The investigation undertaken deals with the development of disturbances in a supersonic wake (free viscous layer and regular wake) behind a flat plate both in its linear and nonlinear stages. The influence of a number of factors (Mach and Reynolds numbers, temperature factor, thickness of the plate, length of its stern) on the wake stability and transition was studied. The development of the artificial disturbances in a wake at Mach number M∞ = 2 was investigated also.

It was found that compressibility of the flow (increasing Mach number) stabilizes the wake disturbances – their amplification rates decrease, and the transition point moves away from the model plate. Cooling of the model surface at M∞ ≈ 7 has a destabilizing influence on the development of disturbances in the wake. With increase of unit Reynolds number the beginning of transition in the wake moves forward to a rear critical point. It was confirmed that a distinctive maximum in the spectral distribution of fluctuations appears, corresponding to Strouhal number (based on frequency of this maximum) of 0.3. With the growth of the model thickness the disturbance amplification rates in the wake increase, which results in earlier transition of a laminar wake into turbulent one. With the growth of length of the plate stern, the position of the wake transition moves back accordingly, while the wake stability increases a little (though very unsignificantly). In the nonlinear stage of development of disturbances, the occurrence of a triad of waves, satisfying the resonant correlation of frequencies, and the growth of harmonics are observed. A monochromatic packet of waves of Tollmien–Schlichting type, rather narrow (in the transversal coordinate) in the boundary layers on a flat plate with an opposite wedge at the stern, was found to extend in the wake. The wake disturbances have a complex wave structure. At the Mach number of free flow 2.0, the three-dimensional disturbances are the most unstable in the wake.

We have performed a series of experiments on the dynamics of sedimenting, surface gravity currents. The physical situation concerns a current, with total density ρC, evolving at the surface of a fluid of greater density, ρA. In turn ρC is made up of interstitial fluid of density ρI and heavy particles with a concentration by weight c and a density ρP. Only the case of the release of a constant volume of particles and interstitial fluid has been considered in detail. It has been found that the sedimentation of the particles, plus some of the interstitial fluid, through the interface between the two fluids has a profound effect upon the motion of the current. When the rejected mixture of particles and upper- and lower-layer fluids reaches the bottom of the experimental tank it generates a secondary gravity current which in turn interacts with the primary current to further modify its behaviour. Using simple models we have been able to rationalize the observations and reveal the dynamical balances which appear to be important. A subsidiary experiment and analysis on the flux characteristics of the interface have been performed in order to further clarify the important effects of the particle motion through that region.

Dispersion of fluid particles in non-homogeneous turbulence was studied for fully developed flow in a channel. A point source at a distance of 40 wall units from the wall is considered. Data obtained by carrying out experiments in a direct numerical simulation (DNS) are used to test a stochastic model which utilized a modified Langevin equation. All of the parameters, with the exception of the time scales, are obtained from Eulerian statistics. Good agreement is obtained by making simple assumptions about the spatial variation of the time scales.

A series of laboratory experiments and numerical simulations have been performed to investigate the rapid fluid-like flow of a finite mass of granular material down a chute with partial lateral confinement. The chute consists of a section inclined at 40° to the horizontal, which is connected to a plane run-out zone by a smooth transition. The flow is confined on the inclined section by a shallow parabolic cross-slope profile. Photogrammetric techniques have been used to determine the position of the evolving boundary during the flow, and the free-surface height of the stationary granular deposit in the run-out zone. The results of three experiments with different granular materials are presented and shown to be in very good agreement with numerical simulations based on the Savage–Hutter theory for granular avalanches. The basal topography over which the avalanche flows has a strong channelizing effect on the inclined section of the chute. As the avalanche reaches the run-out zone, where the lateral confinement ceases, the head spreads out to give the avalanche a characteristic ‘tadpole’ shape. Sharp gradients in the avalanche thickness and velocity began to develop at the interface between the nose and tail of the avalanche as it came to rest, indicating that a shock wave develops close to the end of the experiments.

The motion of three interacting point vortices with zero net circulation in a periodic parallelogram defines an integrable dynamical system. A method for solving this system is presented. The relative motion of two of the vortices can be ‘mapped’ onto a problem of advection of a passive particle in ‘phase space’ by a certain set of stationary point vortices, which also has zero net circulation. The advection problem in phase space can be written in Hamiltonian form, and particle trajectories are given by level curves of the Hamiltonian. The motion of individual vortices in the original three-vortex problem then requires one additional quadrature. A complicated structure of the solution space emerges with a large number of qualitatively different regimes of motion. Bifurcations of the streamline pattern in phase space, which occur as the impulse of the original vortex system is changed, are traced. Representative cases are analysed in detail, and a general procedure is indicated for all cases. Although the problem is integrable, the trajectories of the vortices can be surprisingly complicated. The results are compared qualitatively to vortex paths found in large-scale numerical simulations of two-dimensional turbulence.

