It has been observed that standing surface waves in water may be excited by acoustic fields of very much higher frequency. No special relationship between the two frequencies appears to be required, but there is such a relationship between the spatial variations of the acoustic and surface wave modes. Another requirement is that the lower frequency should be comparable with the resonant and width of the acoustic response of the system. An explanation of such phenomena is proposed and is tested on a somewhat idealized model by the use of techniques which could be extended to deal with more realistic situations. The model serves to explain qualitatively the available experimental observations. It is suggested that the phenomenon of spatial resonance is not confined to the interaction between water waves and acoustic fields, but may occur generally in systems having modes with related spatial patterns but greatly different frequencies.

The phenomenon was observed during experiments in which a beaker containing water was vibrated in one of its bell modes (the inextensional flexural vibrations of the wall). For certain combinations of driving force and frequency, a standing water wave of large amplitude was generated whose peripheral wavenumber might be either zero (i.e. the wave was radially symmetric) or twice that of the bell mode. This relationship between the wavenumbers of the bell mode and water wave, and the fact that the driving frequency was many times that of the water wave, indicated that this was an instance of a general mechanism that has been studied theoretically by Mahony & Smith (1972). For a model situation, allowing for dissipative effects and nonlinear coupling between nearly resonant oscillations at greatly differing frequencies, they derived a relation-ship between the driving force and frequency representing conditions of neutrals tability (i.e. such that the rate of energy transfer from the high frequency to the low frequency oscillations is zero). The aim of the experimental observations reported here was to check this relationship and other predictions of their theory.

When similarity solutions are used to describe convective plumes or thermals, there is always found to be a discrepancy between the work done by buoyancy forces and the kinetic energy of mean motion. It is the main purpose of this paper to set down the ratio of these quantities for a wide variety of forms of buoyant elements and environmental stabilities. For consistency, the remaining fraction of the energy must appear as turbulent kinetic energy and eventually be dissipated, but these processes are not investigated in detail. The results are shown to have some relevance to the problem of convectively driven mixing across a density interface, where the largest scales of motion are dominant, and to the understanding of the transition zone between two self-preserving states of turbulent convection.

Measurements of the thickness and the stability of thin films of liquid (1–150 μmthick) formed on a rotating horizontal disk are presented and correlated in terms of an asymptotic-expansion solution of the thin-film equations. Water, various alcohols and water with wetting activities were used to cover a range of viscosity (1-2.5cP) and surface tension (20-72 dynes/cm). Smooth flow was found to occur in a region defined by the flow rate, rotational speed and physical properties of the liquid. Outside this region various wave patterns were observed (concentric, spiral and irregular waves). A linear theory of the stability of the film based on an extension of classical stability theories for plane films on inclined planes is given and contrasted with the experimental results. Surface phenomena associated with the use of wetting agents were found to have a strong effect on the stability of the film.

Several solutions for the solitary wave have been attempted since the work of Boussinesq in 1871. Of the approximate solutions, most have obtained series expansions in terms of wave amplitude, these being taken as far as the third order by Grimshaw (1971). Exact integral equations for the surface profile have been obtained by Milne-Thomson (1964,1968) and Byatt-Smith (1970), and these have been solved numerically. In the present work an exact operator equation is developed for the surface profile of steady water waves. For the case of a solitary wave, a form of solution is assumed and coefficients are obtained numerically by computer to give a ninth-order solution. This gives results which agree closely with exact numerical results for the surface profile, where these are available. The ninth-order solution, together with convergence improvement techniques, is used to obtain an amplitude of 0.85for the solitary wave of greatest height and to obtain refined approximations to physical quantities associated with the solitary wave, including the surface profile, speed of the wave and the drift of fluid particles.

Two related wave problems are considered for a rotating sea of nearly uniform depth bounded by a coastline which is nearly straight. The depth changes are assumed to be independent of the distance from the coastline. The first problem, which is concerned with the origin of Kelvin waves in a coastal wave record, deals with a system of plane waves incident on the coastline and giving rise, in addition to reflected waves, to a Kelvin wave moving along the coast. Linearized theory is used to obtain details of the Kelvin wave for arbitrary perturbations in coastline and depth. Results suggest that the depth changes have their greatest effect in producing Kelvin waves if the incident wave crests are nearly parallel, but not exactly so, to the line of the depth changes. On the other hand when the wave crests are parallel to the coast, Kelvin waves are produced only by changes in the coastal boundary. In the second problem a Kelvin waye is assumed to be the incident wave. To find the energy propagated away from the coastline it is necessary to extend the theory to second order in the perturbations. It is shown that for a fixed wave period less than a pendulum day this energy has a maximum for a perturbation whose length is of comparable magnitude to the incident wavelength. Finally, the theory is applied to Kelvin waves propagating along the Californian coastline. Results obtained tend to confirm the suspicion that coastal irregularities are responsible for certain anomalies detected in tidal wave constituents by Munk, Snodgrass & Wimbush (1970).

The flow induced by a cylinder performing transverse periodic oscillations in a fluid which is otherwise at rest is investigated. The motion of the cylinder is not necessarily harmonic. Attention is focused upon the induced steady streaming. In particular, the jet-like flow which arises when the streaming Reynolds number is large is studied. The theoretical results obtained are applied to a class of elliptic cylinders, and a simple experimental investigation is carried out which substantiates the main theoretical conclusions.

