A magnetic field is shown to be asymptotically (t → ∞) decaying in a flow of finite conductivity with v = Cr, where C = Cζ(t) is a random matrix. The decay is exponential, and its rate does not depend on the conductivity. However, the magnetic energy increases exponentially owing to growth of the domain occupied by the field. The spatial distribution of the magnetic field is a set of thin ropes and (or) layers.

Measurements of fluctuating pressure and velocity, together with instantaneous smoke-flow visualizations, are presented in order to reveal the unsteady structure of a separated and reattaching flow. It is shown that throughout the separation bubble a low-frequency motion can be detected which appears to be similar to that found in other studies of separation. This effect is most significant close to separation, where it leads to a weak flapping of the shear layer. Lateral correlation scales of this low-frequency motion are less than the reattachment length, however; it appears that its timescale is about equal to the characteristic timescale for the shear layer and bubble to change between various shedding phases. These phases were defined by the following observations: shedding of pseudoperiodic trains of vortical structures from the reattachment zone, with a characteristic spacing between structures of typically 60% to 80% of the bubble length; a large-scale but irregular shedding of vorticity; and a relatively quiescent phase with the absence of any large-scale shedding structures and a significant ‘necking’ of the shear layer downstream of reattachment.

Spanwise correlations of velocity in the shear layer show on average an almost linear growth of spanwise scale up to reattachment. It appears that the shear layer reaches a fully three-dimensional state soon after separation. The reattachment process does not itself appear to impose an immediate extra three-dimensionalizing effect upon the large-scale structures.

A new system of approximating equations is derived for three-dimensional steady viscous compressible flows in which a primary flow direction is present, but in which both transverse velocity components can be large. If the transverse velocity vector which corrects a given potential flow is first decomposed into ‘potential’ and ‘rotational’ vector components, then a re-examination of three-dimensional boundary-layer theory shows that both components (vϕ, wϕ) of the potential-velocity vector may be assumed small, whereas both components (vψ, wψ) of the rotational-velocity vector and hence of the composite secondary flow (v, w) can remain of order unity. An assumption of small scalar potential then leads to a system of governing equations whose characteristic polynomial has a non-elliptic form for arbitrary Mach number, without introducing any direct approximation of either streamwise or transverse pressure gradient terms. These non-elliptic equations can be solved very economically as a well-posed initial/boundary-value problem. Computed results for laminar subsonic flow in a curved square duct confirm the small scalar-potential approximation for both large (R/d = 100) and small (R/d = 2) radius of curvature. Other computations for R/d = 2.3 are in good agreement with the measurements of Taylor, Whitelaw & Yianneskis (1980).

A large (3.05 m long × 0.32 m diameter) heated-surface, axisymmetric body, designed for transition research in a 1.22 m diameter water tunnel is described. Boundary-layer transition data are presented as functions of the heating power supplied to the body and the total concentration of free-stream particulate matter in the water. Body surface temperatures range from 0 to 25°C over the ambient water temperature, and the total heat supplied ranges from 0 to 93.3 kW. Transition-arclength Reynolds numbers are found to vary from 4.5 × 106 for the body operating cold to 3.64 × 107 for the maximum heat level considered. The concentration of free-stream particles is shown to affect the transition Reynolds number. These particles range in diameter from 10 to 70 μm and their concentration ranges from less than 5 to 198 particles per cm3. The decrease in transition Reynolds number due to to the higher concentration of particles is of order 30%.

A thermal-creep flow of a slightly rarefied gas induced axisymmetrically around two unequal spheres is studied on the basis of kinetic theory. The spheres, whose thermal conductivities are assumed to be identical with that of the gas, for simplicity, are placed in an infinite expanse of the gas at rest with a uniform temperature gradient at a far distance. Owing to the poor thermal conductivities of the spheres, a tangential temperature gradient is established on the surfaces, and this causes a thermal-creep flow in its direction. Consequently, the spheres experience forces in the opposite direction.

The flow considered here is a low-Reynolds-number flow in the ordinary fluid-dynamic sense (except for the Knudsen layer), and the solution is obtained in terms of bispherical coordinates, with respect to which the system of equations of Stokes type is well developed. The velocity field around the spheres and the forces acting on them are given explicitly. The results show the interesting feature that the smaller sphere experiences the minimum force at a value of the separation distance that depends on the radius ratio. This is in contrast with the case of the axisymmetric motion of two spheres treated by Stimson & Jeffery (1926) in ordinary fluid dynamics at low Reynolds number.

The ultimate velocities that the spheres would have under the action of the present thermal force when they are freely suspended are also obtained by utilizing the results for the forces of axisymmetric translational problems of two spheres at low Reynolds number. For a given temperature gradient in the gas, both spheres acquire larger velocities than those they would have if they were alone, and the smaller sphere tends to move faster than the larger one in the direction opposite to the temperature gradient.

