The spin-up flow in a cylinder of homogeneous fluid has been examined both experimentally and numerically. The primary motivation for this work was to check numerical solution schemes by comparing the numerical results with laboratory measurements obtained with a rotating laser-Doppler velocimeter. The laser-Doppler technique is capable of high accuracy with small space and time resolution, and disturbances of the flow are virtually negligible. A series of measurements was made of the zonal flow over a range of Ekman numbers (1·06 × 10−3 ≤ E ≤ 3·30 × 10−3) and Rossby numbers (0·10 [les ]|ε| [les ] 0·33) at various locations in the interior of the flow. These measurements exceed previous ones in accuracy. The weak inertial modes excited by the impulsive start are detectable. The numerical simulations used the primitive equations in axisymmetric form and employed finite-difference techniques on both constant and variable grids. The number of grid points necessary to resolve the Ekman layers was determined. A thorough comparison of the simulations and the experimental measurements is made which includes the details of the amplitude and frequency of the inertial modes. Agreement to within the experimental tolerance is achieved. Analytical results for conditions identical to those in the experiments are not available but some similar linear and nonlinear theories are also compared with the experiments.

Local velocity measurements performed in a convecting layer of fluid show that the velocity field can be described by a dominant fundamental velocity mode mixed with an increasing proportion of second and third harmonics as ε, the reduced distance to the convective threshold Rc, is increased from 0 to ∼ 10. The spatial and thermal dependences of the amplitudes of these different modes are reported and compared with theoretical predictions.

This paper is concerned with the behaviour of buoyant plumes driven by a source of bubbles. It is shown experimentally that, when a bubble plume rises through a stratified environment, fluid can be transported vertically for some distance and then some of this fluid can leave the plume and spread out horizontally at its own density level. A simple plume model which regards the plume as a single entity is discussed in order to make a first assessment of the effects of gas expansion and bubble slip velocity in this stratified case. However, the experiments reveal a more complicated plume structure in which the bubbles remain in the centre part of the plume, and only the outer part of the plume spreads out into the environment at certain levels. On the basis of these observations a double-plume model is proposed which regards the plume as being composed of two parts: an inner circular plume (which contains all the bubbles of gas) and an outer annular plume.

A charged particle suspended in an electrolyte solution attracts ions of opposite charge and repels those of like charge. The surface charge and the resulting distributed charge in the fluid comprise an electrical double layer. When a shear flow deforms the diffuse part of the double layer from equilibrium, stresses are generated which make the effective viscosity of the suspension greater than it would be if there were no charges present. In this paper these stresses are calculated for a dilute dispersion of spheres which have small surface charges and which are surrounded by thin double layers. The viscosity is predicted to be Newtonian in extensional flow but shear-thinning with non-zero normal-stress differences in shear flow. For more complex flows a constitutive equation couples the bulk stress directly to the micro-structural deformation responsible for non-Newtonian effects.

A transformation is described which relates the sound generated by low Mach number flow to the flow vorticity. For compact flow fields the apparent sound source is of quadrupole type and linear in the vorticity and therefore also linear in the flow velocity. This scheme is applied to the sound generated by the interaction of two identical thin vortex rings. Then a flow field with a number of compact vortices is discussed. It is found that each vortex can be replaced acoustically by a dipole related to the impulse of the vortex, plus the quadrupole just mentioned plus a spherically symmetric sound source related to the energy of the vortex. An application to low Mach number free-space turbulence shows that the generated sound is related to the vorticity correlation tensor.

Flow-visualization investigations and correlation measurements show that the essentially two-dimensional structures which dominated the turbulent mixing layer of Brown & Roshko (1974) are formed only if the free-stream turbulence is low. If free-stream disturbances are significant, as is likely in most practical cases, including a mixing layer entraining ‘still air’ from the surroundings, three-dimensionality develops at an early stage in transition. Other recent experiments strongly suggest that the Brown-Roshko structure will not form if the initial mixing layer is turbulent or subject to instability modes other than spanwise vortices. Therefore the Brown-Roshko structure will be rare in practice. The alternative large structure in a mixing layer, found by several workers, is intense, but fully three-dimensional and thus less orderly than the Brown-Roshko structure.

The balance of evidence suggests that if the Brown-Roshko structure does appear it will eventually relax into the alternative fully three-dimensional form: the Kármán vortex street behind a bluff body provides a precedent for slow development of three-dimensionality. However the Brown-Roshko structure, if formed, may well relax so slowly as to be identifiable for the full length of a practical flow.

