This paper presents experimental and theoretical results on the internal waves emitted by a bluff body moving horizontally in a linearly stratified fluid. Three different bluff bodies (a sphere, a spheroid and a cylinder) have been used in order to study the effect of the shape of the bluff body, although most of the results are obtained for the sphere. Two types of internal waves have been observed experimentally: large wavelength lee waves generated by the bluff body itself and small wavelength coherent wake waves generated by the turbulent wake. First, the lee waves are separated from the wake waves by averaging the experimental measurements in the frame moving with the bluff body. The velocity amplitude of the lee waves scales as the inverse of the Froude number $F=2U_{B}/(ND)$ for $F>2$ (where $U_{B}$ is the towing velocity, $D$ the diameter and $N$ the buoyancy frequency). This scaling proves that the internal waves are related to the drag of the bluff body which is due to the separation of the flow behind the bluff body. This separation is usually not taken into account in the classical models which assume that the flow is dipolar. The drag can be modelled as a point force in the Navier–Stokes equations, which gives a correct prediction of the structure and the amplitude of the lee waves. Second, the wake waves have been separated from the lee waves by averaging the velocity fields in the frame moving at the phase velocity of the waves. The phase velocity and the wavelength scale as $F^{-2/3}$ and $F^{1/3}$ respectively which correspond to the velocity and distance between same sign vortices of the von Kármán vortex street. A simplified model is derived for the internal waves emitted by the double row of moving point vortices of the von Kármán street. The amplitude of the wake waves is measured experimentally and seems to depend on the Reynolds number.

A wind-forced weakly nonlinear weakly dispersive evolution model is derived for a continuously stratified circular lake of slowly varying depth under the effect of the Earth's rotation. The model was numerically integrated to investigate the evolution of long internal waves of vertical mode one for various sets of environmental parameters. It is demonstrated that the Kelvin wave steepens as it propagates, and the steepened front subsequently generates a train of oscillatory waves. It is demonstrated that Poincaré waves do not steepen, but their amplitude is modulated in an oscillatory manner with time, exhibiting a pseudo recurrence character. The model was applied to the wind forced problem, confirming that Kelvin and Poincaré waves are the dominant response. Energy partition among Kelvin and Poincaré wave modes is estimated as a function of wind-forcing parameters. For large lakes, the most significant wave amplitude is found in the Kelvin wave mode, but the gross field energy is most significantly contained in Poincaré wave modes.

The generation and energy downscaling of wind-forced long internal waves in strongly stratified small-to-medium sized narrow lakes are studied. A two-layer nonlinear model with forcing and damping is employed. Even though the wave field is fundamentally bidirectional in nature, a domain folding technique is employed to simulate the leading-order internal wave field in terms of a weakly nonlinear weakly dispersive model equation of Korteweg–deVries type. Parametric effects of wind-forcing and environmental conditions, including variable topography and variable basin width, are examined. Energy downscaling from basin-scale waves to shorter scales are quantified by means of a time evolution of the wave energy spectra. It is demonstrated that an internal wave resonance is possible when repetitive wind-forcing events arise with a frequency near the linear seiche frequency. An attempt is made to apply the model to describe the shoaling of long waves on sloping endwall boundaries. Modelling of the energy loss and energy reflection during a shoaling event is calibrated against laboratory experiments.

The two-dimensional wake–shear layer forming behind a rectangular-based forebody with independent ambient streams on either side of the forebody is examined by direct numerical simulation. Theoretical aspects of global modes and frequency selection criteria based on local and global stability arguments are tested by computing local stability properties using local, time-averaged velocity profiles obtained from the numerical simulations and making the parallel-flow approximation. The theoretical results based on the assumption of a slightly non-parallel, spatially developing flow are shown to provide a firm basis for the frequency selection of vortex shedding and for defining the conditions for its onset. Distributed suction or blowing applied at the base of the forebody is used as a means of wake flow modification. The critical suction velocity to suppress vortex shedding is calculated. It is shown that local directional control (i.e. vectoring) of the near-wake flow is possible, but only when all global modes are suppressed.

