The thermodynamics of irreversible processes is normally limited to processes that can be adequately described by linear constitutive relations, like those of Fourier and Newton in a simple gas. In this paper we use thermodynamic arguments to derive the (nonlinear) Burnett equations for a monatomic gas, thus avoiding the complicated kinetic theory by which the equations were discovered and which somewhat obscures the origin of the various terms in the equations. Expressions are given for the entropy, its flux and its production rate correct to second-order in Knudsen number. The theory involves five phenomenological parameters, and as there are eleven coefficients in the second-order terms of Burnett's equations, we are able to deduce several necessary constraints between these coefficients. Compact forms for the equations are found that clarify their physical significance. The general method we have developed is applicable to media other than simple gases.

In a final section we use our theory of Burnett's equations to draw some general conclusions concerning the second law of thermodynamics. It is shown that the Clausius-Duhem inequality holds only for the linear theory of constitutive relations; and that axiomatic generalizations of the inequality to nonlinear processes – common in continuum mechanics–fail because the vital distinction between reversible and irreversible processes is not made.

Hot-wire and flow-visualization studies have been carried out in three air jets subjected to pure-tone acoustic excitation, and the instability, vortex roll-up and transition as well as jet response to the controlled excitation have been investigated. The centreline fluctuation intensity can be enhanced by inducing stable vortex pairing to a level much higher than even that at the ‘preferred mode’, but can also be suppressed below the unexcited level under certain conditions of excitation. The conditions most favourable to vortex pairing were determined as a function of the excitation Strouhal number, the Reynolds number (ReD), and the initial shear-layer state, i.e. laminar or turbulent. It is shown that the rolled-up vortex rings undergo pairing under two distinct conditions of excitation: ‘the shear layer mode’ when the Strouhal number based on the initial shear-layer momentum thickness (Stθ) is about 0·012, and ‘the jet column mode’ when the Strouhal number based on the jet diameter (StD) is about 0·85. The former involves pairing of the near-exit thin vortex rings when the initial boundary layer is laminar, irrespective of the value of StD. The latter involves pairing of the thick vortex rings at x/D ≅ 1·75, irrespective of Stθ or whether the initial boundary layer is laminar or turbulent. For laminar exit boundary layer, pairing is found to be stable, i.e., occurring regularly in space and time, for ReD < 5 × 104, but becomes intermittent with increasing ReD or fluctuation intensity in the initial boundary layer.

The trajectories of the vortex centres and their convection velocities during a pairing event have been recorded through phase-locked measurements. In the presence of stable vortex pairing, the time average profiles of fluctuation intensities and Reynolds stress show noticeable deviations from those in the unexcited jet. The vortex pairing phenomenon produce considerably larger excursions of the $\widetilde{uv}(t)$ signal than the time-average Reynolds stress reveals, suggesting that only certain phases of the pairing process may be important in entrainment, and production of Reynolds stress and jet noise.

A previously unpublished theory for describing the internal flow in a gas centrifuge is presented. The theory is based on boundary-layer-type arguments on the side walls of the centrifuge with the additional approximation of neglecting radial diffusion of radial momentum. The effects of the top and bottom end caps are incorporated through Ekman-layer solutions. The results are presented in a form amenable to numerical calculations.

Some sample calculations are presented for the special case of a centrifuge with a linear temperature profile on the wall and the top and bottom of the centrifuge at the same temperature as the corresponding end of the side wall.

Steady potential flow around a two-dimensional bubble with surface tension, either free or attached to a wall, is considered. The results also apply to a liquid drop. The flow and the bubble shape are determined as functions of the contact angle β and the dimensionless pressure ratio γ = (pb − ps)/½ρU2. Here pb is the pressure in the bubble, ps = p∞ + ½ρU2 is the stagnation pressure, p∞ is the pressure at infinity, ρ is the fluid density and U is the velocity at infinity. The surface tension σ determines the dimensions of the bubble, which are proportional to 2σ/ρU2. As γ tends to ∞, the bubble surface tends to a circle or circular arc, and as γ decreases the bubble elongates in the direction normal to the flow. When γ reaches a certain value γ0(β), opposite sides of the bubble touch each other. The problem is formulated as an integrodifferential equation for the bubble surface. This equation is discretized and solved numerically by Newton's method. Bubble profiles, the bubble area, the surface energy and the kinetic energy are presented for various values of β and γ. In addition a perturbation solution is given for γ large when the bubble is nearly a circular arc, and a slender-body approximation is presented for β ∼ ½π and γ ∼ γ0(β), when the bubble is slender.