Also presented, for completeness, are the results for the sphere–plane case and for the case of eccentric spheres, the solutions for which are derived as special cases of the preceding problem of two unequal spheres.

Smith & Townsend's (1982) experimental data on circular Couette flow are re-examined in the framework of surface-layer similarity theory. Surface-layer similarity of horizontally stratified shear flow is shown to have its counterpart in a narrow-gap Couette flow between concentric cylinders. Smith & Townsend's data of mean angular momentum and mean-velocity profiles in a region near a cylinder lend support to the applicability of Monin–Obukhov similarity to circular Couette flow. Only for flows of very high Reynolds numbers is a region of logarithmic variation of mean profiles found close to the cylinder wall. Because of curvature effects on the flow, the mean profiles deviate from the logarithmic profile as distance from the cylinder wall increases. For flows of sufficiently low Reynolds number, but still very high Taylor number, no logarithmic profile seems to exist; instead, profiles in the viscous region and in the outer region are connected to each other by a ‘free-convection (rotation)’ profile. From Smith & Townsend's data the velocity field is not observed to follow the prediction of ‘free-convection’ similarity; however, the ‘free-convection’ profile is found in the distribution of mean angular momentum.

A horizontal layer is heated from below and cooled from above so that the enclosed single-component liquid is frozen in the upper part of the layer. When the imposed temperature difference is such that the Rayleigh number across the liquid is supercritical, there is Bénard convection coupled with the dynamics of the solidification interface. An experiment is presented which shows that the interfacial corrugations that result are two-dimensional when this solid is thin but hexagonal when the solid is thick. A weakly nonlinear convective instability theory is presented which explains this behaviour, and isolates this ‘purely thermal’ mechanism of pattern selection. Jump behaviour is seen in the liquid-layer thickness at the onset of hexagonal convection.

This paper reports experimental and numerical results on the effects of wall conductance on natural convection in a two-dimensional rectangular cavity. Three different configurations in which the external wall is heated from the side, top and bottom and cooled from the side, bottom and top respectively have been investigated. Experiments have been performed in a square enclosure with solid walls made from Lexan and forming a square air-filled cavity. A Mach–Zehnder interferometer was used to determine the temperature distributions in the fluid. Solutions for stationary two-dimensional equations of energy and motion governing heat conduction in the solid and natural convection flow and heat transfer of a Boussinesq fluid contained in the cavity have been obtained numerically. The coupled flow distributions, including the appearance of multicellular flow, temperature profiles and heat-transfer predictions compare favourably with experimental results. Heat conduction in the connecting (unheated) walls is shown to simultaneously stabilize and destabilize the fluid in the cavity.

A linear stability analysis is presented of both hydraulically smooth and transitional flows over an erodible bed. The present theory is developed to account for the formation of ripples. It is essentially an extension of the theory of Richards (1980) to include the effect of viscosity upon the bed wave stability. The theory takes into consideration that the formation of ripples does not depend on flow depths, and that only the bed-load transport is involved in the formation of ripples. The effect of gravity is included in the analysis through the local inclination of the wavy bed surface. The results show that the bed is unstable (i.e. ripples exist) when the grain Reynolds number is less than a certain value. The limiting values of the grain Reynolds number for ripple existence obtained through present analysis are found to be in good agreement with observations.

The three-dimensional laminar flow past a junction formed by a thin wing protruding normally from a locally flat body surface is considered for wings of finite span but short or long chord. The Reynolds number is taken to be large. The leading-edge interaction for a long wing has the triple-deck form, with the pressure due to the wing thickness forcing a three-dimensional flow response on the body surface alone. The same interaction describes the flow past an entire short wing. Linearized solutions are presented and discussed for long and short two-dimensional wings and for certain three-dimensional wings of interest. The trailing-edge interaction for a long wing is different, however, in that the three-dimensional motions on the wing and on the body are coupled together and in general the coupling is nonlinear. Linearized properties are retrieved only for reduced chord lengths. The overall flow structure for a long wing is also discussed, including the traditional three-dimensional corner layer, which is shown to have an unusual singular starting form near the leading edge. Qualitative comparisons with experiments are made.

