A non-Rayleigh mechanism of instability in horizontally homogeneous hydrodynamic systems consisting of two iimmiscible fluids and heated uniformly from above, i.e. ‘anticonvection’, was first investigated theoretically by Welander (1964) and more recently (and independently) by Gershuni & Zhukhovitsky (1980). This paper discusses the possibility of ‘anticonvection’ occurring in a water–air system, taking into account evaporation, stratification with respect to moisture, thermocapillary effects and the presence of a surface heat source at the water–air interface. For this purpose, a linear problem of stability is solved, in which the Rayleigh number analogues in each of the fluids are its eigenvalues in one case and the increments of disturbances in the other. It has been shown that taking into account evaporation and stratification with respect to moisture in the air reveals a new feedback in the system resulting in the disappearance of one of the previously known areas of anticonvection and the formation of new areas of instability. The mechanism of the oscillatory regime of the loss of stability in the system under study was found and considered in detail. Increments and wavelengths of the growing modes are calculated, and the possibility of experimental investigation of moist anticonvection in laboratory and field conditions is discussed.

Disturbances generated by a potential vortex moving past a small hump or dent on the otherwise smooth flat plate are considered. Features peculiar to this problem derive from the fact that the vortex is stuck with a fixed fluid particle; hence the nonlinear dependence of the pressure on the induced velocity field ensues even if the vortex intensity tends to zero. Formulation of the problem on a flow in the viscous wall sublayer given in canonical variables involves four similarity parameters for any particular shape of a roughness. The parallels between the process at hand and sound scattering from a boundary layer with a small obstacle at the bottom are indicated. Results from numerical integration of the boundary-value problem posed allow us to trace the evolution of the wave-packet structure depending on the potential vortex intensity. Overlapping of the peak wings and formation of an almost continuous spectrum in the Fourier decomposition of the signal serve as a guide for explaining the explosive development of the wave packet as distinct from the Tollmien–Schlichting wavetrain that has been registered experimentally.

The theory developed is applied to discussing the so-called bypass mode of transition provoked by external turbulence. Special emphasis is laid on flows in gas turbine engines where bypass transition plays a dominant role owing to extremely high free-stream turbulence levels.

New exact solutions of the Navier–Stokes equations are obtained for the unbounded and bounded oscillatory and impulsive tangential edgewise motion of touching half-infinite plates in their own plane. In contrast to Stokes classical solutions for the harmonic and impulsive motion of an infinite plane wall, where the solutions are separable or have a simple similarity form, the present solutions have a two-dimensional structure in the near region of the contact between the half-infinite plates. Nevertheless, it is possible to obtain relatively simple closed-form solutions for the flow field in each case by defining new variables which greatly simplify the r- and θ-dependence of the solutions in the vicinity of the contact region. These solutions for flow in a half-infinite space are then extended to bounded flows in a channel using an image superposition technique. The impulsive motion has application to the motion near geophysical faults, whereas the oscillatory motion has arisen in the design of a novel oscillating half-plate flow chamber for examining the effect of fluid shear stress on cultured cell monolayers.

Here we consider the mean velocity profile in the core region of a unidirectional turbulent flow, that is, a flow in which the turbulent motion is superposed upon parallel time-averaged streamlines. A kinematical variational principle, originally developed for three-dimensional free-turbulent motions, is shown to be applicable to significant parts of the velocity profiles for flows of both Couette and Poiseuille types. In addition to pure plane Couette and pure plane Poiseuille flows, the motions considered include a variety of admixtures produced by blowing through a wide flat channel one of whose walls comprises a belt which moves either in the direction of the blowing or counter to it.

The asymptotic solution of shock tube flows with homogeneous condensation is presented for both smooth, or subcritical, flows and flows with an embedded shock wave, or supercritical flows. For subcritical flows an analytical expression, independent of the particular theory of homogeneous condensation to be employed, that determines the condensation wave front in the rarefaction wave is obtained by the asymptotic analysis of the rate equation along pathlines. The complete solution is computed by an algorithm which utilizes the classical nucleation theory and the Hertz–Knudsen droplet growth law. For supercritical flows four distinct flow regimes are distinguished along pathlines intersecting the embedded shock wave analogous to supercritical nozzle flows. The complete global solution for supercritical flows is discussed only qualitatively owing to the lack of a shock fitting technique for embedded shock waves. The results of the computations obtained by the subcritical algorithm show that most of the experimental data available exhibit supercritical flow behaviour and thereby the predicted onset conditions in general show deviations from the measured values. The causes of these deviations are reasoned by utilizing the qualitative global asymptotic solution of supercritical flows.