The observation of large-amplitude ‘kink’ waves on the vortex cores produced by an oscillating grid in a rotating fluid (Hopfinger, Browand & Gagne 1982) has motivated the study of such waves under more controlled circumstances. We have experimentally observed the properties of helical waves, rotating, plane standing waves and evolving, isolated kink-waves. Their characteristics have been related to theories based on the localized induction equation of Arms & Hama (1965), the ‘cut-off’ theory of Crow (1970) as extended by Moore & Saffman (1972), and an extension of Pocklington's (1895) dispersion relationship for ‘hollow-core’ vortices. It is shown that the latter dispersion relation and the Moore & Saffman theory are good approximations to our experimental results. Using these, we present new results on solitary kink-wave properties of concentrated vortex flows, and in particular show that envelope solitons are possible only for a restricted range of carrier wavenumbers. A second class of waves was also observed: the axisymmetric solitary waves of Benjamin (1967). These were found to become unstable to spiral disturbances when their amplitude exceeded a certain magnitude, as has been found in the study of the related vortex-breakdown phenomenon. All of these observations are used to interpret the experiments presented by HBG and to discuss qualitatively the dynamics of rotating turbulence. In the Appendix we propose a possible mechanism by which concentrated vortices can be formed in a rotating turbulent fluid.

An analysis is presented which describes the slow-time evolution of an internal gravity wave in an arbitrarily specified stratification. The weakly nonlinear description of a single-wave mode, governed by the nonlinear Schrödinger equation, breaks down when certain resonant conditions are satisfied. One such condition occurs when the group velocity of the wavetrain is equal to the phase velocity of a higher-mode long wave of the system. The resonant interaction occurs on a faster time scale and is described by a coupled pair of nonlinear partial differential equations governing the evolution of both the short-wave and the long-wave modes. This long-wave/short-wave interaction is pursued further in an experimental investigation by measuring the modal interchange of energy between two internal waves of disparate length and time scales. The resulting data are compared with numerical solutions of the long-wave/short-wave resonant interaction equations. In general, the agreement between the theory and the experiment is reasonably good in the range of operating conditions for which the theory is valid.

Nonlinear capillary instability of an axisymmetric infinite liquid column is investigated with an initial velocity disturbance consisting of a fundamental and one harmonic component. A third-order solution is developed using the method of strained co-ordinates. For the fundamental disturbance alone, the solution shows that a cut-off zone of wavenumbers (k) exists such that the surface waves grow exponentially below the cut-off zone, linearly in the middle of the zone (near k = 1), and an oscillatory solution exists for wavenumbers above the boundary of the zone. For an input including both the fundamental and a harmonic, all wave components grow exponentially when the fundamental is below the cut-off zone. Using a Galilean transformation, the solution is applied to a progressive jet issuing from a nozzle. The jet breaks into drops interspersed with smaller (satellite) drops for k < 0·65; no satellites exist for k > 0·65. It is shown theoretically that the formation of satellites can be controlled by forcing the jet with a suitable harmonic added to the fundamental.

The propagation of finite-amplitude internal waves in a shear flow is considered for wavelengths that are long compared to the shear-layer thickness. Both singular and regular modes are investigated, and the equation governing the amplitude evolution is derived. The theory is generalized to allow for a radiation condition when the region outside the stratified shear layer is unbounded and weakly stratified. In this case, the evolution equation contains a damping term describing energy loss by radiation which can be used to estimate the persistence of solitary waves or nonlinear wave packets in realistic environments. A continuous three-layer model is studied in detail and closed-form expressions are obtained for the phase speed and the coefficients of the nonlinear and dispersive terms in the amplitude equation as a function of Richardson number.

The evolution of long, finite amplitude Rossby waves in a horizontally sheared zonal current is studied. The wave evolution is described by the Korteweg–de Vries equation or the modified Korteweg-de Vries equation depending on the atmospheric stratification. In either case, the cross-stream modal structure of these waves is given by the long-wave limit of the neutral eigensolutions of the barotropic stability equation. Both non-singular and singular eigensolutions are considered and the appropriate analysis is developed to yield a uniformly valid description of the motion in the critical-layer region where the wave speed matches the flow velocity. The analysis demonstrates that coherent, propagating, eddy structures can exist in stable shear flows and that these eddies have peculiar interaction properties quite distinct from the traditional views of turbulent motion.