A small-perturbation stability analysis is developed for investigation of the role of the secondary current accompanying channel curvature in the initiation and early development of meanders of alluvial and ice- or rock-incised streams. A small sinusoidal perturbation in the channel alignment of an initially straight prismatic channel is introduced. The velocity of the secondary flow is calculated for uniform quasi-steady flow conditions by application of the equation of the conservation of moment of momentum. The formulation is then closed by introducing the assumption that the differential, between the outer and inner banks, rate of boundary erosion, dissolution or melting (for incised channels) or sediment discharge (for alluvial channels) is proportional to the strength of the secondary flow. This formulation leads to a linear differential equation which is solved for its orthogonal components, which give the rates of meander growth and downstream migration. It is shown that the amplitude of the meanders tends to increase and that the meanders migrate downstream. The dominant wavelength and the corresponding phase shift between channel meandering and the velocity of the spiral motion are calculated as those corresponding to the fastest growth rate. The results are found to be in good agreement with data reported by others.

The validity of the assumption of local isotropy is investigated using measurements of three orthogonal components of the turbulent velocity fields associated with initially high-Reynolds-number geophysical turbulence. The turbulent fields, generated by various large-scale internal motions caused by tidal flows over an estuarine sill, decay under the influence of stable mean density gradients. With measurements from sensors mounted on a submersible, we examine the evolution of spectral shapes and of ratios of cross-stream to streamwise components, as well as the degree of high-wavenumber universality, for the observational range of the parameter I≡ ks/kb = lb/ls. This ratio is a measure of separation between the Kolmogoroff wavenumber ks≡ (ε/ν3)¼ ≡ 2π/ls typical of scales by which turbulent kinetic energy has been dissipated (at rate ε), and the buoyancy wavenumber kb ≡ (N3/ε)½ ≡ 2π/lb typical of scales at which the ambient stratification parameter N ≡ (−gρz/ρ0)½ becomes important. For values of I larger than ∼ 3000, inertial subranges are observed in all spectra, and the spectral ratio ϕ22/ϕ11 of cross-stream to streamwise spectral densities reaches the isotropic value of 4/3 for about a decade in wavenumber. As ks/kb decreases, inertial subranges vanish, but spectra of the cross-stream and streamwise components continue to satisfy isotropic relationships at dissipation wavenumbers. We provide a criterion for when ε may safely be estimated from a single measured component of the dissipation tensor, and also explore questions of appropriate low-wavenumber normalization for buoyancy-modified turbulence.

The deformation of inviscid and slightly viscous drops is studied using slender-body theory. The imposed axisymmetric flow is a combination of a linear extensional flow, with velocity uz = G1 z along the axis of symmetry, together with a cubic flow uz = G3z3. When G3/G1 is sufficiently small the viscous drop breaks in a manner similar to that described by Acrivos & Lo (1978). For larger G3 > 0 the drop breaks by a rapid growth at its end. Steady-state experiments in a 4-roll mill show the ejection of a column of liquid from the tip of the drop, though this is probably caused by a change in the pressure gradient rather than the mechanism described above. The ejected column then breaks into droplets via the Rayleigh instability. It is hypothesized that one or other of these mechanisms corresponds to tip streaming as observed by Taylor (1934).

A third-order regular perturbation solution is developed for laminar flow through a straight pipe that is rotating about an axis not aligned with the pipe axis. Coriolis accelerations produce transverse secondary velocities (similar to those in flow through coiled tubes) and modify the axial-velocity profile. The effects of rotation on the velocity fields are shown to depend on two parameters: (i) the product of axial and rotational Reynolds numbers, and (ii) the square of the rotational Reynolds number itself. Even though their strength increases with increases in parameter magnitudes, transverse circulations are qualitatively insensitive to parametric values. The axial profile, on the other hand, can be significantly modified by the rotation; the zeroth-order parabolic axial profile can be skewed toward the outside, dimpled in the centre with maximums on either side of the centreline, or both, depending on the values of the two parameters. The modification of the axial-velocity profile has important ramifications in the design of heat/mass-transfer devices.

A stability theory for the steady swirling flow above an infinite rotating disk immersed in an otherwise unbounded rigidly rotating fluid is developed in order to corroborate the various numerical computations considered for this problem. An analysis of the initial-value problem for linearized time-dependent perturbations on the steady-state similarity solutions shows that the disturbance equations have a stable continuum spectrum which, under certain conditions, exhibits only algebraic decay in time. In addition, a numerical analysis on the discrete spectrum shows that there are unstable eigenvalues for certain rotational rates of the disk relative to the fluid at infinity. The results obtained are in good agreement with the large-time behaviour of the corresponding solutions of the unsteady similarity equations.

Measurements have been made in flow between concentric cylinders with only the inner one rotating, for Reynolds numbers (based on flow gap) from 17 000 to 120 000, corresponding to Taylor numbers from 8 × 107 to 4 × 109. At the lower speeds (Reynolds numbers less than 30 000), the large-scale motion consists of toroidal eddies, highly uniform in spacing and intensity and convected by a slow axial flow past fixed sensors. By synchronizing an external oscillator with the passage frequency, flow velocity and small-scale turbulent intensity may be sampled at defined stages of the passage cycle and averaged to provide maps of the velocity fields and the associated distributions of small-scale intensity and Reynolds stress.