Isolated vortices in a background flow of constant shear are studied. The flow is governed by the two-dimensional Euler equation. An infinite family of integral invariants, the Casimirs, constrain the flow to an isovortical surface. An isovortical surface consists of all flows that can be obtained by some incompressible deformation of a given vorticity field. It is proved that on every isovortical surface satisfying appropriate conditions there exists a stationary solution, stable to all exponentially growing disturbances, which represents a localized vortex that is elongated in the direction of the external flow. The most important condition is that the vorticity anomaly q in the vortex has the same sign as the external shear. The validity of the proof also requires that q is non-zero only in a finite region, and that 0 < qmin ≤ q ≤ qmax ≤ ∞ in this region (assuming the external shear to be positive).

The stability of an interface between inviscid fluids subjected to a high-frequency magnetic field has been examined previously by Garnier & Moreau (1983). The present paper extends that study to include the viscosity of both fluids in order to estimate the damping rates of the perturbations. Furthermore, Garnier & Moreau made an assumption that the frequency of oscillation of the interface could be neglected compared to the frequency of the applied field; they concluded that the applied field was not destabilizing. That (apparently reasonable) assumption has been lifted in the present work and the consequence is that the magnetic field is seen to lead to instability over a significant range of wavelengths. Application of this analysis to the electromagnetic casting of aluminium is discussed.

Experiments to investigate the formation mechanism and frequency of vortex shedding from a sphere in uniform shear flow were conducted in a water channel using flow visualization and velocity measurement. The Reynolds number, defined in terms of the sphere diameter and approach velocity at its centre, ranged from 200 to 3000. The shear parameter K, defined as the transverse velocity gradient of the shear flow non-dimensionalized by the above two parameters, was varied from 0 to 0.25. The critical Reynolds number beyond which vortex shedding from the sphere occurred was found to be lower than that for uniform flow and decreased approximately linearly with increasing shear parameter. Also, the Strouhal number of the hairpin-shaped vortex loops became larger than that for uniform flow and increased as the shear parameter increased.

The formation mechanism and the structure of vortex shedding were examined on the basis of series of photographs and subsequent image processing using computer graphics. The range of Reynolds number in the present investigation, extending up to 3000, could be classified into three regions on the basis of this study, and it was observed that the wake configuration did not differ substantially from that for uniform flow. Also, unlike the detachment point of vortex loops in uniform flow, which was irregularly located along the circumference of the sphere, the detachment point in shear flow was always on the high-velocity side.

In this article, we considered the steady response of an infinite unbroken floating ice sheet to the uniform motion of a rectangular load. It is assumed that the ice sheet is supported below by water of finite uniform depth. The ice displacement is expressed as a Fourier integral and the method of residues is combined with a numerical quadrature scheme to calculate the displacement of the surface. In addition, asymptotic estimates of the displacement are given for the far field and for the case where the aspect ratio of the load is large. The far-field approximation provides a good description of the surface displacement at distances greater than about one or two wavelengths away from the load. The behaviour of the steady solution at the two critical speeds Um, where the phase speed takes on its minimum, and Ug, the speed of gravity waves on shallow water, observed in Schulkes & Sneyd (1988) for an impulsively started line load is examined to see if these speeds are critical for two-dimensional loads. Unlike the steady part of the solution in Schulkes & Sneyd (1988), the solution is everywhere finite at the critical speed Ug. However, at the load speed Um, the solution is unbounded. At all load speeds the change in surface displacement is greatest near the load. A comparison with the experimental observations of Takizawa (1985) is made. Our calculations show a significant dependence of the amplitude of the ice displacement on the aspect ratio of the load. For wide loads the surface deflection has much more structure than does the surface displacement corresponding to loads of smaller aspect ratios.

The effect of the separation between hot wires in a crossed wire or X-probe on Reynolds stress measurements has been studied analytically and experimentally. Wyn-gaard's (1968) spectral analysis, which assumes isotropic turbulence, has been modified to include the effect of the tangential velocity component and possible asymmetries of the probe. The relaxation of the assumption of isotropy to one of homogeneity allows corrections to be made to Reynolds stress measurements obtained when the separation between the wires is in the spanwise direction. Measurements with two inclined hot wires in the central region of a fully developed turbulent channel flow provide reasonable support for the modified analysis. In the anisotropic wall region, the measurements provide reasonable support for the correction ratios which have been derived by assuming that turbulence is homogeneous in a plane parallel to the wall.

