Inviscid linear perturbations to a columnar trailing line vortex are found in the form of centre-modes. These near-neutral modes, occurring at moderate values of the azimuthal wavenumber n, are the analogue of the ring modes for large n discussed by Stewartson & Capell (1985). The appearance and disappearance of these modes as the swirl parameter varies may partly explain the difficulties encountered by numerical analysts in the computation of such modes. In addition, instabilities are found at higher values of the swirl parameter than have previously been reported.

Measurements are presented of the mean flow in a supersonic turbulent boundary layer subjected to a constant weak transverse pressure gradient. The temperature and longitudinal velocity and the axial shear stress were only slightly affected by the three-dimensionality but a clearly defined crossflow component appeared, in the manner suggested by theory and confirmed in earlier experiments. The flow deflection angle and transverse-velocity component achieved a self-preserving form so long as the transverse-pressure gradient remained constant, and both achieved a maximum at the sublayer edge; the deflection angle seemed to decrease again between the latter and the surface. An empirical relation was found between the pressure-gradient strength and the maximum in the crossflow, and the dependence of the latter on distance from the surface was used to test analytical crossflow predictions. The data are in general agreement with Van Den Berg's law of the wall. The data also support the so-called parabolic law following a relaxation distance, especially if inviscid gradients are accounted for, and if the normal coordinate is contracted by the compressibility transformation.

When drag-reducing additives are confined entirely to the linear sublayer of a turbulent channel flow of water, both the spanwise spacing and bursting rate of the wall-layer structure are the same as those for a water flow and there is no evidence of drag reduction. Drag reduction is measured downstream of the location where the additives injected into the sublayer begin to mix in significant quantities with the buffer region (10 < y+ < 100)The superscript + denotes a dimensionless quantity scaled with the kinematic viscosity ν and the wall shear velocity v* = (τw/ρ)½. of the channel flow. At streamwise locations where drag reduction does occur and where the injected fluid is not yet uniformly mixed with the channel flow, the dimensionless spanwise streak spacing increases and the average bursting rate decreases. The decrease in bursting rate is larger than the corresponding increase in streak spacing. The wall-layer structure is like the structure in the flow of a homogeneous, uniformly mixed, drag-reducing solution. Thus, the additives have a direct effect on the flow processes in the buffer region and the linear sublayer appears to have a passive role in the interaction of the inner and outer portions of a turbulent wall layer.

A mixing-layer flow formed by merging of high- and low-speed streams leads to successive generation of vortices of the same sense that impinge upon a leading edge. Distortion of each incident vortex, secondary-vortex shedding, and 'sweeping’ of flow about the tip of the edge are related to the instantaneous pressure fields via simultaneous flow visualization and pressure measurement. The instantaneous pressure fields are interpreted as downstream travelling waves along the upper and lower surfaces of the edge; in turn, these wavelike pressure variations are linked to the visualized vortex patterns adjacent to each surface.

Near the tip of the edge, where rapid flow distortion occurs, the pressure fields are non-wavelike; on the lower surface of the tip, negligible streamwise phase variations of fluctuating pressure are associated with secondary shedding there, while on the upper surface there is a phase jump. This jump can be as large as π when the incident vortex impinges directly upon, or passes just below, the tip of the edge. Downstream of this near-tip region, the wavelike pressure fields show short and long wavelengths on the lower and upper surfaces respectively. These wavelengths, in turn, differ substantially from the wavelength of the incident-vortex instability.

Irrespective of the transverse location of the incident vortex with respect to the leading edge, maximum pressure amplitude always occurs at the tip of the edge; it takes on its largest value when the scale of secondary shedding from the tip of the edge is most pronounced. Moreover, the fact that the net force on the edge scales with tip-pressure amplitude underscores the crucial role of the local flow distortions in the tip region.