Measurements of the thermal and velocity structure of the near-surface mixing layer of a freshwater lake in moderate wind conditions from fixed or mobile arrays of sensors reveal large-scale coherent structures consisting of narrow fronts across which both the temperature and the horizontal component of the current increase. These fronts are generally transverse to the wind direction and are inclined to the vertical, and appear to be similar to fronts, reported as temperature ‘ramps’, in the near-surface atmospheric boundary layer. The time derivatives of the temperature are skewed in a sense consistent with observations in laboratory and atmospheric boundary layers, and of a magnitude consistent with measurements in the latter. Evidence is presented to show that bubbles generated by breaking waves are carried down in the large-scale pattern of flow associated with the fronts in the mixing layer. The presence of a Langmuir circulation associated with wind rows has not been established in these experiments. The relevance of the observations to the ocean mixing layer is discussed.

The coherent structure dynamics in the near field of a circular jet has been experimentally explored by inducing ‘stable’ vortex pairing through controlled excitation (see Zaman & Hussain 1980) and applying phase-averaging techniques. Hot-wire measurements were made in a 7·62 cm air jet with laminar exit boundary layer at the Reynolds number ReD = 3·2 × 104, excited at the Strouhal number StD = 0·85. At a particular phase during the pairing process, spatial distributions of the phase-average longitudinal and lateral velocity perturbations (〈u)〉, 〈v〉), vorticity, streamlines, the coherent and background Reynolds stresses and turbulence intensities have been educed. These data have been obtained for four different locations occupied by the vortices at the same phase (preceding, during, and following the pairing event), in the region 0 < x/D < 5. Spatial distributions of these measures at four successive phases during the pairing process are also educed in an attempt to further understand the vortex-pairing dynamics. The flow physics is discussed on the basis of measurements over the physical extent of the vortical structures, phase-locked to specific phases of the pairing event and thus do not involve use of the Taylor hypothesis.

The computed pseudostream functions at particular phases are compared with the corresponding streamlines drawn by the method of isoclines. Transition of the vortices is examined on the basis of vorticity diffusion, the superimposed random fluctuation field intensities and Reynolds stress and phase-locked circumferential correlation measurements. The peak vorticity drops rapidly owing to transition and interaction of the vortices during pairing but, farther downstream, the decay can be attributed to destruction of the coherent vorticity by the background turbulence Reynolds stress, especially at the locations of the latter's ‘saddle points’. Controlled excitation enhances the initial circumferential coherence of the vortical structures, but is ineffective in delaying turbulent breakdown near the end of the potential core; the breakdown appears to occur through evolution of the circumferential lobe structures. The coherent structure Reynolds stress is found to be much larger than the background turbulence Reynolds stress for 0 < x/D [lsim ] 3, but these two are comparable near the end of the jet potential core. The zone average of the coherent structure Reynolds stress over the cross-section of the merging vortex pair is much larger than that over a single vortical structure either before or after the completion of pairing. During the pairing process, such average correlations are found to be the largest at an early phase of the process while entrainment, turbulent breakdown as well as rapid diffusion of vorticity occur at a later phase. The regions of alternate positive and negative coherent Reynolds stresses associated with the structures and their interactions help explain ‘negative production’.

The spreading on a water–air interface of a thin liquid film is examined for the situation in which surface tension gradients drive the motion. A similarity solution is obtained numerically for unidirectional spreading when some general restrictions concerning the form of the liquid film constitutive relation is made. This solution gives the size of the film as a function of time and also the velocity and thickness distribution along the spreading film. Experiments are performed which show good agreement with the theory.

The instantaneous velocity vector fields which surround the coherent structures of Perry & Lim (1978) in coflowing jets and wakes have been successfully measured and related to the smoke patterns for Reynolds numbers of order 1000. By the use of critical point theory, a qualitative description of the three-dimensional flow field can be made and is applied to the simplest structures which were classified by Perry & Lim. From these results, the convection of smoke and vorticity from the source and the entrainment properties of the structures are discussed.

Based on the parabolic approximation, a refraction—diffraction model for linear water waves is developed. With the assumption that the water depth (refraction index) is slowly varying, the model equation describes the forward-scattered wavefield. Two examples are considered in particular: (i) wave diffraction by a long thin barrier on a uniform slope, and (ii) wave convergence over a semicircular step shoal. For the former problem, a similarity solution in terms of Fresnel integrals is obtained for the wavefield in the neighbourhood of the shadow boundary. For the latter problem, the resulting Schrödinger equation is solved numerically. The wavefield near the caustics as well as in the shadow region is obtained and compared with experimental data.

