outside the boundary layer were measured and correlated with the wall pressure. A special conditional correlation method was also employed to find the contribution of various velocity fluctuations to the wall pressure. A conditioning signal was formed based upon the signs of u and v and the turbulent–non-turbulent nature of the flow. This signal was time lagged and correlated with the wall pressure signal. It was found that in the outer portion of the boundary layer (y/δ > 0·5), irrotational motions were more highly correlated with the wall pressure than vortical motion.

Analyses are made of the mutual interactions between shock structure and the sidewall laminar boundary layer and their effects on the quasi-steady flat-plate laminar boundary layer in ionizing-argon shock-tube flows. The mutual interactions are studied using effective quasi-one-dimensional equations derived from an area-averaged-flow concept in a finite-area shock tube. The effects of mass, momentum and energy nonuniformities and the wall dissipations in the ionization and relaxation regions on the argon shock structure are discussed. The new results obtained for shock structure, shock-tube laminar side-wall and quasi-steady flat-plate boundary-layer flows are compared with dual-wavelength interferometric data obtained from the UTIAS 10 × 18 cm Hypervelocity Shock Tube. It is shown that the difference between the results obtained from the present method and those obtained by Enomoto based on Mirels’ perfect-gas boundary-layer solutions are significant for lower shock Mach numbers (Ms ∼ 13) where the relaxation lengths are large (∼ 10cm). In general, the present results agree better with our experimental data than our previous results for uncoupled ionizing flows.