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).

A quantitative two-dimensional theoretical model is developed to describe the movement of water and salt along the long narrow extracellular channels which appear to be a common structural feature of all epithelial membranes. This study examines the transport behaviour of both open and closed membrane systems as a function of the geometric specialization of the channel and the active transport site location under the influence of three driving forces: trans-membrane osmotic and hydrodynamic pressure differentials and active transport. The previous one-dimensional hydrodynamic model of Diamond & Bossert (1967) and Segel(1970) was confined to closed channel systems such as the gall bladder in which the only mechanism for water movement is local osmosis due to active transport.

Approximate analytical solutions are presented for long constant-area open channels in which the active transport sites have been idealized as point solute sources. A streamwise co-ordinate straining technique has been used in these solutions to describe the nonlinear effects of convection over long distances. Closed-form solutions are also presented for the pressure and solute concentration distributions within simplified models of channel constrictions with varying degrees of occlusion.

Numerical results of the model have been compared with Cole's (1961, 1962) in vivo and in vitro experiments on the rabbit ciliary body. Satisfying agreement with the measured values of the solute and water fluxes has been obtained for both the living eye and the excised ciliary body. These results strongly suggest that the formation of aqueous humour in the rabbit is a pressure-dependent process in which local osmosis due to active transport accounts for only one-third of the total aqueous flow. The model has also been applied to the gall bladder epithelium using more general boundary conditions than allowed for in the model of Diamond & Bossert. New solutions yielding a vanishing diffusional flux at the channel exit were obtained. However, the model, like that of Diamond & Bossert, does not provide a rational explanation as to how the water in the cell interior is replenished.

A hypersonic gun tunnel has been used to investigate turbulent shock-boundary-layer interaction at a wedge-compression corner. The results extent the Mach number range of existing data, in particular of incipient separation.

A number of mechanisms which transport dissolved constituents and maintain the salt balance in estuaries are described. Although some of these have already been analysed, two which appear to be the most important in many real estuaries have received little previous attention. The Mersey Estuary is used as an example in which to estimate the amount of mass transported by each mechanism. The computations show in part how little is known and how much hypothesis is still required in spit?e of the number of previous estuarine studies; one may conclude, however, that in many real estuaries the most important mass transport mechanism is the net (non-tidal) transverse circulation, which is induced in part by the boundary geometry and in part by the longitudinal density gradient.

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.

The nature of a three-dimensional viscous flow along a corner near its junction has been clarified in this paper by constructing a Stokes slow-flow solution. We have further demonstrated that this Stokes solution can be matched onto an inertial-flow solution in principle by establishing an overlap domain along one sector of an inertial-flow region, namely along the flow symmetry line. This Stokes solution reveals a remarkably complex structure of the flow as characterized by a separating streamwise velocity profile in addition to a sequence of Moffatt's viscous eddies in a cross-flow plane.

The steady, inviscid, axisymmetric, rotating flow past a circular disk in an unbounded liquid is determined on the hypothesis that all streamlines originate in a uniform flow far upstream of the body. The characteristic parameter for the flow is k = 2ωa/U, where ω and U are the angular and axial velocities of the basic flow and α is the radius of the disk. Forward separation is found to occur for k > k = 1.9, in agreement with observation (Orloff & Bossel 1971). The length of the upstream separation bubble is determined on the hypothesis that the previous solution remains valid for k > k, despite the existence of closed streamlines within the upstream separation bubble (which may, but do not necessarily, inva,lidate the solution). This length increases rapidly for k > 3, in qualitative agreement with observation. The hypothesis of unseparated flow implies a singularity at the rim of the disk, just as in potential flow. The strength of this singularity departs only slightly from its potential-flow value for 0 ≤ k ≤ 2, but increases rapidly with k for k > 3, which suggests that (quite apart from the difficulties implied by the existence of closed streamlines) the solution cannot remain valid for sufficiently large k.

The flow of a stratified fluid in a channel with small and large deformations is investigated. The analogy of this flow with swirling flow in tubes with non-uniform cross-sections is studied. The flow near the wall is blocked when the Froude number takes certain critical values. The possibility of preventing the stagnation zones in the flow field is also discussed.

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.

The essential difference, from the theoretical point of view, between an externally excitedlciody and a fish is that the latter can apply lateral vibratory movements at any part of its surface, whereas in the ‘artificial fish’ lateral vibrations are applied only at the point where the external force acts on the body. A good example which illustrates how the artificial fish swims is the ‘Pod’. The Pod is a medical device consisting of a small magnet attached to a plastic ‘tail’. If the Pod is placed in a patient's blood vessel, and an alternating magnetic field is applied, the magnet oscillates angularly and the plastic tail causes it to swim. The purpose of the device is to deliver medicaments at any desired location in the circulatory system.

In this paper the theory of swimming of elastic slender bodies excited by an external force is presented. Special reference is made to the hydrodynamic forces acting on a swimming cylinder in viscous fluctuating flow. The results obtained are used in the analysis of the propulsion mechanism of the Pod.

