This paper studies the effect of profile thickness on the propulsive forces generated by the swimming of a two-dimensional fish. Comparison of numerical calculations with reported experimental data shows good agreement and demonstrates a decrease of thrust with increasing thickness. Previous two-dimensional linearized theories on fish propulsion dealing with the motion of an infinitesimally thin hydrofoil are included in the present contribution as special cases.

The viscous hypersonic flow past an axisymmetric blunt body is analysed based upon the Navier-Stokes equations. It is assumed that the fluid is a perfect gas having constant specific heats, a constant Prandtl number, P, whose numerical value is of order one, and a viscosity coefficient varying as a power, ω, of the absolute temperature. Limiting forms of solutions are studied as the free-stream Mach number, M, and the free-stream Reynolds number based on the body nose radius, R, go to infinity, and ε = (γ − 1)/(γ + 1), where γ is the ratio of the specific heats, and δ = 1/(γ − 1) M2 go to zero.

Random fluctuations in sea level, ζ, in the frequency range 0·1-60 cycles per hour were measured along the coast near Oceanside, California, where the coastline and bottom contours are fairly straight and parallel for 30 km. The two-dimensional covariance $R(\eta, \tau) = \langle \zeta (y,t) \zeta (y + \eta, t+ \tau) \rangle$ was computed for points separated by various distances η along the coast. The Fourier transform $S(f,n) = \int \int R(\eta, \tau)exp [2\pi i (n \eta + f \tau)]d \eta d \tau$ gives the contribution towards the ‘energy’ $\langle \zeta ^2 \rangle$ per unit temporal frequency f per unit spacial frequency (long-shore component) n. It is found that most of the energy is confined to a few narrow bands in (f, n) space, and these observed bands correspond very closely to the gravest trapped modes (or edge waves) computed for the actual depth profile. The bands are 0·02 cycles per km wide, which equals the theoretical resolution of the 30 km array. Very roughly S(f,n) ≈ S(f, -n), corresponding to equal partition of energy between waves travelling up and down the coast. Theory predicts ‘Coriolis splitting’ between the lines f± (n) corresponding to these oppositely travelling waves, but this effect is below the limit of detection. The principal conclusion is that most of the low-frequency wave energy is trapped.

The theory is presented for the generation of secondary vorticity in a stratified fluid. The analysis is a generalization of original work of Hawthorne (1951). It is shown that for an incompressible, inviscid and non-diffusive flow, a flowwise vorticity component will be generated in a curved stream when a density gradient exists in the direction of the bi-normal to the streamline.

When the angular amplitude of oscillation of a sphere in an infinite mass of elastico-viscous fluid is fairly small, so that velocity and stress components may be expanded as power series in this amplitude, the purely periodic primary motion has associated with it a secondary flow which has a steady component as well as a component of double the primary frequency. An expression for the stream function of the steady secondary flow is obtained for all possible frequencies and the results are illustrated by considering in detail a particular fluid. It is shown that the streamline projections on a plane containing the axis of rotation are strongly dependent on the parameters measuring the elasticity of the fluid and on the frequency. The circulatory secondary flow can be in the opposite sense to that in a Newtonian fluid, in either the whole or part of the elastico-viscous fluid.

A new instrument for measuring the velocities of particles suspended in a flowing fluid is described. The instrument is linear and is therefore capable of measuring the mean velocity in a fluctuating stream, even when these fluctuations are greater than this mean value. This particular instrument was developed for free convection work where the velocities to be measured were in the range + k 0.2 in./sec to − 0.2 in./sec, but there seems to be no reason why this range could not be considerably extended.

An analytical investigation is carried out to determine the conditions for instability in a viscous fluid contained between rotating coaxial cylinders of arbitrary radius ratio. A solution method is outlined and then applied to cylinders having radius ratios ranging from 0·95 to 0·1. Consideration is given to both cases wherein the cylinders are rotating in the same direction and in opposite directions. Results are reported for the Taylor numbers and wave-numbers which mark the onset of instability. The present results are also employed to delineate the range of applicability of the closed-form instability predictions of Taylor and of Meksyn, which were derived for narrow-gap conditions.

