Three components of velocity fluctuations were measured in a plane turbulent wall jet which was modulated periodically by a sinusoidal pressure fluctuation in its settling chamber. The experiment was carried out in a closed-loop wind tunnel in the absence of an external stream at Reynolds number Rej = Ujb/v = 6900 and Strouhal number Stj = fb/Uj = 9.5 × 10−3, where b is the width of the slot from which the jet emerges at an efflux velocity Uj. A detailed comparison is provided with similar measurements made in a natural, unexcited turbulent wall jet. One of the purposes of this experiment was to establish the kinetic energy transfers which take place in the wall jet under controlled perturbations. More specifically, we were interested in determining the interactions occurring between the steady mean flow, the coherent eddies and the ‘random’ turbulent fluctuations. We used the triple decomposition of the equations of motion as suggested by Hussain (1983) and quickly observed that the usefulness of this decomposition depends on the definition of coherent motion, which is ambiguous in the presence of phase jitter. Two such definitions were considered and the results are discussed in the experimental case-study provided. An attempt is made to define quantitatively the intensities of the coherent motion in externally excited, wallbounded flows. It is a case-study and not a parametric investigation aimed at maximizing the effects of period oscillations on the wall jet.

A procedure for deriving equations of average unsteady flows in random media of stationary conductivity is developed. The approach is based on applying perturbation methods in the Fourier-Laplace domain. The main result of the paper is the formulation of an effective Darcy's Law relating the mean velocity to the mean head gradient. In the Fourier-Laplace domain the averaged Darcy's Law is given by a linear local relation. The coefficient of proportionality depends only on the heterogeneity structure and is called the effective conductivity tensor. In the physical domain this relation has a non-local structure and it defines the effective conductivity as an integral operator of convolution type in time and space. The mean head satisfies an unsteady integral-differential equation. The kernel of the integral operator is the inverse Fourier-Laplace transform (FLT) of the effective conductivity tensor. The FLT of the mean head is obtained as a product of two functions: the first describes the FLT of the mean head distribution in a homogeneous medium; the second corrects the solution in a homogeneous medium for the given spatial distribution of heterogeneities. This function is simply related to the effective conductivity tensor and determines the fundamental solution of the governing equation for the mean head. These general results are applied to derive the effective conductivity tensor for small variances of the conductivity. The properties of unsteady average flows in isotropic media are studied by analysing a general structure of the effective Darcy's Law. It is shown that the transverse component of the effective conductivity tensor does not affect the mean flow characteristics. The effective Darcy's Law is obtained as a convolution integral operator whose kernel is the inverse FLT of the effective conductivity longitudinal component. The results of the analysis are illustrated by calculating the effective conductivity for one-, two- and three-dimensional flows. An asymptotic model of the effective Darcy's Law, applicable for distances from the sources of mean flow non-uniformity much larger than the characteristic scale of heterogeneity, is developed. New bounds for the effective conductivity tensor, namely the effective conductivity tensor for steady non-uniform average flow and the arithmetic mean, are proved for weakly heterogeneous media.

Convection driven by spatially variable heat transfer across the water surface is an important transport mechanism in many geophysical applications. This flow is modelled in a rectangular tank with an aspect ratio, H/L, of 0.1 (where H and L are the tank height and length, respectively). Heat fluxes are applied through horizontal copper plates of length 0.1 L located at the top of one end of the tank and at the bottom of the other end. Experimental flows have been forced with heating at the bottom of the tank and cooling at the top, which gives rise to unstable convection in the end regions. Using water and a glycerol/water mix as the experimental fluids, flow visualization studies and measurements of temperature, velocity and heat flux have been made. Flow visualization studies revealed that complex unsteady turbulent flows occupied the end regions, while cubic velocity profiles characterized the horizontal laminar flow in the interior of the tank. Simple scaling arguments were developed for steady-state velocity and temperature fields, which are in good agreement with the experimental data. In the current experiments the portion of the plates closest to the tank interior (and to the tank endwall in the case of the glycerol/water experiments) were occupied by laminar boundary layers, while the remainder of the plates were occupied by turbulent flow. An effective Rayleigh number Ra* was defined, based upon the portion of the plate occupied by turbulent flow, as was a corresponding modified Nusselt number Nu*. The heat transfer was well predicted by classical Rayleigh-Bénard scaling with the Nusselt number Nu* ∼ Ra*1/3. The range of Ra* was 4.3 × 105 ≤ Ra* ≤ 1.7 × 108. Scaling arguments predicted the triple occupancy of the plates by differing boundary layer regimes within the range of 105 ≤ Ra* ≤ 1014.