An analytical and experimental study of thermally induced instability in horizontal two-fluid layers is reported. A liner stability analysis for two initially motionless, viscous immiscible fluids confined between horizontal isothermal solid surface and subject to both density (Bénard) and surface-tension-grandient (Marangoni) drving mechanisms is presented. Calculations for the labortory configuaration reported below predict instability for heating from above or below. Response is strongly department on the ratios of the properties of the fluids, the total depth of the layer and the depth fraction of one fluid. Three different response modes occur(interfacial-tension-gradient dominated, buoyancy dominated and surface-deflexion dominated) depending on the fluid depth fractions when the heating is from above, the buoyanvy mechanism is stabilizing for most wavenumbers, including the xritical one. Heating from below lowere the critical Marangoni number and adds a buoyancy driven response mode. Results of experimental measurement of the critical Marangoni number exceeds the predicted critical value by as much as five times. The critical Rayleigh number observe for heating from below fallos between the critical values predicted with and without the Marangoni effect. The presence of surface contamination is belived to be responsible for the apparent lack of convection when heating is from above and for the different between the predicted and measured critical Rayleigh number when heating is from below.

A reservoir is assumed to be filled with water which has a linear variation of density with depth. The geometry of the boundaries is simplified to a parallel walled duct with the line sink at the centre of the fluid. The primary focus is on partitioning the flow into distinct flow regimes and predicting the withdrawal-layer thickness as a function of the distance from the sink; the predictions are verified experimentally.

For fluids with a Schmidt number of order unity, the withdrawal layer is shown to be composed of distinct regions in each of which a definite force balance prevails. The outer flow, where inertia forces are neglected, changes from a parallel uniform flow upstream to a symmetric self-similar withdrawal layer near the sink. For distances from the sink smaller than a critical distance, dependent on the flow parameters, inertia forces become of equal importance to buoyancy and viscous forces. The equations valid in this inner region are derived. Using the inner limit of the outer flow as the upstream boundary condition, these inner equations are solved approximately for the withdrawal-layer thickness by an integral method. The inner and outer variations of δ, the withdrawal-layer thickness, are combined to yield a composite solution and it is seen that the inclusion of inertia forces yields layers thicker than those obtained from a strict buoyancy-viscous force balance. In terms of the inner variables the only parameter remaining is the Schmidt number.

Laboratory experiments were carried out to verify the theoretical conclusions. The observed withdrawal-layer thicknesses were shown to be closely predicted by the integral solution. Furthermore, the data could be represented in terms of the inner variables by a single curve dependent only on the Schmidt number.

Eulerian measurements of microscale fluctuations in static pressure are used, in conjunction with measurements of air velocity, to describe some of the properties of the static pressure fluctuations that occur within the turbulent flow of the lower atmospheric boundary layer. Using an instrument developed to measure the static pressure at a point within the boundary layer, data were collected at heights ranging from the surface up to about 6 m. The results are presented as power spectra, cross-spectra, coherence and phase. For all observations over a flat boundary the root-mean-square pressure produced by the boundary-layer turbulence is about 2.6 times the mean stress. The pressure spectra are found to have a, well-defined shape which does not change with height above the surface; at the higher frequencies the spectra show a power-law behaviour with a mean slope of −1·7. A number of observations with two pressure sensors are used to describe the structure and propagation velocity of individual pressure pulses.

A dominant feature of the pressure-velocity relationship is that the large-scale pressure fluctuations are approximately in phase with the downstream velocity fluctuations; at small scales there is a large phase difference (∼−135°). These phase differences are interpreted to be the result of interaction of the large pressure-producing scales with the earth's surface, the small scales being ‘free’ of the surface. Prom the simultaneous measurements of pressure and downstream velocity the effect of pressure forces on the energy flux out of the downstream velocity fluctuations was evaluated. Typical values are about 0-45 of the net energy source to the downstream component. By means of pressure and vertical velocity measurements an estimate of the pressure divergence term in the net energy budget of a boundary layer is made. It was found to be about 1/10 of the energy feeding term.

Dynamo action associated with the motion generated by a random body force f(x, t) in a conducting fluid rotating with uniform angular velocity ω is considered. It is supposed that, in the Fourier decomposition off, only waves having a phase velocity V satisfying V. ω > 0 are present and that the Fourier amplitudes of f are isotropically distributed. The resulting velocity field then lacks reflexional symmetry, and energy is transferred to a magnetic field h0(x, t) provided the scale L of h0 is sufficiently large. Attention is focused on a particular distribution of h0 (x, t) (a circularly polarized wave) for which this dynamo action is most efficient. Under these conditions, the mean stresses acting on the fluid are irrotational and no mean flow develops. It is supposed that \[ \lambda \ll \Omega l^2,\quad \lambda\ll h_0l\quad{\rm and}\quad\nu/\lambda = O(1)\quad\hbox{or smaller}, \] where l ([Lt ] L) is the scale of the f-field, and ν and λ are the kinematic viscosity and magnetic diffusivity of the fluid. The response to f is then dominated by resonant contributions near the natural frequencies of the free undamped system. As h0 grows in strength, these frequencies change, and the dynamo process is rendered less efficient. Ultimately the magnetic energy M (and also the kinetic energy E) asymptote to steady values. Expressions for these values are obtained for the particular situation when ν [Lt ]λ and when the frequency ω0 characteristic of the f-field is small compared with other relevant frequencies, notably ω and h0/l; under these conditions, it is shown that \[ \frac{M}{E}\sim C\left(\frac{\Omega}{\omega_0}\right)^{\frac{1}{2}}\left(\frac{\nu}{\lambda}\right)^{\frac{1}{2}}\frac{L}{l}, \] where C is a number of order unity determined by the spectral properties of the f-field. The implications for the terrestrial dynamo are discussed.