This paper reports an experimental investigation of the instantaneous structure of a supersonic turbulent boundary layer (M = 2.86, Reθ = 82000) over a short region of longitudinal concave surface curvature. The radius of curvature was 12 initial boundary-layer thicknesses and the turning angle was 16°. Severe distortion of the boundary layer occurred, as evidenced by an alteration of the mean velocity profiles and an increase in wall shear stress of 125%. The large-scale organized motions in the boundary layer were significantly altered as illustrated by changes in the character of the mass flux ‘fronts’ (large gradients in the fluctuating streamwise mass flux).

Laminar vortex pairs with small Froude number were generated by a submerged delta wing at negative angle of attack or by a pair of vertically oriented, counter-rotating flaps. The vortex pairs thus generated rise and interact with the free surface. The surface and subsurface flow field was studied using flow visualization and particle image velocimetry. Initial surface deformations, striations, are shown to be caused by stretching and interaction of cross-stream vortices near the surface. With small amounts of surface contamination, contamination fronts (producing Reynolds ridges) form on the surface and secondary vorticity, generated beneath the surface beyond the fronts, rolls up to form vortices with opposite rotation outboard of the primary vortices. The circulation associated with the secondary vortices is as much as 1/3 that of the primary vortices. The secondary vortices cause the primary vortex pair to rebound from the surface. Slight surface deformations, scars, are caused by the primary and secondary vortices.

An experiment in a supersonic mixing layer at convective Mach number Mc = 0.62 was performed to study the evolution of a flow from a turbulent boundary layer to a fully developed mixing layer. Turbulence measurements were taken and are interpreted with a diffusion model, which is well adapted to these flows. These measurements show that the level of turbulent friction varies with Mc proportionally to the spread rate. Our measurements appear to be consistent with the spreading rate of the layer and suggest that compressibility does not significantly alter the diffusion scheme at Mc = 0.62. This is also confirmed by a review of the existing data. Moreover, in the present flow, the anisotropy of the turbulent stresses seems to be affected by compressibility. The evolution of the radiated noise shows an increase corresponding to the developed part of the layer. Quantitative assessments of compressibility effects on turbulent quantities are given and are related to modifications in the structure of the flow.

The behaviour of dipolar vortices in a rotating fluid with a sloping bottom (simulating the variation of the Coriolis parameter on the Earth, with the direction of steepest bottom slope corresponding with the northern direction) has been investigated in the laboratory. Dipoles were generated by moving a vertical cylinder through the fluid. Dye photographs provided qualitative information, whereas quantitative information about the evolving flow field was obtained by streak photography. Dipoles initially directed under a certain angle relative to the west–east axis showed meandering or cycloid-like trajectories. Soeme symmetries between east-travelling dipoles (ETD's) and west-travelling dipoles (WTD's) were observed. ETD's are stable in the trajectory sense: a small deviation from zonal motion results in small oscillations around the equilibrium latitude. WTD's are unstable: small initial deviations produce large displacements in northern or southern directions. This asymmetry arises because the vorticity of a dipole moving westward is anticorrelated with the ambient vorticity, while the vorticities are correlated when the dipole moves eastward. ETD's increase in size and eventually split into two independent monopoles, the rate of growth depending on the gradient of planetary vorticity. WTD's are initially more compact but owing to the large displacements in the meridional direction strong asymmetries in the circulation of the two halves are produced, resulting in a large deformation of the weaker part. The experimental observations show good qualitative agreement with analytical and numerical results obtained using a modulated point-vortex model.

The temporal evolution of thermally driven flow in a shallow laterally heated cavity is studied for the nonlinear regime where the Rayleigh number R based on cavity height is of the same order of magnitude as the aspect ratio L (length/height). The horizontal surfaces of the cavity are assumed to be thermally insulating. For a certain class of initial conditions the evolution is found to occur over two non-dimensional timescales, of order one and of order L2. Analytical solutions for the motion throughout most of the cavity are found for each of these timescales and numerical solutions are obtained for the nonlinear time-dependent motion in end regions near each lateral wall. This provides a complete picture of the evolution of the steady-state flow in the cavity for cases where instability in the form of multicellular convection does not occur. The final steady state evolves on a dimensional timescale proportional to l2/κ, where l is the length of the cavity, κ is the thermal diffusivity of the fluid and the constant of proportionality depends on the ratio R/L.