Unsteady circular jets are treated experimentally and numerically. The time evolution of circular pulse jets is investigated systematically for a wide range of jet strength, with the focus on the jet evolution, in particular the formation processes of Mach disks in the middle stage and of shock-cell structures in the later stage. It is shown that unsteady second shocks are realized for all sonic underexpanded jets and they either breed conical shocks for lower pressure ratios or truncated cones (Mach disk and reflected shock) for higher pressure ratios. The vortex ring produced near the nozzle lip plays an important role in the formation of the shock-cell structure. In particular, interactions between the vortex ring and the Mach disk connected with a strong second shock affect remarkably the formation process of the first shock cell. Different formation processes of the first cell structure are found. It is also made clear that the Kelvin–Helmholtz instability along slip surfaces originating from the triple point at the outer edge of the Mach disk is responsible for the generation of large second vortices which entrain the first vortex. This results in strong mixing between the primary jet and surrounding gas for higher pressure ratios. Numerical simulations with a TVD-scheme for the Euler equations are also performed and the numerical results are compared with the experimental ones to understand and predict the flow characteristics of the pulse jets.

This paper describes the results of a study examining the flow and acoustic characteristics of an axisymmetric supersonic jet issuing from a sonic and a Mach 1.5 converging–diverging (C–D) nozzle and impinging on a ground plane. Emphasis is placed on the Mach 1.5 nozzle with the sonic nozzle used mainly for comparison. A large-diameter circular plate was attached at the nozzle exit to measure the forces generated on the plate owing to jet impingement. The experimental results described in this paper include lift loss, particle image velocimetry (PIV) and acoustic measurements. Suckdown forces as high as 60% of the primary jet thrust were measured when the ground plane was very close to the jet exit. The PIV measurements were used to explain the increase in suckdown forces due to high entrainment velocities. The self-sustained oscillatory frequencies of the impinging jet were predicted using a feedback loop that uses the measured convection velocities of the large-scale coherent vortical structures in the jet shear layer. Nearfield acoustic measurements indicate that the presence of the ground plane increases the overall sound pressure levels (OASPL) by approximately 8 dB relative to a corresponding free jet. For moderately underexpanded jets, the influence of the shock cells on the important flow features was found to be negligible except for close proximity of the ground plane.

We present experimental force and power measurements demonstrating that the power required to propel an actively swimming, streamlined, fish-like body is significantly smaller than the power needed to tow the body straight and rigid at the same speed U. The data have been obtained through accurate force and motion measurements on a laboratory fish-like robotic mechanism, 1.2 m long, covered with a flexible skin and equipped with a tail fin, at Reynolds numbers up to 106, with turbulence stimulation. The lateral motion of the body is in the form of a travelling wave with wavelength λ and varying amplitude along the length, smoothly increasing from the front to the tail end. A parametric investigation shows sensitivity of drag reduction to the non-dimensional frequency (Strouhal number), amplitude of body oscillation and wavelength λ, and angle of attack and phase angle of the tail fin. A necessary condition for drag reduction is that the phase speed of the body wave be greater than the forward speed U. Power estimates using an inviscid numerical scheme compare favourably with the experimental data. The method employs a boundary-integral method for arbitrary flexible body geometry and motions, while the wake shed from the fish-like form is modelled by an evolving desingularized dipole sheet.

A fluid stably stratified by a salinity gradient and enclosed between two vertical boundaries can become unstable when it is subjected to a temperature difference between the walls. The linear stability of such a fluid in a vertical slot is investigated. Errors in earlier results are found, confirming recent results of Young & Rosner (1998). Four different asymptotic regimes on the stability boundary are identified. One of these, the limit of a strong salinity gradient, has previously been analysed. The analyses of the separate asymptotic limits of weak salinity gradient, large temperature difference and small wavenumber are also given. These four cases make up much of the total boundary between stability and instability for double-diffusive instabilities in a vertical slot, and so most of this boundary can be mapped out for general Prandtl numbers and salt/heat diffusivity ratios using these results.