Theoretical results based on the methods of Freeman and Garr & Marrone show that the stand-off distance and flow pattern of non-equilibrium dissociating flow of nitrogen over the front part of a blunt body can be correlated in terms of a single reaction rate parameter ω taking account of parameters describing the speed, density, dissociation and temperature of the free stream. The density pattern, which is sensitive to the reaction rate, consists of two distinct regions dominated by the effects of reaction and pressure respectively. The shape and size of these regions depend on Q. Experimental results obtained by optical interferometry in a free-piston shock tunnel confirm the theoretical results. A scale effect consistent with the induction time phenomenon suggested by Shui, Appleton & Keck modifies the theoretical results considerably in the case of small models.

Measurements of mass flow rate and mean density have been made in separated laminar boundary layers with large transverse density gradients. Two-dimensional shear layers were formed by exhausting a half-jet of one gas into a reservoir of another gas with a different molecular weight. Two freons with a density ratio of 1-98 and unusual properties which permitted the measurement of the mass flow rate with a single hot wire were used. A n analysis of the mass flow rate fluctuations showed that a negative density gradient (i.e. light gas flowing into heavy) increases the amplification rate of the instability oscillations and reduces the frequency and wave number. Opposite trends were observed when the density gradient was positive. These findings are in agreement with recent theoretical predictions.

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.

The flow driven by variations in surface tension round a hemispherical gas or vapour bubble on a heated wall has been investigated numerically for steady-state conditions over a wide range of values of dimensionless parameters, and experimentally for one set of conditions. Although six parameters are needed to specify the flow conditions, the magnitude of the liquid flow normal to the heated wall is determined primarily by tihe Marangoni number, Prandtl number and the Biot number based on the effective heat-transfer coefficient at the liquid-gas interface. The interior temperature of the bubble depends in addition on the thermal conductivity ratio of the liquid and the wall material. The flow is very sensitive t o the presence of surface-active contaminants. For water, calculations and experimental observations both indicate that contamination which lowers the static surface tension by only 0.1% may suppress the thermocapillary motion.

If a region of reverse flow remains confined within a boundary layer the conventional boundary-layer equations should continue to apply downstream of the point of detachment of the surface streamline (ω = 0). Nevertheless, standard numerical techniques fail in the presence of backflow since these methods become highly unstable and, in addition, neglect the upstream flow of information. A procedure for numerically integrating the boundary-layer equations through a region of reverse flow which takes downstream influence into account is therefore presented. This method is then applied to the problem of uniform flow past a parallel flat plate of finite length whose surface has a constant velocity directed opposite to that of the main stream. Although singularities occur at both the point of detachment (xs) and reattachment (xr) of the ω = 0 streamline, this integration technique provides a solution which ceases to apply only in the close proximity of these singular points. From this solution it is evident that, throughout a large portion of the separated region, the flow is strongly affected by conditions near xr, thereby demonstrating the importance of allowing information to be transmitted upstream in a region of backflow. Near (xs), however, it is found that, in spite of the presence of reverse flow, the solution has a self-similar form in this particular example.

In this paper we study the generation and propagation of hydromagnetic waves during the spin-up of an electrically conducting, viscous fluid. The time-dependent motion is set up by the impulsive rotation of an infinitely conducting plane which is initially in rigid-body rotation with the fluid, the applied magnetic field being parallel to the axis of rotation. The hydromagnetic flow is permeated by two distinct wave modes and the region between their wave fronts supports harmonic waves produced by the inertial oscillations. The characteristics of these modes are discussed for some limiting cases of interest.

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.

The eigenvalue problem for internal waves in a thermocline for which the density profile may exhibit finite discontinuities is formulated as a homogeneous Fredholm integral equation. The corresponding quadratic functional yields both upper and lower bounds for the dominant-mode eigenvalue and lower bounds for the remaining eigenvalues (which are proportional to the square of the wave speed) for any value of the wavenumber. The lower bounds based on simple trial functions appear to provide adequate approximations for typical density profiles and all wavenumbers. The upper bound (which is based on a Schwarz inequality and does not require the choice of a trial function) is sharp only for relatively long waves. A simple approximation is developed for the effect of the free surface on the dominant mode. Two algebraic formulations are given for a thermocline of homogeneous layers separated by a finite number of sheets, across each of which the density is discontinuous. The various approximations are compared with the exact results for a thermocline with a hyperbolic-tangent density profile, a three-sheeted thermocline, and a five-sheeted model of the summer thermocline in the Mediterranean.

An experimental study of the structure of the internal layer which grows down-stream from a rough-to-smooth surface change shows it to be essentially different from that studied by Antonia & Luxton (1971 b) for the case of a smooth-to-rough perturbation. The rate of growth of the internal layer is less than that for the smooth-to-rough step and it appears that the more intense initial rough-wall flow dictates the rate of diffusion of the disturbance for a considerable distance. Inside the internal layer the mixing length I is increased relative to the equilibrium distribution I = KY. A turbulent energy budget shows that the advection is comparable with the production or dissipation, whilst there seems to be some diffusion of energy into the internal-layer region close to the wall. The boundary layer, as a whole, recovers much more slowly following a rough-to-smooth change than following a smooth-to-rough change, and at the last measuring station (16 boundary-layer thicknesses from the start of the smooth surface) the distributions of mean velocity and Reynolds shear stress are far from self-preserving.

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.