On the basis of the theory for infragravity waves induced by short-wave groups developed by Schäffer (1993), three-dimensional infragravity waves are analysed. The theory relies on the linearized depth-integrated conservation equations for mass and momentum combined to give a second-order long-wave equation with forcing expressions in terms of the radiation stress. This forcing gives a dynamic set-up originating from oscillations of the break-point position and a dynamic set-down bound to the short-wave groups. For small angles of incidence leaky-mode solutions are found while trapped modes appear when the primary waves are sufficiently oblique. In the latter case resonant edge-wave excitation may occur. A semi-analytical steady-state solution for the infragravity motion is presented. The solution is restricted to periodicity along a plane beach connected to a shelf and valid only for small primary-wave modulations.

An experimental study of the interaction of weak shock waves in a liquid with bubbles and solid particles has been conducted. Cavities were punched, and solid particles were cast, into a thin sheet of gelatine clamped between two transparent blocks. A shock of pressure 0.3 GPa was introduced by impacting the gelatine layer with a flyer plate. The subsequent collapse of the cavities was photographed using high-speed framing cameras, and waves in the gelatine were visualized using schlieren optics. Assorted cavity/particle geometries were studied. In the first, cavity and particle were aligned on an axis parallel to the incident shock front. The jet crossing the cavity was found to deviate from the perpendicular to the shock front. This deviation was towards the solid particle when separations were small and away from the particle when separations were increased. When a cavity was placed upstream of a solid particle the collapse time was reduced. Conversely, when a cavity was placed downstream of a solid particle, collapse time was increased and the closure was more symmetrical. These observations were explained in terms of wave reflections. Collapses where the cavity/particle axis was inclined to the incident shock showed features of each of the geometries described above.

Diode-array velocimetry is an optical technique for measuring turbulent flows. It involves timing the passage of seed particles through a small section of a light beam by imaging the light they scatter onto one or more photodiode arrays. The arrays have a few carefully shaped elements, the shapes and positions of which are used to control the measurement-volume geometry and thus select the measurement made. Measurement volumes sensitive to velocity, position and acceleration may be designed. Measurements in highly turbulent and reversing flows are possible.

A diode-array velocimeter (DAV) for one-component velocity measurements has been developed to demonstrate this concept. This uses a single laser beam to illuminate particles and a photodiode array with two rectangular elements to sense their motion. The sensitivity of this DAV to electrical noise in the photodiode circuitry decreases with reduction in measurement-volume size. The angle response is closely cosinusoidal to about 60°. Changes to the photodiode-array design could substantially increase this limit.

Measurements of mean velocity, normal turbulence stress and velocity skewness made with this DAV in two attached boundary-layer flows compare well with hot-wire measurements. Useful DAV measurements were made as close as 0.2 mm from the wall. DAV measurements made in a separated flow formed downstream of a fence are also presented. These show all the expected features of the separated shear layer and recirculation including the sub-boundary layer formed beneath the backflow. Histograms measured in the reversing part of this flow show a hole near zero velocity that is a consequence of the imperfections in the DAV angle response and limitations on the maximum transit time. These are not fundamental problems, however, and the hole could be minimized or eliminated by using a different photodiode array design and/or measurement strategy.

Instantaneous streamwise fluctuations of the wall shear stress have been measured using a hot-element probe in a thick axisymmetric turbulent boundary layer on a cylinder aligned parallel to the flow. The measurements were made at a momentum-thickness Reynolds number Rθ = 3050 and a ratio of boundary-layer thickness to cylinder radius of δ/a = 5.7. The ratio of the r.m.s. of the fluctuation to the mean value of the wall shear stress, $\tau_{rms}/\bar{\tau}$, is about 0.32, a value slightly lower than that for recent measurements for flow over a flat plate. The probability density function of the wall shear stress is similar to that for planar wall-bounded flows within experimental error. The power spectral density of the wall shear stress shows that a cylindrical boundary layer contains less energy at lower frequencies and more energy at higher frequencies than other wall-bounded flows. Analysis of simultaneous measurement of the streamwise wall shear stress and the streamwise velocity using VITA and peak detection suggests that transverse curvature has little effect on the near-wall burst–sweep cycle compared to planar wall-bounded flows. The angle of inclination of the structures is similar to that measured for large-scale structures in planar wall-bounded flows. However, measurements of the cross-correlation between the shear stress and the velocity suggest the existence of smaller structures yawed to the axis of the cylinder. The coherence between shear stress and velocity shows a low frequency associated with the inclined structures and a higher frequency associated with the yawed structures. The yawed structures could have an arrowhead or half-arrowhead shape and may be associated with fluid from the outer flow washing over the cylinder.