A weakly nonlinear analysis of the downstream evolution of weakly unstable disturbances in a stably stratified mixing layer with a large Reynolds number is carried out. No other requirements are imposed upon velocity and density profiles, thus making it possible to overcome the restrictions placed in earlier studies (Brown & Stewartson 1978; Brown et al. 1981; Churilov & Shukhman 1987, 1988) by a particular choice of weakly supercritical flow models assuming symmetry. For each of the two critical layer regimes possible here, viscous and unsteady, evolution equations are obtained, their solutions and competition between nonlinearities in the course of instability development are analysed, and evolution scenarios for unstable disturbances are constructed for different levels of their supercriticality. It is established that the regime with a nonlinear critical layer does not arise in an evolutionary manner, except for the previously studied case of a weak stratification (Shukhman & Churilov 1997). It is shown that while in the viscous critical layer regime the relaxation of assumptions of the symmetry and weak supercriticality of the flow produces no fundamental changes in the theory, in the unsteady critical layer regime a new (non-dissipative cubic) nonlinearity appears which governs the instability development on equal terms with two already known nonlinearities. Results are illustrated by calculations for two families of flow models with a controlled degree of asymmetry.

A stochastic model, implemented as a Monte Carlo simulation, is used to compute statistical properties of velocity and scalar fields in stationary and decaying homogeneous turbulence, shear flow, and various buoyant stratified flows. Turbulent advection is represented by a random sequence of maps applied to a one-dimensional computational domain. Profiles of advected scalars and of one velocity component evolve on this domain. The rate expression governing the mapping sequence reflects turbulence production mechanisms. Viscous effects are implemented concurrently.

Various flows of interest are simulated by applying appropriate initial and boundary conditions to the velocity profile. Simulated flow microstructure reproduces the −5/3 power-law scaling of the inertial-range energy spectrum and the dissipation-range spectral collapse based on the Kolmogorov microscale. Diverse behaviours of constant-density shear flows and buoyant stratified flows are reproduced, in some instances suggesting new interpretations of observed phenomena. Collectively, the results demonstrate that a variety of turbulent flow phenomena can be captured in a concise representation of the interplay of advection, molecular transport, and buoyant forcing.

An experimental study of entrainment of sand-sized particles in turbulent boundary layers has been performed in a high-speed wind tunnel at square-pulse flow speeds of 27 to 101 ms−1 and for soil bed lengths varying from 2.1 to 5.8 m. Because of high particle drag-to-weight ratios (D/W = 100–1000) and friction velocities (uf) well above soil threshold friction velocities (uft; 10 [les ] uf/uft [les ] 40), the present results correspond to the suspension regime of dust lofting, in contrast to low-speed saltation flows (1 [les ] uf/uft [les ] 5; D/W / 15). Results are obtained characterizing particle entrainment for both a natural soil (White Sands Missile Range (WSMR) sand; 50% finer-by-weight diameter, D50 = 180 μm) and a monosized sand sample (Ottawa sand, D50 = 250 μm). Measurements of local boundary layer velocities and dust densities were performed with traversing state-of-the-art diagnostics. Scouring rate data (0.015 [les ] ms [les ] 0.30 g cm−2 s−1) and streamwise soil flux (10 [les ] Q [les ] 150 g cm−1 s−1) as a function of bed length and velocity were determined.

Scouring rates were found to increase as the 3/2-power of velocity, but decay as the inverse square root of dust bed length. Corresponding streamwise soil fluxes (also known as soil loss rates) increased to the 3/2-power of velocity in contrast to the cube power dependence for low-speed results (ufree-stream [les ] 15 m s−1; Q [les ] 1.5 g cm−1 s−1). Comparison of scouring rate data (from pre/post-test soil loss measurements) with derived data based on the rate of change of streamwise flux with distance was favourable. WSMR rates were always lower than Ottawa sand rates, a result consistent with the lower repose angle for the Ottawa sand sample.

Both sets of soil data demonstrate that dust edges extend vertically to higher elevations than corresponding velocity edges. This result implies that the turbulent Schmidt number for the present flows is less than unity and of the order of 0.7. Favourable collapsing of the scouring rate data base was achieved when measured rates were normalized by the friction velocity mass flux, square root of edge Mach number and sand repose angle ratio. A universal rate of 0.3±0.1 correlated well with the bulk of the data.

Natural convection in a rectangular cavity is examined, utilizing the second law of thermodynamics. Through an application of the second law the rate of entropy generation associated with the convective pattern changes is evaluated for the onset of natural convection in a cavity with free boundaries, for which an exact solution is sought, as well as with rigid boundaries which is studied numerically. Entropy to be generated from the perturbed temperature and velocity fields is shown to depend on AR (aspect ratio of the cavity), Rac (the critical Rayleigh number) and a non-dimensional parameter, Ω, which is related to the ratio of entropy generation by viscous friction to that by thermal transport. The convective pattern change is related to a change in the spatial distributions of the rate of entropy generation due to heat transfer and due to dissipation, demonstrating that an application of the second law helps examine convective pattern changes quantitatively by dealing with temperature and velocity fields in a unified manner.