The effect of an unsteady shear flow on the planform of convection in a Boussinesq fluid heated from below is investigated. In the absence of the shear flow it is well-known, if non-Boussinesq effects can be neglected, that convection begins in the form of a supercritical bifurcation to rolls. Subcritical convection in the form of say hexagons can be induced by non-Boussinesq behaviour which destroys the symmetry of the basic state. Here it is found that the symmetry breaking effects associated with an unsteady shear flow are not sufficient to cause subcritical convection so the problem reduces to the determination of how the orientations of roll cells are modified by an unsteady shear flow. Recently Kelly & Hu (1993) showed that such a flow has a significant stabilizing effect on the linear stability problem and that, for a wide range of Prandtl numbers, the effect is most pronounced in the low-frequency limit. In the present calculation it is shown that the stabilizing effects found by Kelly & Hu (1993) do survive for most frequencies when nonlinear effects and imperfections are taken into account. However a critical size of the frequency is identified below which the Kelly & Hu (1993) conclusions no longer carry through into the nonlinear regime. For frequencies of size comparable with this critical size it is shown that the convection pattern changes in time. The cell pattern is found to be extremely complicated and straight rolls exist only for part of a period.

Numerical solutions are derived for a viscous, buoyant drop spreading below a free fluid surface. The drop has zero interfacial tension, and we consider viscosity contrasts 0.1 < λ < 10 with the surrounding fluid half-space. The density contrast between the drop and outer fluid is assumed to be small compared with the density contrast at the fluid surface. The numerical solutions for the approach and initial spread of the drop below the fluid surface are obtained using the boundary integral method. To facilitate an investigation over a larger range of viscosity contrasts and for longer time periods, we solve for the motion of gravity currents at the fluid surface. For this geometry we also solve the boundary integral equations for the cases λ = 0 and 1/λ = 0.

For extensive drop spreading, the motion is described by asymptotic solutions. Three asymptotic solutions are derived, which apply for different values of the viscosity contrast relative to the aspect ratio ((radial extent R)/(drop thickness a)). For very low-viscosity drops (λ [Lt ] a/R[ln(R/a)]-1), the greatest resistance to spreading occurs at the drop rim, and the asymptotic solution is found using slender body theory. Drops with intermediate viscosity contrast (a/R [Lt ] λ [Lt ] R/a) are slowed primarily by shear stresses at the lower drop surface, and a lubrication solution (Lister & Kerr 1989) applies. The greatest resistance to the spread of very viscous drops (λ [Gt ] R/a) comes from the radial stresses within the drop, and the asymptotic solution is independent of the outer fluid. All drops having 0 [Lt ] λ [Lt ] ∞ will eventually spread according to lubrication theory, when their aspect ratio becomes sufficiently large relative to viscosity contrast.

Theoretical results are compared with numerical and experimental results for drops and gravity currents spreading at a fluid surface. The solutions can be applied to aspects of planetary mantle flow where temperature variations cause significant viscosity contrasts. The low-viscosity solution has been applied to study the encounter of a hot, low-viscosity upwelling plume with a planet surface (Koch 1994). Here we apply the high-viscosity asymptotic solution to study how cold downwelling slabs spread at a depth of neutral buoyancy in the Earth's mantle.

The low Reynolds number buoyancy-driven translation of a deformable drop towards and through a fluid–fluid interface is studied using boundary integral calculations and laboratory experiments. The Bond numbers characteristic of both the drop and the initially flat fluid–fluid interface are sufficiently large that the drop and interface become highly deformed, substantial volumes of fluid may be entrained across the interface, and breakup of both interfaces may occur. Specifically, drops passing from a higher- to lower-viscosity fluid are extended vertically as they pass through the interface. For sufficiently large drop Bond numbers, the drop may deform continuously, developing either an elongating tail or enlarging cavity at the back of the drop, analogous to the deformation characteristic of a single deformable drop in an unbounded fluid. The film of fluid between the drop and interface thins most rapidly for those cases that the drop enters a more viscous fluid or has a viscosity lower than the surrounding fluids. In the laboratory experiments, bubbles entering a less viscous fluid are extended vertically and may break into smaller bubbles. The column of fluid entrained by particles passing through the interface may also break into drops. Further experiments with many rigid particles indicate that the spatial distribution of particles may change as the particles pass through interfaces: particles tend to form clusters.

