A corrugated plate is translating in a rotating fluid. Assuming low Reynolds number and small amplitudes compared to the Ekman thickness, a perturbation solution is found to second order. The resistance and power due to drag depend on the relative orientation of the corrugations with the motion. In certain instances, it is easier to move a corrugated plate than a flat plate in a rotating fluid.

The trapping of linear water waves over two-dimensional topography is investigated by using the mild-slope approximation. Two types of bed profile are considered: a local irregularity in a horizontal bed and a shelf joining two horizontal bed sections at different depths. A number of results are derived concerning the existence of trapped modes and their multiplicity. It is found, for example, that the maximum number of modes which can exist depends only on the gross properties of the topography and not on its precise shape. A range of problems is solved numerically, to inform and illustrate the analysis, using both the mild-slope equation and the recently derived modified mild-slope equation.

A series solution approach to the forced and damped quasi-geostrophic barotropic vorticity equation is considered in order to examine the strongly forced and inertial limits of ocean gyre dynamics. The strongly forced limit is the limit investigated numerically by Veronis (1966b). It is shown that this limit, although superficially having the same symmetry properties as the inertial limit, is distinguishably different from the latter. After isolating the inertial limit in an appropriate way it is shown that our series solution method is able to find the ‘free mode’ and its ‘almost free correction’, that the ‘free mode’ obeys the integral criteria of Niiler (1966) and Pierrehumbert & Malguzzi (1984) and that the relationship between the streamfunction and the absolute vorticity is in general a nonlinear one.

The energy–Casimir method is applied to the problem of symmetric stability in the context of a compressible, hydrostatic planetary atmosphere with a general equation of state. Formal stability criteria for symmetric disturbances to a zonally symmetric baroclinic flow are obtained. In the special case of a perfect gas the results of Stevens (1983) are recovered. Finite-amplitude stability conditions are also obtained that provide an upper bound on a certain positive-definite measure of disturbance amplitude.

Experiment have shown that the well-known vortex pairing process may take place first in defect regions where the fundamental structure is weakest. A model is introduced here to describe this defect-induced pairing process. The model is constructed in such a way that, in a certain parameter range, a stable fundamental mode and a stable subharmonic mode may coexist. The numerical simulation demonstrates that, when initial conditions consist of a dominant fundamental with one or more defects, the subharmonic component is preferentially generated in the cores of these defects. Moreover, the results also indicate that pairing may first commence wherever the fundamental mode is weakest provided the white-noise level of the subharmonic is high enough. The numerical results are in good agreement with experimental observations.

Flow of a conducting fluid along the annular channel between two non-conducting circular cylinders is examined by a numerical method for concentric and eccentric cases. Solutions have been obtained for Hartmann numbers ranging from 0·1 to 40 and, for some of these, details of velocity distribution and of induced current are given. The results obtained enable the development of the patterns of velocity and of current flow to be traced as the Hartmann number increases. The details of the development of the current flow patterns for eccentric cylinders are particularly interesting and are discussed in detail. At the higher values of Hartmann number studied the solutions are in excellent agreement with the results of Todd's (1967) high Hartmann number analysis and it is possible to determine at what value of Hartmann number Todd's analysis becomes applicable within a specified accuracy. The effect of eccentricity of the cylinders on the flow rate at a fixed pressure gradient is shown to diminish rapidly with increasing Hartmann number. The net flow of current around the annulus, which occurs when the cylinders are eccentric, has a maximum value for each case studied at a Hartmann number of 3, approximately.

A useful parametrical model for the vertical structure of the pressure field induced by wind blowing over a field of surface gravity waves is proposed. The model is a linear expansion in a set of empirical orthogonal functions, derived from a set of 110 complex pressure profiles computed according to the theory of Miles (1957), and provides a compact, quantitative description of those profiles. The model has been used as an element in the analysis of a body of experimental data on wave-induced atmospheric pressure fluctuations obtained by Snyder et al. (1980).

The purpose of this note is to construct a local solution that eliminates a residual velocity discontinuity in the inviscid portion of a solution obtained in a recent paper by Goldstein, Leib & Cowley (1992). This result is of importance because it shows that the solution obtained in that paper is entirely non-singular outside the viscous wall boundary layer and that any singularity in the problem will have to arise in the usual way through a breakdown in the viscous boundary layer.