Unsteady flow in a circular conduit with a smooth expansion is studied in detail by numerical integration of the equation of motion in the axisymmetric approximation. The values of governing parameters are chosen to be relevant to medical problems, and the geometry corresponds to a scenario of post-surgical conditions. The flow determined by an oscillatory volume is characterized by a sequence of vortex rings moving in the expanded part of the tube. The development of wall shear stress is governed by the separated translating vorticity which induces an evolving band of large intensity for about a complete oscillation cycle. This influences the dynamics of unsteady separation whose space-time development has revealed features of some generality which have been classified. The time variation of the pressure jump is dominated by inertial effects. The dependence of the details of the flow on the dimensionless parameters has been investigated systematically. The results obtained here have been compared with experimental and numerical studies of similar problems, similarities have been pointed out and differences discussed. Finally, the relevance of these results to physiological applications has been quantified by simulating the flow induced by a pulsatile flow rate.

Vapours of retrograde fluids, i.e. media with large values of the specific heats, may have the remarkable property that sonic conditions are reached three times rather than once during isentropic expansion or compression. As a result, the acceleration of such a fluid through a converging-diverging Laval nozzle under steady flow conditions may lead to the occurrence of an expansion shock discontinuity. Theoretical considerations then suggest that nozzles with two throats should be designed to achieve a full shock-free subsonic-supersonic expansion.

In this study the unsteady flow of a dense, retrograde gas through slender nozzles (with one and two throats) is considered. The combination of the Navier-Stokes equations supplemented with a non-classical equation of state for the fluid yields a generalized wave equation, with its validity restricted to flow conditions near the critical value M = 1. This equation is used to study the transition process which sets in if a steady subsonic solution is perturbed by lowering the pressure at the end of the nozzle.

Using direct simulations of the incompressible Navier-Stokes equations with rigid upper and lower boundaries at fixed temperature and periodic sidewalls, scaling with respect to Rayleigh number is determined. At large aspect ratio (6:6:1) on meshes up to 288 × 288 × 96, a single scaling regime consistent with the properties of ‘hard’ convective turbulence is found for Pr = 0.7 between Ra = 5 × 104 and Ra = 2 × 107. The properties of this regime include Nu ∼ RaβT with βT = 0.28 ≈ 2/7, exponential temperature distributions in the centre of the cell, and velocity and temperature scales consistent with experimental measurements. Two velocity boundary-layer thicknesses are identified, one outside the thermal boundary layer that scales as Ra−1/7 and the other within it that scales as Ra−3/7. Large-scale shears are not observed; instead, strong local boundary-layer shears are observed in regions between incoming plumes and an outgoing network of buoyant sheets. At the highest Rayleigh number, there is a decade where the energy spectra are close to k−5/3 and temperature variance spectra are noticeably less steep. It is argued that taken together this is good evidence for ‘hard’ turbulence, even if individually each of these properties might have alternative explanations.

Evidence for the existence in the nearshore surf zone of energetic alongshore propagating waves with periods O(100 s) and wavelengths O(100 m) was found from observations by Oltman-Shay et al. (1989). These oscillations have wavelengths that are much too short to be surface gravity waves at the observed frequencies. The existence and properties of the wave-like motions were found to be related to the presence, strength and direction of an alongshore current in the surf zone. Based on a linear stability analysis of a mean alongshore current with offshore scale O(100 m), Bowen & Holman (1989) described these fluctuations as unstable waves associated with a shear instability. Good agreement of wavelengths and wave speeds from observations and from predictions based on the most unstable linear mode was obtained by Dodd et al. (1992). The nonlinear dynamics of finite-amplitude shear instabilities of alongshore currents in the surf zone are studied here utilizing numerical experiments involving finite-difference solutions to the shallow water equations for idealized forced dissipative initial-value problems. Plane beach (i.e. constant slope) geometry is used with periodic boundary conditions in the alongshore direction. Forcing effects from obliquely incident breaking surface waves are approximated by an across-shore-varying steady force in the alongshore momentum equation. Dissipative effects are modelled by linear bottom friction. The solutions depend on the dimen-sionless parameter Q, which is the ratio of an advective to a frictional time scale. The steady frictionally balanced, forced, alongshore current is linearly unstable for Q less than a critical value Qc. The response of the fluid is studied for different values of ΔQ = Qc - Q. In a set of experiments with the alongshore scale of the domain equal to the wavelength 2π/k0 of the most unstable linear mode, disturbances that propagate alongshore in the direction of the forced current with propagation velocities similar to the linear instability values are found for positive ΔQ. The disturbances equilibrate with constant amplitude for small ΔQ and with time-varying amplitudes for larger ΔQ. For increasing values of ΔQ the behaviour of this fluid system, as represented in a phase plane with area-averaged perturbation kinetic energy and area-averaged energy conversion as coordinates, is similar to that found in low-dimensional nonlinear dynamical systems including the existence of non-trivial steady solutions, bifurcation to a limit cycle, period-doubling bifurcations, and irregular chaotic oscillations. In experiments with the alongshore scale of the domain substantially larger than the wavelength of the most unstable linear mode, different behaviour is found. For small positive ΔQ, propagating disturbances grow at wavelength 2π/k0. If ΔQ is small enough, these waves equilibrate with constant or spatially varying amplitudes. For larger ΔQ, unstable waves of length 2π/k0 grow initially, but subsequently evolve into longer-wavelength nonlinear propagating steady or unsteady wave-like disturbances with behaviour dependent on ΔQ. The eventual development of large-scale nonlinear propagating disturbances appears to be a robust feature of the flow response over plane beach geometry for moderate, positive values of ΔQ and indicates the possible existence in the nearshore surf zone of propagating finite-amplitude shear waves with properties not directly related to results of linear theory.

