This paper describes an experimental study of the starting process in a reflected-shock tunnel, and compares the results with numerical calculations reported previously (Smith 1962). It is shown that an unsteady expansion wave dominates the transient flow, and the shock-wave system plays a minor role. The effects of initial pressure in the nozzle were investigated, and the behaviour of the secondary shock wave was noted. It was found that initial pressures larger even than the steady-flow static pressure can be tolerated without prolonging the starting process, despite the presence of a strong secondary shock wave. Other analyses, based on the ‘steady-state’ model of the starting process, are discussed and shown to give an unrealistic description of the flow field.

This is a study of the propagation of gravity waves over a basin in which the propagation distance is large compared with the scale of the bottom topography, which, in turn, is large compared with the depth. Special emphasis is given to the low-frequency part of the spectrum and to geometries containing a beach (see figure 1) because of their importance in tidal wave phenomena. Both reflexion phenomena and the dispersive character of the propagation are accounted for and the non-linear aspects of the large amplification associated with the beach climbing are also included. However, the analysis of problems in which the waves break is valid only up to the inception of breaking; post-breaking phenomena are not treated.

The principle of exchange of stabilities (exchange principle) for the thermal stability problem has been proved by Pellew & Southwell (1940) for fluids bounded by two infinite, horizontal parallel planes. Chandrasekhar (1952) discussed the establishment of the exchange principle for the same geometry when the fluid is an electrical conductor and when an arbitrary oriented, uniform, external magnetic field is applied in the vertical direction.

In this paper, the exchange principle is examined for fluids completely confined in an arbitrary region with rigid bounding surfaces that are good electrical conductors with respect to the fluid. The uniform magnetic field is applied in an arbitrary direction. A generalized thermal boundary condition is imposed which includes the fixed temperature and prescribed heat-flux conditions as special cases.

If no magnetic field is applied to the fluid, the present work reduces to a generalization (for completely confined fluids) of the Pellew & Southwell proof of the exchange principle. In the magnetohydrodynamic (MHD) thermal stability problem, the exchange principle is found to be valid if the total kinetic energy associated with an arbitrary disturbance is greater than or equal to its total magnetic energy. In a special case it is demonstrated that a sufficient condition which will establish the exchange principle is k ≤ η, where k is the fluid thermal diffusivity and η is the fluid electrical resistivity.

This paper is concerned with unsteady laminar boundary layers on solid bodies in the presence of a fluctuating external flow of small amplitude. Any containing enclosures are assumed to be at infinity. Compressibility is ignored and conditions are given under which this and other approximations are valid. Special attention is focussed on the phenomenon of the formation of a steady-streaming flow, induced by the Reynolds stresses in the oscillatory boundary layer: it is shown that, if the characteristic Reynolds number of the steady streaming is large, there is an outer boundary layer within which the steady-streaming velocity decays to zero. The thickness of this outer layer is large compared with that of the inner (oscillatory) layer, but small compared with a typical dimension of the body.

The partial differential equation for the flow in the outer layer is solved in a typical case by a generalization of a series-expansion method due to Fettis. Similarity solutions of the equation are also described.

The theory is applied specifically to the case of flow generated by a circular cylinder oscillating along a diameter in an infinite fluid. Qualitative agreement is obtained with experiments performed by Schlichting.

A solution is obtained for the boundary of the magnetic field of two arbitrary line currents immersed in a plasma at uniform pressure. The linear dimensions of the boundary, which are determined for several sets of data, are proportional to the intensity of the line currents (assuming that their ratio is constant) and inversely proportional to the square root of the plasma pressure. The cusps over the boundary, which when the two line currents are equal and opposite are symmetrical with respect to the line currents, move towards the weaker current until they eventually disappear on the line joining the two currents. When the distance between the currents is such that when the cusps disappear the two line currents lie in the same cavity, some plasma gets trapped inside the cavity. When the cavities of two line currents of the same sign touch we get an abrupt instability; the plasma is suddenly pushed out by the surface currents and this results in the formation of a larger field cavity.