The wall-jet is the flow of fluid emanating from a narrow slot and blowing over a rigid wall. The configuration of the turbulent wall-jet is that of a very narrow, plane, turbulent half-jet investigated by Liepmann & Laufer (1947). The width of the slot is of the order of the boundary layer on the infinite wall and the jet, in this case, mixes with a stream moving with constant velocity. This flow has drawn considerable basic and applied interest in the past few years for it has the characteristics of both a boundary-layer and a free-mixing flow.

A theoretical analysis is given of the unsteady flow of a liquid within a cylinder of finite length started suddenly so as to spin about its axis. It is found that a secondary flow, caused by the end walls of the cylindrical container, has a strong effect on the generation of spin in the liquid. In the vicinity of the end walls the fluid motion is characterized by a boundary-layer flow, which can be either laminar or turbulent. The fluid within the boundary layers rotates faster than that at a large distance from the end walls, and therefore is thrown, by centrifugal forces, radially outwards. The radial outflow in the boundary layer creates a slow secondary motion within the spinning liquid. Due to the secondary flow, the transport of angular momentum from the walls to the interior is accomplished by convection rather than diffusion. A treatment is given for both laminar and turbulent end-wall boundary layers. The theoretical results are compared with experimental observations and good agreement is found.

We have made a theoretical and experimental study of the effect of radiative transfer on the onset of convection by means of comparative experiments in dry air and ammonia contained between horizontal aluminium plates maintained at different temperatures.

The first effect of radiative transfer is to distort the linear, diffusive profile in the initial, pre-convective state. A non-grey theory is developed and is shown to predict the non-linear profiles profiles with satisfactory accuracy. The change of radiative flux with pressure of ammonia is also predicted and confirmed. This constitutes the first successful attempt to confirm the methods used in atmospheric studies in controlled experiment.

A non-grey theory of the onset of convection is developed, separating effects associated with the distortion of the static state and the dissipative effect of radiative transfer on temperature fluctuations.

Experiments indicate that the critical Rayleigh number in ammonia can be greatly increaesd over the best value for air (Rac = 1786); the maximum observed being Rac = 4870. Theory and experiment are shown to agree within reasonable limits.

This work confirms the validity of methods which are of great importance to astrophysics and atmospheric physics.

Experimental confirmation of some streamline patterns suggested by Taylor (1961) is described. It is shown, also, that when a viscous fluid is expelled from a tube by an inviscid fluid, the interface has a ‘localized’ effect on the fluid ahead of the interface between the two liquids, that is, the usual Hagen–Poiseuille law is obeyd in the viscous fluid except for the region behind a point about 1½ tube diameters ahead of the bubble.

Use of a recently developed tungsten-iodide lamp is also described.

We consider here flow past an obstacle on the lower of two rotating horizontal planes which bound a viscous fluid. It is found that when the Taylor number is large viscous effects are confined to Ekman boundary layers on the solid surfaces and to a free shear layer coincident with the vertical cylinder circumscribing the bottom obstacle. The flow in the main body of the fluid outside the cylinder proves to be two-dimensional with zero relative vorticity, while inside the cylinder the fluid is stagnant in the rotating frame. The shear layer provides a continuous transition between the exterior and interior of the cylinder, and in addition provides a means by which fluid from the Ekman layers on the horizontal planes is exchanged with fluid outside the Ekman layers and exterior to the circumscribing cylinder. The predicted flow proves to be in agreement with many of the experimental results.

The logical design method of Owen & Zienkiewicz (1957), for the generation of linear shear flow, is successfully applied to the case of symmetrical velocity profiles in a two-dimensional duct. Shear parameters as high as 0·8 (corresponding to $\hat{V}| \overline {V} = 1\cdot4$) are obtained experimentally. Some slight modification to the theoretical grid spacing is required because of the non-uniformity of the upstream flow.

The decay of the profiles is confined to that due to the developing boundary layer and to the breakdown of the physically impossible condition at the centre, where symmetry implies a change in sign of the uniform shear.