The problem of determining the steady axially symmetrical motion induced by a sphere rotating with constant angular velocity about a diameter in an incompressible viscous fluid which is at rest at large distances from it is considered. The basic independent variables are the polar co-ordinates (r, θ) in a plane through the axis of rotation and with origin at the centre of the sphere. The equations of motion are reduced to three sets of nonlinear second-order ordinary differential equations in the radial variable by expanding the flow variables as series of orthogonal Gegenbauer functions with argument μ = cosθ. Numerical solutions of the finite set of equations obtained by truncating the series after a given number of terms are obtained. The calculations are carried out for Reynolds numbers in the range R = 1 to R = 100, and the results are compared with various other theoretical results and with experimental observations.

The torque exerted by the fluid on the sphere is found to be in good agreement with theory at low Reynolds numbers and appears to tend towards the results of steady boundary-layer theory for increasing Reynolds number. There is excellent agreement with experimental results over the range considered. A region of inflow to the sphere near the poles is balanced by a region of outflow near the equator and as the Reynolds number increases the inflow region increases and the region of outflow becomes narrower. The radial velocity increases with Reynolds number at the equator, indicating the formation of a radial jet over the narrowing region of outflow. There is no evidence of any separation of the flow from the surface of the sphere near the equator over the range of Reynolds numbers considered.

The shape of a vertical slender jet of fluid falling steadily under the force of gravity is studied. The problem is formulated as a nonlinear free boundary-value problem for the potential. Surface tension effects are neglected. The use of perturbation expansions results in a system of equations that can be solved by an efficient numerical procedure. Computations were made for jets issuing from orifices in various shapes including an ellipse, a rectangle, and an equilateral triangle. Computational results are presented illustrating the propagation of discontinuities and the formation of thin sheets of fluid.

The evolution of the shape of a slender inviscid drop in an axisymmetric straining motion is studied at low Reynolds numbers. It is found that the shape equation can be solved by polynommals with time-dependent coefficients. A global stability result can be used to show simply that only one possible equilibrium is stable. It is further shown that if the slender drop starts with a long-wavelength waist then it cannot go to this stable equilibrium and must either extend indefinitely or burst. In the class of trinomial shapes, it is shown that the drop either bursts or goes to the stable equilibrium, depending on whether or not the initial shape has a waist.

The frequency of vortex shedding from a circular cylinder in a uniform shear flow and the flow patterns around it were experimentally investigated. The Reynolds number Re, which was defined in terms of the cylinder diameter and the approaching velocity at its centre, ranged from 35 to 1500. The shear parameter, which is the transverse velocity gradient of the shear flow non-dimensionalized by the above two quantities, was varied from 0 to 0·25. The critical Reynolds number beyond which vortex shedding from the cylinder occurred was found to be higher than that for a uniform stream and increased approximately linearly with increasing shear parameter when it was larger than about 0·06. In the Reynolds-number range 43 < Re < 220, the vortex shedding disappeared for sufficiently large shear parameters. Moreover, in the Reynolds-number range 100 < Re < 1000, the Strouhal number increased as the shear parameter increased beyond about 0·1.

The flow of a rotating, incompressible fluid over isolated topography whose non-dimensional height (i.e. topographic height divided by the mean fluid depth) is large compared with the Rossby number is studied. Attention is restricted to flow which is sufficiently shallow that the free-surface equations provide an adequate description. The flow is forced laterally by a specified upstream inflow (obtained from solutions of the zonally symmetric model equations) and by a prescribed surface stress. Dissipation is incorporated using a Rayleigh friction acting anti-parallel to the flow.

Steady-state solutions for uniform inflow on an f-plane are found for (a) linear viscous flow, (b) quasi-geostrophic flow with and without friction and (c) inviscid flow with and without a rigid lid. The presence of friction produces an upstream–downstream flow asymmetry over the obstacle and an associated topographic drag while inertial terms produce left-right (relative to an observer looking downstream) asymmetry. The blocking efficiency B (the percentage of the incident mass flux going around the obstacle rather than over it) of a Gaussian obstacle is largest (∼ 100%) for case (a) when viscous effects are small. In contrast quasi-geostrophic theory calculates no flow blocking (B ≡ O). For inviscid inertial theory, B ∼ 10% and is independent of the Rossby number. The presence of a free surface decreases the blocking for small-Rossby-number flow.