At higher speeds, the passage of toroidal eddies becomes too irregular to establish the passage cycle, but, by comparing the velocity fluctuations from four inclined hot wires placed near the outer cylinder, the current location of large-scale flow separation from the outer cylinder can be approximately determined. Statistics of the temporal variations of the location show that the large-scale motion still approximates to the toroidal form, but that there are azimuthal variations of separation position and velocity that indicate a change from toroidal to helical eddies. Conditional averages of flow velocity and small-scale turbulent intensity, based on relative distance from the position of flow separation, are very similar in form and magnitude to phase-selected averages obtained at lower speeds.

The considerable changes in the large-scale motion that occur as the Reynolds number increases from 300 to 1200 times the critical value are believed to arise from increase in the ‘turbulent Taylor number’ of the central flow, based on variation of angular momentum and on the eddy diffusion coefficients for linear and angular momentum. Effects on the motion of the slow axial flow, always less than 1% of the peripheral flow velocity, are also discussed.

The interference of passive thermal fields produced by two (and more) line sources in decaying grid turbulence is studied by using the inference method described by Warhaft (1981) to determine the cross-correlation coefficient ρ between the temperature fluctuations produced by the sources. The evolution of ρ as a function of downstream distance, for 0.075 < d/l < 10, where d is the wire spacing and l is the integral lengthscale of the turbulence, is determined for a pair of sources located at various distances from the grid. It is found that ρ may be positive or negative (thereby enhancing or diminishing the total temperature variance) depending on the line-source spacing, their location from the grid and the position of measurement. It is also shown that the effects of a mandoline (Warhaft & Lumley 1978) may be idealized as the interference of thermal fields produced by a number of line sources. Thus new light is shed on the rate of decay of scalar-variance dissipation. The thermal field of a single line source is also examined in detail, and these results are compared with other recent measurements.

A laboratory experiment is used to study the transient flow in an initially isothermal cavity at temperature T0 following the rapid change of the two vertical endwalls to temperatures T0 ± ΔT respectively. Individual temperature records are taken and the transient flow in the entire cavity is visualized with the aid of a tracer technique. It is shown that an oscillatory approach to final steady-state conditions exists for certain flow regimes, although the form of the oscillatory response is different to that suggested by previous work. It is argued that this oscillatory behaviour is due to the inertia of the flow entering the interior of the cavity from the sidewall boundary layers, which may lead to a form of internal hydraulic jump if the Rayleigh number is sufficiently large.

Galerkin finite-element approximations are combined with computer-implemented perturbation methods for tracking families of solutions to calculate the steady axisymmetric flows in a differentially rotated cylindrical drop as a function of Reynolds number Re, drop aspect ratio and the rotation ratio between the two end disks. The flows for Reynolds numbers below 100 are primarily viscous and reasonably described by an asymptotic analysis. When the disks are exactly counter-rotated, multiple steady flows are calculated that bifurcate to higher values of Re from the expected solution with two identical secondary cells stacked symmetrically about the axial midplane. The new flows have two cells of different size and are stable beyond the critical value Rec. The slope of the locus of Rec for drops with aspect ratio up to 3 disagrees with the result for two disks of infinite radius computed assuming the similarity form of the velocity field. Changing the rotation ratio from exact counter-rotation ruptures the junction of the multiple flow fields into two separated flow families.

Surface waves travelling in water of finite depth may be scattered by a region of undulating bottom topography. The present study is concerned with the idealized two-dimensional situation in which long-crested surface waves are incident upon a patch of long-crested regular bottom ripples. The principal question examined concerns the amount of incident wave energy that is reflected by the ripple patch. Linear perturbation theory is used to show that the reflection coefficient is both oscillatory in the quotient of the length of the patch and the surface wavelength, and also strongly dependent upon the quotient of the surface and bed wavelengths. In particular, there is a Bragg resonance between the surface waves and the ripples, which is associated with the reflection of incident wave energy. A secondary question concerns the nature of the wave field in the immediate vicinity of the ripple patch. In resonant cases, it is shown how the partially standing wave on the upwave side of the ripple patch gives way, in an almost linear manner over the patch itself, to a progressive transmitted wave on the downwave side. The theoretical predictions are compared with an extensive set of laboratory observations made in a wave tank. Comparisons relating both to the reflection coefficient, and also to the wave field over the ripple patch, are shown to give consistently good agreement. Finally, the implications of the results for sediment transport on an erodible bed are examined.