Using Auton's force law for the unsteady motion of a spherical bubble in inhomogeneous unsteady flow, two key dimensionless groups are deduced which determine whether isolated vortices or shear-layer vortices can trap bubbles. These groups represent the ratio of inertial to buoyancy forces as a relaxation parameter [tcy ] = ΔU2/2gx and a trapping parameter [Gcy ] = ΔU/VT where ΔU is the velocity difference across the vortex or the shear layer, x is streamwise distance measured from the effective origin of the mixing layer and VT is the terminal slip speed of the bubble or particle. It is shown here that whilst buoyancy and drag forces can lead to bubbles moving in closed orbits in the vortex flows (either free or forced), only inertial forces result in convergent trajectories. Bubbles converge on the downflow side of the vortex at a location that depends on the inertial and lift forces. It is important to note that the latter have been omitted from many earlier studies.

A discrete-vortex model is used to simulate the large-scale unsteady flows within horizontal and vertical mixing layers between streams with velocity difference ΔU. Trajectories of non-interacting small bubbles are computed using the general force law. In the horizontal mixing layer it is found that Γ needs to have a value of about 3 to trap about 50% of the bubbles if Π is about 0.5 and greater if Π is less. The pairing of vortices actually enhances their trapping of bubbles. In the vertical mixing layer bubbles are trapped mainly within the growing vortices but bubbles are concentrated on the downflow side of the vortices as Γ and Π increase. In a companion paper we show that lateral dispersion of bubbles can be approximately described by an advective diffusion equation with the diffusivity about equal to the eddy viscosity, i.e. rather less than the diffusivity of heat or other passive scalars.

A large-Reynolds-number asymptotic theory is presented for the problem of a vortex tube of finite circulation [Gcy ] subjected to uniform non-axisymmetric irrotational strain, and aligned along an axis of positive rate of strain. It is shown that at leading order the vorticity field is determined by a solvability condition at first-order in ε = 1/R[Gcy ] where R[gcy ] = [gcy ]/ν. The first-order problem is solved completely, and contours of constant rate of energy dissipation are obtained and compared with the family of contour maps obtained in a previous numerical study of the problem. It is found that the region of large dissipation does not overlap the region of large enstrophy; in fact, the dissipation rate is maximal at a distance from the vortex axis at which the enstrophy has fallen to only 2.8% of its maximum value. The correlation between enstrophy and dissipation fields is found to be 0.19 + O(ε2). The solution reveals that the stretched vortex can survive for a long time even when two of the principal rates of strain are positive, provided R[gcy ] is large enough. The manner in which the theory may be extended to higher orders in ε is indicated. The results are discussed in relation to the high-vorticity regions (here described as ‘sinews’) observed in many direct numerical simulations of turbulence.

Scaling analysis and experiments are used to study the evolution of thermals in the presence of background rotation. When the ambient environment is homogeneous, the thermal rises and expands until it reaches a critical height where the Rossby number becomes ∼ 1. The thermal then stops expanding and rises in a column. Both the critical height and column radius scale with (F0f-2)1/4. F0 is the initial thermal buoyancy and f is the Coriolis frequency. The thermal vertical velocity is independent of f. When the background is stratified with buoyancy frequency N, the thermal rises to a neutral buoyancy level which scales with (F0N-2)1/4. For N/f [Lt ] 0.6 column formation occurs before the thermal reaches the neutral level. For N/f [Gt ] 0.6 the thermal reaches the neutral level before rotation is important. In both regimes, geostrophic adjustment eventually causes the formation of a baroclinic vortex consisting of an anticyclonic lens of thermal fluid at the neutral level and cyclonic circulation below. The lens has Nh/fl ∼ 1. The lens thickness 2h and the radius l obey relations of the form (F0N-2)1/4 (N/f)m. However, the exponents m are different in the two regimes. The relevance of these results to deep-ocean convection and hydrothermal venting is discussed.

