A numerical study of the superharmonic instabilities of short-crested waves on water of finite depth is performed in order to measure their time scales. It is shown that these superharmonic instabilities can be significant-unlike the deep-water case-in parts of the parameter regime. New resonances associated with the standing wave limit are studied closely. These instabilities ‘contaminate’ most of the parameter space, excluding that near two-dimensional progressive waves; however, they are significant only near the standing wave limit. The main result is that very narrow bands of both short-crested waves ‘close’ to two-dimensional standing waves, and of well developed short-crested waves, perturbed by superharmonic instabilities, are unstable for depths shallower than approximately a non-dimensional depth d= 1; the study is performed down to depth d= 0.5 beyond which the computations do not converge sufficiently. As a corollary, the present study predicts that these very narrow sub-domains of short-crested wave fields will not be observable, although most of the short-crested wave fields will be.

The instantaneous structure of the near wake of a cylinder subjected to small-amplitude perturbations is characterized using high-image-density particle image velocimetry. Emphasis is on control of the small-scale shear-layer vortices, which feed into the Kármán vortices. Modifications of the Kármán vortex formation are classified according to patterns of modulated and locked-on shear-layer vortices. The formation length of the Kármán vortices can be dramatically shortened and, in the limiting case, occur adjacent to the base of the cylinder when it is perturbed at the inherent instability frequency of the shear layer and its subharmonics. Moreover, the induced shear-layer vortices can lead to large-amplitude transverse undulations of the entire near-wake region during formation of the Kármán vortices.

These variations of the near-wake structure are further elucidated by considering the transient response of the wake, induced by abrupt cessation and onset of periodic motion of the cylinder. Distinctive intermediate states of the wake arise during relaxation to its asymptotic state; such relaxation requires a very large number of periods of the inherent instability of the shear layer.

The three-dimensional vortex flow that develops around a close-coupled canard-wing configuration is characterized by a strong interaction between the vortex generated at the canard and the aircraft wing. In this paper, a theoretical potential flow model is devised to uncover the basic structure of the pressure and velocity distributions on the wing surface. The wing is modelled as a semi-infinite lifting-surface set at zero angle of attack. It is assumed that the vortex is a straight vortex filament, with constant strength, and lying in the freestream direction. The vortex filament is considered to be orthogonal to the leading-edge, passing a certain height over the surface. An incompressible and steady potential flow formulation is created based on the three-dimensional Laplace's equation for the velocity potential. The boundary-value problem is solved analytically using Fourier transforms and the Wiener-Hopf technique. A closed-form solution for the velocity potential is determined, from which the velocity and pressure distributions on the surface and a vortex path correction are obtained. The model predicts an anti-symmetric pressure distribution along the span in region near the leading-edge, and a symmetric pressure distribution downstream from it. The theory also predicts no vertical displacement of the vortex, but a significant lateral displacement. A set of experiments is carried out to study the main features of the flow and to test the theoretical model above. The experimental results include helium-soap bubble and oil-surface flow pattern visualization, as well as pressure measurements. The comparison shows good agreement only for a weak interaction case, whereas for the case where the interaction is strong, secondary boundary-layer separation and vortex breakdown are observed to occur, mainly owing to the strong vortex-boundary layer interaction. In such a case the model does not agree well with the experiments.

Two-dimensional mixing driven by an instability mechanism which is concentrated near one of the boundaries is considered, with particular application to Langmuir circulations driven by a wave spectrum. The question of how to define the equivalent of the Rayleigh number is attacked using the energy balance equations and simple truncated models of the instability. Given a particular horizontal wavelength for the disturbance, the strength of the forcing on the cells, and thus the growth rate, is determined by a tradeoff between maximizing the depth-averaged forcing and maximizing the depth of penetration. As a result of this tradeoff, long-wavelength cells grow more slowly, but penetrate more deeply and have a larger equivalent Rayleigh number. At finite amplitude, these long-wavelength cells come to dominate the flow field. The depth of penetration of, and density transport accomplished by, Langmuir cells is considered as a function of the mean stratification and diffusion. An application to oceanic mixed layers is considered assuming the Mellor-Yamada 2½-level turbulence closure model to define the background level of turbulent mixing. For many realistic cases, Langmuir cells are predicted to dominate the vertical transport of momentum and density.

The problem of capillary-driven flow in a V-shaped surface groove is addressed. A nonlinear diffusion equation for the liquid shape is derived from mass conservation and Poiseuille flow conditions. A similarity transformation for this nonlinear equation is obtained and the resulting ordinary differential equation is solved numerically for appropriate boundary conditions. It is shown that the position of the wetting front is proportional to (Dt)½ where D is a diffusion coefficient proportional to the ratio of the liquid-vapour surface tension to viscosity and the groove depth, and a function of the contact angle and the groove angle. For flow into the groove from a sessile drop source it is shown that the groove angle must be greater than the contact angle. Certain arbitrarily shaped grooves are also addressed.