Results from a direct numerical simulation of a shear-free turbulent mixing layer are presented. The mixing mechanisms associated with the turbulence are isolated. In the first set of simulations, the turbulent mixing layer decays as energy is exchanged between the layers. Energy spectra with E(k) ∼ k2 and E(k) ∼ k4 dependence at low wavenumber are used to initialize the flow to investigate the effect of initial conditions. The intermittency of the mixing layer is quantified by the skewness and kurtosis of the velocity fields: results compare well with the shearless mixing layer experiments of Veeravalli & Warhaft (1989). Eddies of size of the integral scale (k3/2/∈) penetrate the mixing layer intermittently, transporting energy and causing the layer to grow. The turbulence in the mixing layer can be characterized by eddies with relatively large vertical kinetic energy and vertical length scale. In the second set of simulations, a forced mixing layer is created by continuously supplying energy in a local region to maintain a stationary kinetic energy profile. Assuming the spatial decay of r.m.s. velocity is of the form u &∞ yn, predictions of common two-equation turbulence models yield values of n ranging from -1.25 to -2.5. An exponent of -1.35 is calculated from the forced mixing layer simulation. In comparison, oscillating grid experiments yield decay exponents between n = -1 (Hannoun et al. 1989) and n = -1.5 (Nokes 1988). Reynolds numbers of 40 and 58, based on Taylor microscale, are obtained in the decaying and forced simulations, respectively. Components of the turbulence models proposed by Mellor & Yamada (1986) and Hanjalić & Launder (1972) are analysed. Although the isotropic models underpredict the turbulence transport, more complicated anisotropic models do not represent a significant improvement. Models for the pressure-strain tensor, based on the anisotropy tensor, performed adequately.

The effect of the nose radius of a body on boundary-layer receptivity is analysed for the case of a symmetric mean flow past a body with a parabolic leading edge. Asymptotic methods based on large Reynolds number are used, supplemented by numerical results. The Mach number is assumed small, and acoustic free-stream disturbances are considered. The case of free-stream acoustic waves, propagating obliquely to the symmetric mean flow is considered. The body nose radius, rn, enters the theory through a Strouhal number, S = ωrn/U, where ω is the frequency of the acoustic wave and U is the mean flow speed. The finite nose radius dramatically reduces the receptivity level compared to that for a flat plate, the amplitude of the instability waves in the boundary layer being decreased by an order of magnitude when S = 0.3. Oblique acoustic waves produce much higher receptivity levels than acoustic waves propagating parallel to the body chord.

An investigation of topological features of the velocity gradient field of turbulent channel flow has been carried out using results from a direct numerical simulation for which the Reynolds number based on the channel half-width and the centreline velocity was 7860. Plots of the joint probability density functions of the invariants of the rate of strain and velocity gradient tensors indicated that away from the wall region, the fine-scale motions in the flow have many characteristics in common with a variety of other turbulent and transitional flows: the intermediate principal strain rate tended to be positive at sites of high viscous dissipation of kinetic energy, while the invariants of the velocity gradient tensor showed that a preference existed for stable focus/stretching and unstable node/saddle/saddle topologies. Visualization of regions in the flow with stable focus/stretching topologies revealed arrays of discrete downstream-leaning flow structures which originated near the wall and penetrated into the outer region of the flow. In all regions of the flow, there was a strong preference for the vorticity to be aligned with the intermediate principal strain rate direction, with the effect increasing near the walls in response to boundary conditions.