Numerical solutions of the appropriate initial, boundary-value problem for the complete model equations confirm these results and extend them to include the effects of (i) horizontal shear in the upstream inflow, (ii) the magnitude and shape of the topography, and (iii) variations in the Coriolis parameter (β-effect).

The authors consider an homogeneous non-isotropic turbulence which develops without mean velocity gradient so that it should return to isotropy. This turbulence has been obtained by application of two successive plane strains to a grid-generated turbulence, and this configuration has already been described in a preceding paper. It is shown in particular that the nonlinear effects make no significant contribution to the rotation of the principal axes of the Reynolds stress tensor. In the case of the return to isotropy, an important parameter connected with the turbulent energy distribution between three directions comes into play. In the present experiment it has a positive sign whereas in previous experiments this sign was negative. In particular, the authors conclude that, when this parameter is positive, the return to isotropy is slower than in the opposite case.

Non-stationary MHD interaction of a horizontal magnetic field with a three-dimensional cellular convection is studied by means of computational methods and methods of mean field electrodynamics.

For a given magnetic field drop across the convective layer, the rate of magnetic flux penetration through this layer is characterized by two integral coefficients: the first one describing the topological pumping effect arises from the antisymmetric part of the α-effect, while the second coefficient accounts for the enhancement of the effective diffusion due to the convective motions. In the magnetic-Reynolds-number range studied (−5 [les ] Rm [les ] 5) these coefficients are found to be, correspondingly, odd and even functions of Rm only. The net magnetic flux escape rate into vacuum decreases at Rm > 2·2 when compared with a case of a layer without cellular motions. Here the topological pumping prevails not only over the convective enhancement of diffusion but begins to suppress even the background diffusion action.

Thus, the asymmetry in the transport properties of cellular motion is again demonstrated, and their difference from those of random turbulence is identified.

Conditions are found for the appearance of non-uniform progressive waves of permanent form from a long-wave modulation of a finite-amplitude Stokes wave on deep water. The waveheight at which the modulated waves can occur is a very slowly decreasing function of the modulation wavelength for values up to 150 times the original wavelength. Some qualitative remarks are made about the problem of determining the stability of the new waves.

Measurements of the shock stand-off distance on cones of various base diameters in carbon dioxide and nitrogen flows with dissociative relaxation show that the detachment process occurs more gradually with relaxation than in a perfect gas, as the cone semi-angle is increased. This is in agreement with a prediction which is made on the basis of the behaviour of the sonic surface in the flow field. The phenomenon is similar to that observed previously with wedge flow but shows interesting effects peculiar to the cone flow. The cone experiments also eliminate the end effect and permit easy variation of the relaxation rate parameter without changing the gas. Perfect-gas argon experiments provide a convenient check.

This paper describes a new balance, suitable for direct measurement of skin friction in turbulent boundary layers with severe pressure gradients. The gaps between the floating element and the surrounding wall are filled with a liquid in order to eliminate disturbing pressure forces on the element. The resulting friction forces are measured with piezo-electric transducers with high sensitivity and extremely small element displacement.

Skin friction measurements were taken in the turbulent boundary layer of a wind tunnel with circular cross-section at M [les ] 0·25. Severe adverse pressure gradients were generated by means of a step on the wall or, alternatively, by a conical centre body.

The new apparatus was mainly used to investigate the error of Preston tubes in adverse pressure gradients. It was necessary to develop a new measuring technique to improve the repeatability of the Preston tube readings.

The Preston tube error was found to depend on both the local pressure gradient P = (dp/dx) ν/ρ3τ and on the Preston tube diameter uτd/ν and to be independent of the upstream pressure distribution for the range of parameters covered by the experiments.

A laser-Doppler velocimeter (LDV) study of velocity profiles in the laminar boundary layer adjacent to a heated flat plate revealed that the seed particles used for the LDV measurements were driven away from the plate surface by thermophoretic forces, causing a particle-free region within the boundary layer of approximately one half the boundary-layer thickness. Measurements of the thickness of this region were compared with particle trajectories calculated according to several theories for the thermophoretic force. It was found that the theory of Brock, with an improved value for the thermal slip coefficient, gave the best agreement with experiment for low Knudsen numbers, λ/R = O(10−1), where λ is the mean free path and R the particle radius.

Data obtained by other experimenters over a wider range of Knudsen numbers are compared, and a fitting formula for the thermophoretic force useful over the entire range 0 [les ] λ/R [les ] ∞ is proposed which agrees within 20% or less with the majority of the available data.