The Reynolds-averaged equations for turbulent flow over a deep-water sinusoidal gravity wave, z = acoskx ≡ h0(x), are formulated in the wave-following coordinates ζ, η, where x = ζ, z =η + h(ζ, η), h(ζ, 0) = h0(ζ) and h is exponentially small for kη [Gt ] 1, and closed by a viscoelastic consitutive equation (a mixing-length model with relaxation). This closure is derived from Townsend's boundary-layer-evolution equation on the assumptions that: the basic velocity profile is logarithmic in η + z0, where z0 is a roughness length determined by Charnock's similarity relation; the lateral transport of turbulent energy in the perturbed flow is negligible; the dissipation length is proportional to η + z0. A counterpart of the Orr-Sommerfeld equation for the complex amplitude of the perturbation stream function is derived and used to construct a quadratic functional for the energy transfer to the wave. A corresponding Galerkin approximation that is based on independent variational approximations for outer (quasi-laminar) and inner (shear-stress) domains yields an energy-transfer parameter β that is comparable in magnitude with that of the quasi-laminar model (Miles 1957) and those calculated by Townsend (1972) and Gent & Taylor (1976) through numerical integration of the Reynolds-averaged equations. The calculated limiting values of β for very slow waves, with Charnock's relation replaced by kz0 = constant, are close to those inferred from observation but about three times the limiting values obtained through extrapolation of Townsend's results.

The problem of gas motion in a tube closed at one end and driven at the other by an oscillating poston is studied theoretically. When the piston vibrates with a finite amplitude at the first acoustic resonance frequency, periodic shock waves are generated, travelling back and forth in the tube. A perturbation method, based on a small Mach number. M and a global mass conservation condition, is employed to formulate a solution of the problem in the form of two standing waves separated by a jump (shock front). By expanding the equations of motion in a series of a small parameter ε = M½, all hydrodynamic properties are predicted with an accuracy to second-order terms, i.e. to ε2. It is found that the first-order solution coincides with the previous theories of Betchov (1958) and Chester (1964), while additional terms predict a non-homogeneous time-averaged pressure along the tube. This prediction compares favourably with experimental results from the literature. The importance of the phenomenon is discussed in relation to different transport processes in resonance tubes.

The inertial waves excited in a uniformly rotating fluid passing through a long circular tube are studied numerically. The waves are excited either by a local deformation of the tube wall or by an obstacle located on the tube axis. When the flow is subcritical, i.e. when the phase and group velocity of the fastest wave mode in their long-wave limit are larger than the incoming axial flow velocity, the excited waves propagate upstream of the excited position. The non-resonant waves have many linear aspects, including the upstream-advancing speed of the wave and the coexisting lee wavelength. When the flow is critical (resonant), i.e. when the long-wave velocity is nearly equal to the axial flow velocity, the large-amplitude waves are resonantly excited. The time development of these waves is described well by the equation derived by Grimshaw & Yi (1993). The integro-differential equation, which describes the strongly nonlinear waves until the axial flow reversal occurs, can predict the onset time and position of the recirculation eddies observed in the solutions of the Navier-Stokes equations. The numerical results and the theory both show that the flow reversal most probably occurs on the tube axis and also when the waves are excited by a contraction of the tube wall. The structure of the recirculation eddies obtained in the solutions of the Navier-Stokes equations at Re = 105 is similar to the axisymmetric or ‘bubble-type’ breakdown observed in the experiments of the vortex-breakdown which used a different non-uniform (Burgers-type) rotation. In uniformly rotating fluids the formation of the recirculation eddies has not been observed in the previous numerical studies of vortex breakdown where a straight tube was used and thus the inertial waves were not excited. This shows that the generation of the recirculation eddies in this study is genuinely explained by the topographically excited large-amplitude inertial ‘waves’ and not by other ‘instability’ mechanisms. Since the wave cannot be excited in a straight tube even in the non-uniformly rotating flows, the generation mechanism of the recirculation eddies in this study is different from the previous numerical studies for the vortex breakdown. The occurrence of the recirculation eddies depends not only on the Froude number and the strength of the excitation source but also on the Reynolds number since the wave amplitude generally decreases by the viscous effects. Some relations to the experiments of vortex breakdown, which have been exclusively done for non-uniformly rotating fluids but done in a ‘non-uniform tube’, are discussed. The flow states, which are classified as supercritical, subcritical or critical in hydraulic terminology, changes along the flow when the upstream flow is near resonant conditions and a non-uniform tube is used.