The stability of Couette flow is discussed in the case in which the cylindes rotate in opposite directions by an asymptotic method in which the Taylor number is treated as a large parameter. On assuming the principle of exchange of stabilities to hold, the problem is then governed by a sixth-order differential equation with a simple turning point. It is shown how the solutions of this equation can be represented asymptotically in terms of the solutions of the comparison equation yvi = xy. The solutions of this comparison equation have recently been tabulated and we thus have an explicit representation of the solution of the stability problem in terms of tabulate functions. Detailed results for the critical Taylor number and wave-number at the onset of instability and the associated eigenfunctions are given for the limiting case μ → − ∞, where μ = Ω2/Ω1, and Ω1 and Ω2 are the angular velocities of the inner and outer cylinders respectively. In this limiting case it is found that there exists and infinite number of cells between the cylinders, but that the amplitude of the secondary motion in all but the innermost cell is small.

A compact cluster of 3 to 6 rigid equal spheres is falling under gravity in a viscous liquid. The small effects of intertia on a horizontal regular polygonal configuration are that the polygon expands as it falls and small perturbations from this configuration die out, although when the polygon is large enough it becomes weakly unstable. This is an extension of the analysis of Hocking (1964, which was applied to the experiments of Jayaweera, Mason & Slack (1964).

First- and second-order boundary-layer theory are examined in detail for some specific flow cases of practical interest. These cases are for flows over blunt axisymmetric bodies in hypersonic high-altitude (or low density) flow where second-order boundary-layer quantities may become important. These cases consist of flow over a hyperboloid and a paraboloid both with free-stream Mach number infinity and flow over a sphere at free-stream Mach number 10. The method employed in finding the solutions is an implicit finite-difference scheme. It is found to exhibit both stability and accuracy in the examples computed. The method consists of starting near the stagnation-point of a blunt body and marching downstream along the body surface. Several interesting properties of the boundary layer are pointed out, such as the nature of some second-order boundary-layer quantities far downstream in the flow past a sphere and the effect of strong vorticity interaction on the second-order boundary layer in the flow past a hyperboloid. In several of the flow cases, results are compared with other theories and experiments.

The problem of the flow near a stagnation point when the main stream outside the boundary layer fluctuates in magnitude but not in direction about a steady mean is discussed. The velocity distribution is found in the two limiting cases of small and large values of the frequency of the oscillation. The corresponding two approximate solutions give similar results in an overlapping range of frequency.

The problem of flow over a circular cone inclined slightly to a uniform stream is solved using the technique of matched asymptotic expansions. The outer expansion is equivalent to Stone's solution of the problem. The inner expansion, valid in a thin layer near the body, represents Ferri's vortical layer. The solution to first order in angle of attack so obtained is uniformly valid everywhere in the flow field. In the second-order expansion an additional non-uniformity appears near the leeward ray. This defect is removed by inspection. The first-order solution is in agreement with that of Cheng, Woods, Bulakh and Sapunkov. Formulas are given that may be used to render Kopal's numerical result uniformly valid to second order in angle of attack.

A simple numerical method is presented for solving the eigenvalue problem which governs the stability of Couette flow. The method is particularly useful in obtaining the eigenfunctions associated with the various modes of instability. When the cylinders rotate in opposite directions, these eigenfunctions exhibit an exponentially damped oscillatory behaviour for sufficiently large values of − μ, where μ = Ω2/Ω1. In terms of the stream function which describes the motion in planes through the axis of the cylinders, this means that weak, viscously driven cells appear in the outer layes of the fluid which, according to Rayleigh's criterion, are dynamically stable. For μ = − 3, for example, four cells are present, the amplitudes of which are in the ratios 1·0:0·0172:0·013:0·00125.

General solutions for the linearized three-dimensional unsteady motion of a relaxing gas, including the effects of direct heat addition, are obtained using a Green's function technique. The possibility of direct heat addition into each separate mode of energy storage must be catered for, and the solutions have some bearing on the question of the heating of a gas by radiation.

Examples are given of initial-value and heat-source solutions in an unbounded domain and the boundary-value problem is exemplified by a study of the motion created by a spherical piston.