A control-volume analysis of a hydraulic jump is used to obtain the mean vorticity downstream of the jump as a function of the Froude number. To do this it is necessary to include the conservation of angular momentum. The mean vorticity increases from zero as the cube of Froude number minus one, and, in dimensionless form, approaches a constant at large Froude number. Digital particle imaging velocimetry was applied to travelling hydraulic jumps giving centre-plane velocity field images at a frequency of 15 Hz over a Froude number range of 2–6. The mean vorticity determined from these images confirms the control-volume prediction to within the accuracy of the experiment. The flow field measurements show that a strong shear layer is formed at the toe of the wave, and extends almost horizontally downstream, separating from the free surface at the toe. Various vorticity generation mechanisms are discussed.

Direct numerical simulations of a highly constrained plane Couette flow are employed to study the dynamics of the structures found in the near-wall region of turbulent flows. Starting from a fully developed turbulent flow, the dimensions of the computational domain are reduced to near the minimum values which will sustain turbulence. A remarkably well-defined, quasi-cyclic and spatially organized process of regeneration of near-wall structures is observed. This process is composed of three distinct phases: formation of streaks by streamwise vortices, breakdown of the streaks, and regeneration of the streamwise vortices. Each phase sets the stage for the next, and these processes are analysed in detail. The most novel results concern vortex regeneration, which is found to be a direct result of the breakdown of streaks that were originally formed by the vortices, and particular emphasis is placed on this process. The spanwise width of the computational domain corresponds closely to the typically observed spanwise spacing of near-wall streaks. When the width of the domain is further reduced, turbulence is no longer sustained. It is suggested that the observed spacing arises because the time scales of streak formation, breakdown and vortex regeneration become mismatched when the streak spacing is too small, and the regeneration cycle at that scale is broken.

According to numerous experimental observations and theoretical models vibrated layers composed of large granules behave like a solid plastic body. In contrast, in this study experimental data are presented that reveal that, for constant vibration amplitudes A ≥ 1 cm with the frequency ω increasing from zero, all layers pass through three vibrational states, with the respective behaviours being as of (i) a solid plastic body, (ii) a liquid, (iii) a gas. In the liquid-like vibrational state transverse waves propagating along the layer width were observed. These waves were shown to be gravitational resonance waves, with the corresponding frequencies well correlated by the known formula for incompressible liquids. In the gas-like vibrational state compression (shock) and expansion waves propagating across the layer height, were observed.

A theoretical model for time-periodic collisional vibrational regimes was developed on the basis of the Euler-like equations of a granular gas composed of inelastic spheres. The model shows that the vibrational granular state (bed porosity, shock wave speed, granular pressure and kinetic energy) is inter alia governed by the dimensionless parameter V = (Aω)/(hmg)1/2, with g, hm being the gravitational acceleration and the height of the resting layer, respectively. This is in contrast with the previous studies, where the behaviour of vibrated granular layers was interpreted in terms of the dimensionless acceleration Δ = (Aω2)/g. The proposed model was tested by processing the data obtained from photographs of the particle distribution within vibrated layers. Theoretical predictions of the particle average concentration compared favourably with the experimental data.

Other phenomena observed in vibrated granular layers include the formation of caverns, circulatory motion of granules and synchronized periodic motion of two adjacent vibrated layers of different widths. The importance of the observed phenomena in relation to various technological processes involving bulk materials (vibromixing, vibroseparation, etc.) is discussed.

Experiments show that cavitation, if moderately developed, makes three kinds of vortical coherent structures visible inside the turbulent wake of a two-dimensional obstacle: Bénard–Kármán vortices, streamwise three-dimensional vortices and finally the vortices which appear on the borders of the very near wake. The latter, which are called here near-wake vortices, result by successive pairing in the first ones and there is some indication that they are also the origin of streamwise vortices. Cavitation is not a passive agent of visualization, as can be established on the basis of fundamental arguments, and it reacts with the flow as soon as it appears; when it is developed, it breaks the connection between the elongation rate and the vorticity rate of the vortex filaments. Then the subsequent evolution of a cavitating vortex and its final implosion are rather complicated. Despite its active character, cavitation in rotational structures, if properly interpreted, can give information of interest on the basic non-cavitating turbulent flow. By adapting a simple model due to Kermeen & Parkin (1957) and Arndt (1976), and counting near-wake vortices, it is possible to accurately predict the conditions of cavitation inception: consideration of coherent rotational structures is probably the best approach to explain, in an almost deterministic way, the large difference between the absolute value of the mean pressure coefficient at the obstacle base and the incipient cavitation number.