We present a fresh theoretical analysis of fully developed forced convection in a fluid-saturated porous-medium channel bounded by parallel plates, with imposed uniform heat flux or isothermal condition at the plates. As a preliminary step, we obtain an ‘exact’ solution of the Brinkman-Forchheimer extension of Darcy's momentum equation for flow in the channel. This uniformly valid solution permits a unified treatment of forced convection heat transfer, provides the means for a deeper explanation of the physical phenomena, and also leads to results which are valid for highly porous materials of current practical importance.

Results are reported from a highly accurate, global numerical stability analysis of the periodic wake of a circular cylinder for Reynolds numbers between 140 and 300. The analysis shows that the two-dimensional wake becomes (absolutely) linearly unstable to three-dimensional perturbations at a critical Reynolds number of 188.5±1.0. The critical spanwise wavelength is 3.96 ± 0.02 diameters and the critical Floquet mode corresponds to a ‘Mode A’ instability. At Reynolds number 259 the two-dimensional wake becomes linearly unstable to a second branch of modes with wavelength 0.822 diameters at onset. Stability spectra and corresponding neutral stability curves are presented for Reynolds numbers up to 300.

Turbulent Boussinesq convection under the influence of rapid rotation (i.e. with comparable characteristic rotation and convection timescales) is studied. The transition to turbulence proceeds through a relatively simple bifurcation sequence, starting with unstable convection rolls at moderate Rayleigh (Ra) and Taylor numbers (Ta) and culminating in a state dominated by coherent plume structures at high Ra and Ta. Like non-rotating turbulent convection, the rapidly rotating state exhibits a simple power-law dependence on Ra for all statistical properties of the flow. When the fluid layer is bounded by no-slip surfaces, the convective heat transport (Nu − 1, where Nu is the Nusselt number) exhibits scaling with Ra2/7 similar to non-rotating laboratory experiments. When the boundaries are stress free, the heat transport obeys ‘classical’ scaling (Ra1/3) for a limited range in Ra, then appears to undergo a transition to a different law at Ra ≈ 4 × 107. Important dynamical differences between rotating and non-rotating convection are observed: aside from the (expected) differences in the boundary layers due to Ekman pumping effects, angular momentum conservation forces all plume structures created at flow-convergent sites of the heated and cooled boundaries to spin-up cyclonically; the resulting plume/cyclones undergo strong vortex-vortex interactions which dramatically alter the mean state of the flow and result in a finite background temperature gradient as Ra → ∞, holding Ra/Ta fixed.

Asymptotic analysis of ignition within the supersonic hydrogen/air mixing layer is performed using reduced mechanisms. Two distinct reduced mechanisms for the high-temperature and the low-temperature regimes are used depending on the characteristic temperature of the reaction zone relative to the crossover temperature at which the reaction rates of the H + 02 branching and termination steps are equal. Each regime further requires two distinct analyses for the hot-stream and the viscous-heating cases, depending on the relative dominance of external and internal ignition energy sources. These four cases are analysed separately, and it is shown that the present analysis successfully describes the ignition process by exhibiting turning point or thermal runaway behaviour in the low-temperature regime, and radical branching followed by thermal runaway in the high-temperature regime. Results for the predicted ignition distances are then mapped out over the entire range of the parameters, showing consistent behaviour with the previous one-step model analysis. Furthermore, it is demonstrated that ignition in the low-temperature regime is controlled by a larger activation energy process, so that the ignition distance is more sensitive to its characteristic temperature than that in the high-temperature regime. The ignition distance is also found to vary non-monotonically with the system pressure in the manner of the well-known hydrogen/oxygen explosion limits, thereby further substantiating the importance of chemical chain mechanisms in this class of chemically reacting boundary layer flows.

This paper describes the behaviour of a turbulent boundary layer on a smooth, axisymmetric body exposed to an adverse pressure gradient of sufficient strength to cause a short region of mean reverse flow ('separation’). The pressure distribution is tailored such that the boundary layer reattaches and then develops in a nominally zero pressure gradient. Hot-wire and pulsed-wire measurements are presented over the separated region and downstream of reattachment. The response of the turbulence quantities to separation and to reattachment is discussed, with emphasis on the relaxation behaviour after reattachment. Over the separation bubble, the response is characteristic of that seen by other workers: the Reynolds stresses in the inner region are reduced and stress peaks develop away from the wall. At reattachment, the skewness of the fluctuating wall shear stress vanishes, as it is known to do at separation. After reattachment, the outer-layer stresses decay towards levels typical of unperturbed boundary layers. But the inner-layer relaxation is unusual. As the viscous wall stress increases downstream of reattachment, the recovery does not start at the wall and travel outward via the formation of an ‘internal’ layer, the process observed in many other relaxing flows. In fact, the inner layer responds markedly more slowly than the outer layer, even though response times are shortest near the wall. It is concluded that the large-scale, outer structures in the turbulent boundary layer survive the separation process and interfere with the regeneration of Reynolds stresses in the inner region after reattachment. This behaviour continues for at least six bubble lengths (20 boundary-layer thicknesses) after reattachment and is believed to have profound implications for our understanding of the interaction between inner and outer layers in turbulent boundary layers.

