The linearized problem of two-dimensional gravity waves in a viscous incompressible stratified fluid occupying the upper half-space z > 0 is investigated. It is assumed that the dynamic viscosity coefficient μ is constant and that the density distribution ρ(z) is exponential. This leads to a fourth-order differential equation in the z co-ordinate, the coefficients of which depend on ρ(z) and on a dimensionless parameter ε which is proportional to μ/σ, σ being the frequency of the oscillation. The problem is solved for small ε. It is found that there is a region in which the solutions behave like certain solutions of the inviscid problem (with ε = 0). However, when the solutions of the inviscid problem are wave-like in z, they do not satisfy the radiation condition. This is because the viscosity, in addition to damping the motion for large z, reflects waves. The appropriate solution of the inviscid problem consists, therefore, of an incident and a reflected wave. As μ → 0, the ratio of the amplitudes of the reflected and the incident wave approaches exp (− 2π2H/Λ), where Λ is the vertical wavelength, and H the density scale height. The solution, however, does not have a limit since the reflecting layer shifts, altering the phase of the reflected wave. The results of the analysis are supplemented by a number of numerically computed solutions, which are then used to discuss the validity of the linearization.

For the flow of a stably-stratified fluid in the inlet region of a rectangular duct, it is shown experimentally that the upper and lower critical Reynolds numbers are functions of the interfacial Froude number F, and that if F is large they are lower than for a homogeneous flow. In stratified flows the disturbances leading to turbulent flow sometimes arise at the interface and lead to interfacial waves, whose wavelength at breaking is equal to the conduit depth.

We consider, in this paper, boundary-layer flows which are induced when an isothermal rigid-body rotation is disturbed by heating the fluid. The basic rigid-body rotation is sustained by one or more rotating planes at which the temperature differences are initiated. Conditions of both uniform and unsteady heating are discussed.

The wake behind a two-dimensional bluff body has been photographed in water in order to investigate the modifying effect of base bleed. With this technique it has been possible to measure velocities at chosen points and from these make simultaneous estimates of the base pressure and of the strength of individual vortices in the wake. The results suggest that the observed decay in the vortex structure of the wake is related to variations in the conditions of mixing between the base fluid and the external stream.

The principal characteristics of jet penetration are the appearance of free stream-lines at the sides of the jet and of a dividing streamline, which separates the jet and penetrated fluid. Kinematic analysis of such flow via free-streamline theory and the notched hodograph is developed with one unspecified parameter, the ratio of jet to counterstream velocity in the steady flow case. The kinetics of the problem, appearing when the jet and penetrated (or counterstream) fluid differ in density, is simply related to the kinematic solution via the square root of the density ratio. Experiments, both steady state and transient with several liquids, are presented which generally verify the theory. The experiments also yield information on the magnitude of the parameter and indicate its variation with the density ratio.

When attempts are made to use thin film anemometers in airflow to measure fluctuating velocity it is found that the dynamic sensitivity cannot be obtained from a steady-flow calibration. It is found that the dynamic sensitivity is considerably less than that predicted by static calibration and that the sensitivity is frequency-dependent. It is shown that thermal feedback from the substrate, on which the gauge is mounted, to the heated element is responsible for the variation of sensitivity with frequency, despite constant-temperature operation of the probe, and this variation is examined theoretically and experimentally.

This paper describes an experimental study of the shape of a shock diffracting around a corner made up of two plane walls, for corner angles from 15 to 165° (in 15° steps) and shock Mach numbers from M0 = 1·0 to 4·0. The results are compared with profiles determined from the diffraction theory of Whitham (1957, 1959). The agreement is shown to be good for an incident shock Mach number of 3·0, and fair in other cases. The behaviour is found to follow the trends established by Lighthill (1949) in a linearized theory. Results for the Mach number of the wall shock are also presented. The shock does not degenerate to a sound wave even for large corner angles and low Mach numbers.

The boundary-layer equations for the steady laminar flow of a vertical jet, including a buoyancy term caused by temperature differences, are solved by similarity methods. Two-dimensional and axisymmetric jets are treated. Exact solutions in closed form are found for certain values of the Prandtl number, and the velocity and temperature distribution for other Prandtl numbers are found by numerical integration.

An analysis is made of the effect of a transverse gravity field on a two-dimensional fully cavitating flow past a flat-plate hydrofoil. Under the assumption that the flow is both irrotational and incompressible, a non-linear method is developed by using conformal mapping and the solution to a mixed-boundary-value problem in an auxiliary half plane. A new cavity model, proposed by Tulin (1964a), is employed. The solution to the gravity-affected case was found by iteration; the non-gravity solution was used as the initial trial of a rapidly convergent process. The theory indicates that the lift and cavity size are reduced by the gravity field. Typical results are presented and compared to Parkin's (1957) linear theory.