The mixing layer bounding the exhaust plume associated with hypersonic highaltitude rockets is analysed as a laminar binary mixture of perfect gases with Lewis and Prandtl numbers of unity. A far-field approximation to the undisturbed jet core and a Newtonian pressure balance between the jet and ambient gases are used to construct the mixing-layer location. Longitudinal pressure variations are neglected and resultant errors are evaluated. Boundary conditions at the edge of the mixing layer are evaluated by streamline tracing to shock entry points. The sensitivity of properties in the mixing layer to variations in the plume angle of attack, engine nozzle efficiency and engine thrust are examined, and an approximate density and thrust scaling of mixing-layer overall properties is developed.

Forced axial flow in an annular gap of a cylindrical rotor is investigated analytically and experimentally. At small rotation rates and narrow gap widths, the axial flow is a simple Poiseuille flow over most of the rotor. The distance required for this Poiseuille flow to get established is estimated. An instability is observed at large rotation rates with certain input geometries.

This paper is concerned with understanding the development of a free surface and the velocity of a thick creeping film emerging from a slit onto a plate. There is a difference between free surface flows with film thickness of 10 to 20 mm and thin film flows of less than 1 to 2 mm due to surface tension influence.

A laser–Doppler velocimeter of high spatial and temporal resolution has been used to measure the decreasing thickness of slowly flowing liquid and the velocity profiles at the exit of the slit and in the transition region of the plate. The hydrodynamic entrance length can be calculated from an empirical dimensionless relation that includes only the plate inclination angle β as a parameter.

The investigation by Hayes (1964a) of the behaviour of a constant-density inviscid rotational flow in the neighbourhood of a stagnation point on a plane wall has been extended to include the effects of viscosity. The principal effect is the manner in which the singularity in vorticity discovered by Hayes is removed. A solution of only the boundary-layer equatiosn indicates the vorticity decays algebraically from the wall. Application of the method of matched asymptotic expansions, however, shows that the difference between boundary layer and outer vorticity, when carried out to second order in the outer flow, does not contribute to an algebraic decay. These results suggest that an infinite number of higher-order outer terms are generated which match the algebraic terms thereby yielding the conventional exponential decay. Numerical results are presented which also support this conclusion. The main contribution of the wall shear stress in the immediate neighbourhood of the stagnation point is shown to come from the external lateral vorticity.

A generalized linear theory is developed for a compressible shear flow by extending the Fourier integral representations for the pressure field disturbed by pressure dipoles, and it is applied to a transonic shear flow past a thin aerofoil.

A method of determining the pressure distribution on the aerofoil surface is shown. Some numerical examples are presented and discussed.

It is found that the three-dimensional effect due to non-uniformity of the Mach number appears in the greatest degree at lower supersonic span-stations. Even within the scope of the linearized theory not such a great lift force arises near the sonic station as would be expected from the linearized uniform flow theory.

The conditions under which stationary waves may exist on a stream of water of finite depth are investigated theoretically for the case of a current which is uniform except for a constant defect in velocity in a region near the free surface. The analysis is extended to provide a two-dimensional theory for the surface profile induced by a simplified model of a hovering craft. The relevance of this work to the use of high speed flumes is discussed, and an example demonstrates the importance of the velocity distribution near the free surface.

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.

The internal waves produced by a moving body are generally longer in the direction of motion than the corresponding surface waves. This difference is accentuated when the density variation is slight and the body velocity is large in which case a very long towing tank may be required for the simulation of a steady-state condition. The following theoretical study of transient waves is intended as a step in relating test conditions and requisite towing-tank sizes.

A source–sink pair travelling for a finite time is used to represent the restricted motion of a body in a tank. The approximate length and volume of the body are fixed, but its precise shape (somewhat irregular and slightly time dependent) is assumed to be of secondary importance and is not calculated here. The density-stratified fluid is assumed to have a constant Brunt–Väisälä frequency.

A solution in the form of a triple sum over the tank eigenfunctions applies quite generally for the internal wave system (neglecting surface waves and the potential-flow-type solution near the body). Examples covering the large-scale structure of the flow field have been solved for two values of an approximate similarity parameter. The value of the similarity parameter indicates how closely steady-state conditions are approached. The first (larger) value chosen produces a well-defined quasi-steady state near the body with transient fluctuations of the order of ± 10%. The second (smaller) value gives a poorly defined quasisteady state with fluctuations of the order of ±50%. More elaborate studies varying the tank length, width and depth could be made by programming the calculations.

The effect of a collapsing wake has not been considered here, but might possibly be treated by similar methods.