Individual travelling cavitation bubbles were examined as they interacted with the flow over a two-dimensional hydrofoil. Each bubble was produced from a single nucleus created upstream of the hydrofoil, and the flow near the hydrofoil was visualized using particle imaging velocimetry (PIV). Travelling bubbles were observed to generate a local region of turbulence as they passed close to an unstable laminar boundary layer. By producing a locally turbulent region, the bubbles could temporarily sweep away a portion of attached cavitation at the foil midchord. Also, the bubbles were observed to strongly interact with a turbulent boundary layer, producing local regions of patch cavitation.

The aim of the paper is to present a new transport process which is likely to have great importance for understanding the internal constitution of the stars.

In order to set the problem in context, we first give a short presentation of the physical properties of the Sun and stars, described usually under the names Standard Solar Model or Standard Stellar Models (SSM). Next we show that an important shortcoming of SSM is that they do not explain the age dependence of the lithium deficiency of stars of known age: stars of galactic clusters and the Sun. It was suggested a long time ago that the presence of a macroscopic diffusion process in the radiative zone should be assumed, below the surface convective zone of solar-like stars. It is then possible for the lithium present in the convective zone to be carried to the thermonuclear burning level below the convective zone. The first assumption was that differential rotation generates turbulence and therefore that a turbulent diffusion process takes place. However, this model predicts a lithium abundance which is strongly rotation dependent, contrary to the observations. Furthermore, as the diffusion coefficient is large all over the radiative zone, it prevents the possibility of gravitational separation by diffusion and consequently leads to the impossibility of explaining the difference in helium abundance between the surface and the centre of the Sun. The consequence is obviously that we need to take into account another physical process.

Stars having a mass M < 1.3M[odot ] have a convective zone which begins close to the stellar surface and extends down to a depth which is an appreciable fraction of the stellar radius. In the convective zone, strong stochastic motions carry, at least partially, heat transfer. These motions do not vanish at the lower boundary and generate internal waves into the radiative zone. These random internal waves are at the origin of a diffusion process which can be considered as responsible for the diffusive transport of lithium down to the lithium burning level. This is certainly not the only physical process responsible for lithium deficiency in main sequence stars, but its properties open the way to a completely consistent analysis of lithium deficiency.

The model of generation of gravity waves is based on a model of heat transport in the convective zone by diving plumes. The horizontal component of the turbulent motion at the boundary of the convective zone is assumed to generate the horizontal motion of internal waves. The result is a large horizontal component of the diffusion coefficient, which produces in a short time an horizontally uniform chemical composition. It is known that gravity waves, in the absence of any dissipative process, cannot generate vertical mixing. Therefore, the vertical component of the diffusion coefficient is entirely dependent on radiative damping. It decreases quickly in the radiative zone, but is large enough to be responsible for lithium burning.

Owing to the radial dependence of velocity amplitude, the diffusion coefficient increases when approaching the stellar centre. However, very close to the centre, nonlinear dissipative and radiative damping of internal waves become large and the diffusion coefficient vanishes at the very centre.

The anisotropic behaviour of density-gradient fluctuations in stably stratified grid turbulence and the consequences for simplified (isotropic) estimates of scalar dissipation rates χ were experimentally studied in a thermally stratified wind tunnel at moderate Reynolds numbers (Reλ ≃ 20). Strong stable stratifications were attained, with Brunt-Väisälä frequency N as high as 4 rad s−1. The correlation method was used to estimate the mean-square cross-stream and streamwise density gradients. Cross-stream gradients were measured using two cold wires. The mean-square vertical gradients were found to become larger than the streamwise gradients by as much as a factor of 2.2 for the largest dimensionless buoyancy times (Nt = 7). This corresponds to a 40% error in the scalar dissipation estimates based on ∂θ/∂x alone, and assuming the validity of the isotropic relations. Gradient spectral relations show that this buoyancy-induced anisotropy persists at all length scales. Better closure of the scalar variance balance was attained than in previously reported measurements by other researchers. This is attributed to our use of cold-wire temperature sensors having larger length-to-diameter ratio than used in the previous measurements.