A horizontal fluid layer whose lower surface temperature is made to vary with time is considered. The stability analysis for this situation shows that the criterion for the onset of instability in a fluid layer which is being heated from below, depends on both the method and the rate of heating. For a fluid layer with two rigid boundaries, the minimum Rayleigh number corresponding to the onset of instability is found to be 1340. For slower heating rates the critical Rayleigh number increases to a maximum value of 1707·8, while for faster heating rates the critical Rayleigh number increases without limit.

Two specific types of heating are investigated in detail, constant flux heating and linearly varying surface temperature. These cases correspond closely to situations for which published data exist. The results are in good qualitative agreement.

The hypersonic weak-interaction regime for the flow of a viscous, heat-conducting compressible fluid past a flat plate is analysed using the Navier-Stokes equations as a basis. The fluid is assumed to be a perfect gas having constant specific heats, a constant Prandtl number, σ, of order unity, and a viscosity coefficient varying as a power, ω, of the absolute temperature. Limiting forms of solutions are studied for the free-stream Mach number, M, the free-stream Reynolds number (based on the plate length), RL, and the reciprocal of the weak-interaction parameter, (ξ*)−1 = [Fscr ](M, RL, ω, σ), greater than order unity.

By means of matched asymptotic expansions, it is shown that, for (1 − ω) > 0, the zone between the shock wave and the plate is composed of four distinct regions for which similarity exists. The behaviour of the flow in these four regions is analysed.

A theory is developed to determine the shape of water-bells. The motion of the gas induced by the moving walls is taken into account in this analysis. A rapidly converging iterative procedure leads to a theoretical shape which agrees well with the experimental shape of the water-bell.

A theoretical study is made of a simple design for an underwater shock gun, which consists of a chamber in the form of a hollow circular cone, with a spherical sector of explosive charge fitted into the apex. When the explosive is initiated at the apex, the resulting sector of a spherical blast wave will be diffracted by expansion waves moving inwards after the leading shock has emerged from the rim of the cone.

The progress of the expansion wave-fronts is calculated, and the results show a surprising inability of the diffraction process to ‘eat into’ the full-strength sector of spherical blast. It is found to be possible to design such a gun so that it is capable of projecting a high intensity shock-pressure beam over a considerable range, using only a very small explosive charge.

Experiments were performed studying the formation of a dip on the surface of an initially stationary liquid draining from a cylindrical tank through an axisym-metrically placed circular orifice. Based upon the information obtained from the experiments, a simple analytical expression was derived predicting the height of the liquid surface in the tank at which this dip forms. A comparison was made between the experimental data and the results of the analysis and good agreement was found between theory and data.

In this article the problem of describing free convection near either horizontal cylinders or vertical axisymmetric bodies with fairly arbitrary body contours is studied. The solutions of two, coupled, partial differential equations, for the temperature and stream functions, are represented by series which are universal with respect to body contours within a specified class of body shapes (e.g. round-nosed cylinders). The series appear to converge rapidly so that a minimum of computational effort is required, even for classes of body shapes which do not admit the usual similarity transformations. For either horizontal, circular cylinders or spheres the series converge faster than expansions of the Blasius type and one-term approximations compare favourably with some of the existing experimental data.

An exact rear stagnation point solution is sought for a viscous, incompressible conducting fluid in the presence of a magnetic field. It is found that a steady solution exists only if [Nscr ] ≥ 2, where [Nscr ] = σB2/ρα is the interaction parameter of the flow based upon the normal component of the magnetic field at the wall. Here α is a positive rate of strain, which, for a finite body with length l and velocity U0, is of the order of U0/l.

The steady solution is found, and from its existence it is inferred that separation of the viscous boundary layer does not begin at the rear stagnation point when [Nscr ] ≥ 2, and that such separation can be prevented. This supports theoretical work by Moreau (1964) and experimental work of Tsinober, Shtern & Shcherbinin (1963).

When [Nscr ] < 2, the flow is necessarily unsteady, and in this case an asymptotic analysis (as t → ∞) similar to that of Proudman & Johnson (1962) is undertaken. For [Nscr ] < 1, the magnetic and non-magnetic flows are qualitatively alike, in that there is a growing inviscid region dominated by eddies, and an ultimately steady layer at the wall representing a viscous forward stagnation point flow.

For 1 < [Nscr ] < 2, the inviscid region again grows with time, but no eddies appear. It is thus suggested that for this range of [Nscr ] separation occurs without reversed flow.