The solutions of the nonlinear and linearized Navier-Stokes equations are computed to investigate the instabilities and the secondary two- and three-dimensional regimes in the flow of an incompressible viscous fluid in a thin gap between two concentric differentially rotating spheres. The numerical technique is finite difference in the radial direction, spectral in the azimuthal direction, and pseudo-spectral in the meridional direction. The study follows the experiments by Yavorskaya, Belyaev and co-workers in which a variety of steady axisymmetric and three-dimensional travelling wave secondary regimes was observed in the case of a thin layer and both boundary spheres rotating. In agreement with the experimental results three different types of symmetry-breaking primary bifurcations of the basic equilibrium are detected in the parameter range under consideration.

Hydrodynamic diffusion refers to the fluctuating motion of non-Brownian particles (or droplets or bubbles) in a dispersion, which occurs due to multiparticle interactions. For example, in a concentrated sheared suspension, particles do not move along streamlines but instead exhibit fluctuating motions as they tumble around each other (figure 1a). This leads to a net migration of particles down gradients in particle concentration and in shear rate, due to the higher frequency of encounters of a test particle with other particles on the side of the test particle which has higher concentration or shear rate. As another example, suspended particles subject to sedimentation or fluidization do not generally move relative to the fluid with a constant velocity, but instead experience diffusion-like fluctuations in velocity due to interactions with neighbouring particles and the resulting variation in the microstructure or configuration of the suspended particles (figure 1b). In flowing granular materials, the particles interact through direct collisions or contacts; these collisions also cause the particles to undergo fluctuating motions characteristic of diffusion processes. Although the existence and importance of hydrodynamic diffusion of particles have been embraced only in the past several years, the subject has already captured the attention of a growing number of researchers in several diverse fields (e.g. suspension mechanics, fluidization, materials processing, and granular flows).

We consider the large-time behaviour of the disturbances associated with an initial acceleration of a body in or near a free surface. As a canonical problem, we study the case of a body starting impulsively from rest to a constant velocity U. For a constant-strength translating point source (or dipole) started impulsively, it is known that the unsteady part of the Green function oscillates at the critical frequency ωc=g/4U (g is the gravitational acceleration) with an amplitude that decays with time, t, as t−1/2 and t−1 for t [Gt ] 1 in two (Havelock 1949) and three (Wehausen 1964) dimensions respectively. These classical results turn out to be non-realistic in that for an actual body, the associated source strengths are in general time dependent and a priori unknown, and must together satisfy the kinematic condition on the body boundary. We consider such an initial-boundary-value problem using a transient wave-source distribution on the body surface. Through asymptotic analyses, the unsteady behaviour of the solution at large time is obtained explicitly. Specifically, we show that for a general class of bodies satisfying a simple geometric condition (Γ ≠ 0), the decay rate of the transient oscillations (at frequency ωc) in the wave resistance and velocity potential is an order of magnitude faster: as t−3/2 and t−2, as t → ∞, in two and three dimensions respectively. For body geometries satisfying T = 0, for which the single source is a special case, the classical Green function results are recovered. These results are confirmed by an analysis in the frequency domain and substantiated by direct time-domain numerical simulations.

The flows considered here are those where a container or confined region is being filled by a substantial flow of liquid. The case of especial interest is where the incoming flow fills a large part of the cross-section of the container, for example where a nearly full flowing conduit has one end suddenly closed and hence fills rapidly, or where a water wave propagates close to the under surface of a horizontal structure and then rapidly fills the available space. These flows are taken to be so rapid that gravity is unimportant and yet not so violent that compressibility effects become significant. Important features, such as the greatly enhanced pressures and a thin high-velocity return jet are evaluated. The calculated pressures are very significantly greater than those associated with the incoming flow velocity and can be especially large when there is little clearance between the flow and the container boundary. One of many possible applications is in the extension of cracks and openings in coastal cliffs and structures. The flows could also be relevant to estimating the forces on the underside of some marine structures. A simple two-dimensional irrotational free-surface solution is found for the flow, which is steady in a suitably moving frame of reference.

Reversing the direction of one of these filling flows gives the case of a narrow high-speed jet which may be used to flush liquid out of cavities and containers. The optimum size of jet is calculated.