The draining of thin fluid layers between rigid or deformable surfaces has been extensively studied in the limit of thin films where inertial effects are of negligible importance. In the present investigation, which is in two parts, we shall examine the inertial draining of a thin fluid layer between planar parallel surfaces under the action of a constant normal force. This is a simple model for dropping a sheet of paper or a book on a table or applying a piston to a microchip. The novelty of the problem is that we shall consider both the inertia of the object and that of the fluid for all Reynolds numbers where the flow remains laminar. In Part 1 of the study we shall derive a simplified Navier–Stokes equation for the general case which contains the dynamic equation for the motion of the object. Solutions will be presented for the time-dependent motion of the object and the intervening fluid in the gap for all ratios of object to fluid inertia in the limit of infinite Reynolds number and for small Reynolds numbers (Re < 10) in the limit where the time rate of change of momentum of the object is small compared with that of the fluid in the gap. In Part 2, we shall examine the limit where time-dependent boundary layers develop along the top and bottom surfaces in response to the time-varying core flow and also present a new exact Navier–Stokes solution for a time-dependent double-axisymmetric stagnation-point flow.

The draining of a fluid layer between rigid plane parallel boundaries under a constant normal force is considered. In Part 1 the effect of fluid inertia was considered in the inviscid and low- but finite-Reynolds-number limits along with the inertia of the moving body; in Part 2, we consider the case of negligible inertia of the moving body. We develop an approximate large-Reynolds-number solution, valid until the boundary layers of the rigid surfaces begin to overlap, and present a new exact solution of the full Navier–Stokes equations for a time-dependent double-axisymmetric stagnation-point flow. These solutions exhibit interesting new features that illustrate the coupling of a time-dependent inviscid core flow with the growth of an unsteady boundary layer started from rest and the effect of Reynolds number on the merging of the boundary layers at large time.

The stability of three-dimensional salt fingers to three-dimensional perturbations is considered. It is found that when square fingers are subjected to long-wavelength perturbations, then the same types of instability exist as for two-dimensional salt fingers. There are quantitative changes to the growth rates and the positions of marginal stability.

Recent measurements of wave spectra and observations by remote sensing of the sea surface indicate that the author's (1958) conception of an upper-limit asymptote to the spectrum, independent of wind stress, is no longer tenable. The nature of the equilibrium range is reexamined, using the dynamical insights into wave–wave interactions, energy input from the wind and wave-breaking that have been developed since 1960. With the assumption that all three of these processes are important in the equilibrium range, the wavenumber spectrum is found to be of the form $(\cos\theta)^p u_{*} g^{-\frac{1}{2}}k^{-\frac{7}{2}}$, where p ∼ ½ and the frequency spectrum is proportional to u*gσ−4. These forms have been found by Kitaigorodskii (1983) on a quite different dynamical basis; the latter is consistent with the form found empirically by Toba (1973) and later workers. Various derived spectra, such as those of the sea-surface slope and of an instantaneous line traverse of the surface, are also given, as well as directional frequency spectra and frequency spectra of slope.

The theory also provides expressions for the spectral rates of action, energy and momentum loss from the equilibrium range by wave-breaking and for the spectrally integrated rates across the whole range. These indicate that, as a wave field develops with increasing fetch or duration, the momentum flux to the underlying water by wave-breaking increases asymptotically to a large fraction of the total wind stress and that the energy flux to turbulence in the water, occurring over a wide range of scales, increases logarithmically as the extent of the equilibrium range increases. Interrelationships are pointed out among different sets of measurements such as the various spectral levels, the directional distributions, the total mean-square slope and the ratio of downwind to crosswind mean-square slopes.

Finally, some statistical characteristics of the breaking events are deduced, including the expected length of breaking fronts (per unit surface area) with speeds of advance between c and c+dc and the number of such breaking events passing a given point per unit time. These then lead to simple expressions for the density of whitecapping, those breaking events that produce bubbles and trails of foam, the total number of whitecaps passing a given point per unit time and, more tenuously, the whitecap coverage.