The motion of a two-dimensional packet of capillary–gravity waves on water of finite depth is studied. The evolution of a packet is described by two partial differential equations: the nonlinear Schrödinger equation with a forcing term and a linear equation, which is of either elliptic or hyperbolic type depending on whether the group velocity of the capillary–gravity wave is less than or greater than the velocity of long gravity waves. These equations are used to examine the stability of the Stokes capillary–gravity wave train. The analysis reveals the existence of a resonant interaction between a capillary–gravity wave and a long gravity wave. The interaction requires that the liquid depth be small in comparison with the wavelength of the (long) gravity waves and the evolution equations describing the dynamics of this interaction are derived.

The boundary layer on the upper surface of a horizontal plane in a diffusive, stratified flow is examined. The analysis shows that density diffusion increases the role of the buoyancy forces and causes a significant change in the properties of the boundary layer when compared to the non-diffusive case. A uniformly valid first approximation for moderate Russell numbers is derived, and the effects of buoyancy and diffusion are evaluated by solving the resulting equations numerically.

The boundary layers forming on the walls of an aligned cylinder in a rotating fluid in axial motion are studied theoretically. The analysis shows that the side-wall boundary layer is of the Blasius type when the Rossby number exceeds the inverse square root of the Reynolds number and is transformed to the Stewartson $\frac{1}{3}$-layer when the Rossby number is less than this value. A second thicker boundary layer is superimposed on the $\frac{1}{3}$-layer whenever the difference between the azimuthal velocities of the ambient fluid and the boundary exceeds the axial velocity. Its thickness varies according to the relative magnitudes of these velocities and yields the Stewartson ¼-layer thickness only when the ratio of the azimuthal velocity difference to the axial velocity is of order E⅙, where E is the Ekman number. A uniformly valid solution is obtained for the first case when the boundary layer is of the Blasius type.

The development of the boundary layer on the upper surface of a horizontal flat plate in a non-diffusive, stratified flow is described. It is shown that the flow can be characterized by two basic parameters, the Reynolds (RL) and Russell (RuL) numbers, and that, depending on the relative magnitude of these two parameters, three different régimes of flow can be defined. The delineation of these régimes and the description of the flow in each of them is obtained by deriving a uniformly valid first approximation to the Boussinesq equations of motion for a flow contained in the two-dimensional parameter space RuL > 0, RL > 1. The critical stratification for the self-blocking of a horizontal boundary layer is shown to be given by the condition RuL = O(RL½).

A simple model is developed, based on an approximation of the Boussinesq equation, that considers the weakly nonlinear evolution of an initial interface disturbance in a closed basin. The solution consists of the sum of the solutions of two independent Korteweg–de Vries (KdV) equations (one along each characteristic) and a second-order wave–wave interaction term. It is demonstrated that the solutions of the two independent KdV equations over the basin length [0, L] can be obtained by the integration of a single KdV equation over the extended reflected domain [0, 2L]. The main effect of the second-order correction is to introduce a phase shift to the sum of the KdV solutions where they overlap. The results of model simulations are shown to compare qualitatively well with laboratory experiments. It is shown that, provided the damping timescale is slower than the steepening timescale, any initial displacement of the interface in a closed basin will generate three types of internal waves: a packet of solitary waves, a dispersive long wave and a train of dispersive oscillatory waves.

An extended Korteweg–de Vries (KdV) equation is derived that describes the evolution and propagation of long interfacial gravity waves in the presence of a strong, space–time varying background. Provision is made in the derivation for a spatially varying lower depth so that some topographic effects can also be included. The extended KdV model is applied to some simple scenarios in basins of constant and varying depths, using approximate expressions for the variable coefficients derived for the case when the background field is composed of a moderate-amplitude ultra-long wave. The model shows that energy can be transferred either to or from the evolving wave packet depending on the relative phases of the evolving waves and the background variation. Comparison of the model with laboratory experiments confirms its applicability and usefulness in examining the evolution of weakly nonlinear waves in natural systems where the background state is rarely uniform or steady.

A methodology for vectoring the near-wake flow behind a bluff body without any mechanical movement of the physical boundaries of the generating body is described. The sole control input is suction applied at the fixed base of the forebody. Once the suction volume flux exceeds a critical value needed to suppress the global dynamics associated with vortex shedding, local directional control of the near wake can be achieved. The distribution of suction velocities across the base can be varied to obtain proportional directional control. The role of symmetries in stimulating aerodynamic vectoring of a streaming flow is emphasized and illustrated.