Laboratory measurements have been made of the one-dimensional spectra of the duration-limited wind waves which are generated when a wind abruptly begins to blow over a water surface, maintaining a constant speed during the succeeding period of time. The duration dependences of the wave energy E and the spectral peak frequency fm determined from the measured spectra are slightly different from those inferred from the fetch dependences of these quantities. The normalized spectra of the duration-limited wind waves are also slightly different from those of fetch-limited wind waves: the concentration of the normalized spectral energy near the spectral peak frequency is smaller, in many cases, for the duration-limited wind waves than for fetch-limited wind waves. The exponential growth rates β of the duration-limited wind-wave spectra are generally larger than those of fetch-limited wind-wave spectra. Furthermore, both for the duration-limited wind waves and for fetch-limited wind waves the exponential growth rate has a behaviour which is different from the empirical formula of Snyder & Cox (1966). A new empirical formula for the growth rate of the wave spectrum is proposed, from which the empirical formula of Snyder & Cox (1966) can be derived as a special case. Agreement between the new empirical formula and the experimental results is satisfactory for fetch-limited wave spectra, but is confined to the qualitative features for the duration-limited wave spectra.

In this paper the slip flow of viscous fluid at low Reynolds numbers past a flat plate aligned with the flow is studied theoretically on the basis of Oseen-Stokes equations of motion. An integral equation for the distribution of fundamental singularities representing the plate is derived and solved approximately in the vicinity of the edge and main portion of the plate. A formula for the local skin friction is obtained and discussed numerically. It is also shown that the slippage of the flow gives rise to reduction of the drag force on the plate by an amount O(K|ln K|), where K is the Knudsen number. The velocity change near the edge of the plate is of particular interest and is found to be logarithmically singular there.

We explore two types of instability which may develop when a highly conducting gas rotates rapidly in the presence of a radial gravitational force and an azimuthal magnetic field. Beyond a critical radius (equal to twice the isothermal scale height) a decrease of magnetic flux (per unit mass) outwards leads to the appearance of eastward-propagating waves by the mechanism of ‘magnetic buoyancy’. Within the critical radius an increase of magnetic flux outwards leads to westward-propagating waves by a totally different mechanism. Provided that the effects of Ohmic dissipation are not too large, either instability may set in for quite modest magnetic flux gradients, even when the magnetic energy of the system is very much smaller than the rotational energy.

The linear stability of the Stewartson layer in a compressible fluid is studied. The viscosity and the heat conductivity are shown to be negligible for a special kind of infinitesimal disturbance. The basic equations of the disturbance are shown to reduce to those for a Boussinesq fluid subject to a virtual radial stratification. A Miles-type sufficient condition for stability and a Howard-type semicircle theorem are derived. The growth rates of unstable modes with wavenumber and shear strength are summarized in stability diagrams for typical cases. The results clarify the situation in which the stability of the Stewartson layer is governed by a balance between the shear strength and the temperature stratification in the layer.

Most methods of calculating steep gravity waves (of less than the maximum height) encounter difficulties when the radius of curvature R at the crest becomes small compared with the wavelength L, or some other typical length scale. This paper describes a new method of calculation valid when R/L is small.

For deep-water waves, a parameter ε is defined as equal to q/2½c0, where q is the particle speed at the wave crest, in a frame of reference moving with the phase speed c. Hence ε is of order (R/L)½. Three zones are distinguished: (1) an inner zone of linear dimensions ε2L near the crest, where the flow is described by the inner solution found previously by Longuet-Higgins & Fox (1977); (2) an outer zone of dimensions O(L) where the flow is given by a perturbed form of Michell's solution for the highest wave; and (3) a matching zone of width O(L). The matching procedure involves complex powers of ε.

The resulting expression for the square of the phase velocity is found to be \[ c^2 = (g/k)\{1.1931-1.18\epsilon^3\cos(2.143\ln \epsilon + 2.22)\} \] (see figures 5a, b), which is in remarkable agreement with independent calculations based on high-order series. In particular, the existence of turning-points in the phase velocity as a function of wave height is confirmed.

Similar expressions, valid to order ε3, are found for the wave height, the potential and kinetic energies and the momentum flux or impulse of the wave.

The velocity field is extended analytically across the free surface, revealing the existence of branch-points of order ½, as predicted by Grant (1973).

A model of Wilson Cloud formation following a low-altitude nuclear detonation is developed. It is shown that, for detonation yields between 10−3 kt and 100 kt, simple scaling laws characterize the evolution and physical properties of the Wilson Cloud.