Off-axis collisions of equal-strength vortex rings were experimentally examined. Two equal-strength vortices were generated which moved toward each other along parallel, but offset, trajectories. Two colour laser-induced fluorescence visualization techniques were used to observe these phenomena and gain insight into their importance in vortex interactions. The most prominent features of this interaction were rapid growth and rotation of the rings and formation of evenly spaced ringlets around the cores of the original rings. Large-scale motions are described using simple vortex induction arguments. The small scales are caused by nonlinear amplification of instabilities during the asymmetric interaction.

It has been found theoretically and experimentally that a non-propagating soliton in a small rectangular water tank manifests dynamic behaviour when subjected to a modulated oscillation. A modification of the cubic Schrödinger equation was generalized for this case and analysed by the inverse-scattering perturbation method. The problem was reduced to a lower-dimensional one, i.e. to a pair of first-order ordinary differential equations for the amplitude and phase of the soliton, which were solved numerically. It was found that the soliton executes multi-periodic and chaotic motions under the periodically modulated oscillation. Corresponding experiments were carried out and both qualitative and quantitative agreement was obtained for the phenomena predicted and the parameter ranges in which they occur.

Laboratory observations and numerical simulations reveal that, in addition to monopoles, dipoles and tripoles, yet another stable coherent vortex may emerge from unstable isolated circular vortices. This new vortex is the finite-amplitude result of the growth of an azimuthal wavenumber-3 perturbation. It consists of a triangular core of single-signed vorticity surrounded by three semicircular satellites of oppositely signed vorticity. The stability of this triangular vortex is analysed through a series of high-resolution numerical simulations and by an investigation of point-vortex models. This new compound vortex rotates about its centre and is stable to small perturbations. If perturbed strongly enough, it undergoes an instability in which two of the outer satellites merge, resulting in the formation of an axisymmetric tripole, which subsequently breaks down into either a pair of dipoles or a dipole plus a monopole. The growth of higher-azimuthal-wavenumber perturbations leads to the formation of more intricate compound vortices with cores in the shape of squares, pentagons, etc. However, numerical simulations show that these vortices are unstable, which agrees with results from point-vortex models.

In a previous study (Longuet-Higgins & Cleaver 1994) we calculated the stability of the flow near the crest of a steep, irrotational wave, the ‘almost-highest’ wave, considered as an isolated wave crest. In the present paper we consider the modification of this inner flow when it is matched to the flow in the rest of the wave, and obtain the normal-mode perturbations of the modified inner flow. It is found that there is just one exponentially growing mode. Its rate of growth β is a decreasing function of the matching parameter ε and hence a decreasing function of the wave steepness ak. When compared numerically to the rates of growth of the lowest superharmonic instability in a deep-water wave as calculated by Tanaka (1983) it is found that the present theory provides a satisfactory asymptote to the previously calculated values of the growth rate. This suggests that the instability of the lowest superharmonic is essentially due to the flow near the crest of the wave.

The dynamics and interaction of turbulent-boundary-layer eddy structures was experimentally emulated. Counter-rotating streamwise vortices and low-speed streaks emulating turbulent-boundary-layer wall eddies were generated by a Görtler instability mechanism. Large-scale motions associated with the outer region of turbulent boundary layer were emulated with — ωz spanwise vortical eddies shed by a periodic non-sinusoidal oscillation of an airfoil. The scales of the resulting eddy structures were comparable to a moderate-Reynolds-number turbulent boundary layer. Results show that the emulated wall-eddy breakdown was triggered by streamwise acceleration associated with the outer region of turbulent boundary layer. This breakdown involved violent mixing between low-speed fluid from the wall eddy and accelerated fluid associated with the outer structure. Although wall eddies can break down autonomously, the presence of and interaction with outer-region — ωz eddies hastened their breakdown. Increasing the — ωz eddy strength resulted in further hastening of the breakdown. Conversely, + ωz eddies were found to delay wall-eddy breakdown locally, with further delays resulting from stronger + ωz eddies. This suggests that the outer region of turbulent boundary layers plays a role in the bursting process.