When a potential is applied between two electrodes immersed in a flowing chemi-luminescent solution a blue glow appears at the surface of the anode. This glow may be used to observe the behaviour of liquid flows past solid surfaces. An electrochemical system suitable for generating the glow is described. Photographic studies of separated flows past cylinders, flat plates and cones are presented showing the application of the technique of electrochemiluminescence to flow visualization.

The case of a dielectric sphere executing small-amplitude oscillations in an incompressible, conducting fluid with a uniform magnetic field aligned along the axis of oscillation is studied. For the case of large Hartmann and Reynolds numbers, the MHD equations are linearized. Solutions correct to O(Rm) are obtained for the velocity, pressure, current, and electric and magnetic fields in the fluid. The MHD drag on an oscillating dielectric sphere in mercury was experimentally determined in aligned fields to 0·8 Wb/m2. The experimental results agree well with the theory. The theory and experiment were extended to include the régime where the perturbed velocity is not small compared with the velocity present in the absence of a magnetic field. The validity of using the inviscid velocity to compute the current is verified by measuring the angular dependence of the induced electric field.

In this exploratory study, schlieren photography has been used to reveal a variety of convection patterns in pools of evaporating liquids. Pure materials as well as binary solutions were investigated, both in the presence and absence of surface contamination, which was shown to exert a considerable influence on the convective flow. It was found that, with the exception of water, the observed flow structures were largely dependent on the depth of the evaporating pool and to a much lesser extent on the properties of the liquid. Also, it was possible to identify certain flow patterns as being induced by a surface-tension-driven instability and others as being due to buoyancy-driven convection; still other patterns seemed to be uniquely associated with the presence of surface contamination.

Interactions between waves in a stably stratified fluid with a free or fixed upper surface may occur at second order when the horizontal wave-numbers, ki, and frequencies, σi, of the three interacting waves satisfy the relations \[ {\bf k}_1 \pm{\bf k}_2 \pm {\bf k}_3 = 0,\quad \sigma_1 \pm \sigma_2 \pm \sigma_3 = 0. \] These relations may be satisfied in the case when two free surface waves interact with an internal wave, or in the case when all three waves are internal, provided that they do not all belong to the same mode. The theory is applied to situations which might be realized in the laboratory.

A viscous vortex ring is considered as an initial disturbance to a uniformly rotating fluid. Inertial waves are generated by the disturbance and propagate through the fluid affecting the diffusion of the vortex ring with time t. The rate of diffusion is found to be proportional to $t^{\frac{3}{2}}$. This result is compared with the diffusion rates for non-rotating fluids and for conducting fluids under a uniform magnetic field.

The solution given by Gerstner for water waves of finite amplitude, which is valid for a semi-infinite liquid of arbitrary stratification, is reconsidered. By a transformation of co-ordinates, it is shown to represent edge waves propagating along a sloping shore.

The attenuation of progressive, dispersive, oscillatory wave systems by dissipation within the viscous boundary layer in a long laboratory channel was studied both experimentally and theoretically, for the conditions of uniform water depth and over uniform impermeable slopes. In general, the observed dissipation exceeded that predicted by linear, small-amplitude theory for the boundary layer on the sides and bottom of the channel. On the hypothesis that the additional dissipation might be due to the presence of a similar boundary layer at the free water surface, the theory is extended to include the surface effect. The experimental results essentially confirm the theory—even in the markedly nonlinear region near shore.

The von Kármán (1921) rotating disk problem is extended to the case of flow started impulsively from rest; also, the steady-state problem is solved to a higher degree of accuracy than previously by a simple analytical-numerical method which avoids the matching difficulties in Cochran's (1934) well-known solution. Exact representations of the non-steady velocity field and pressure are given by suitable power-series expansions in the angle of rotation, Ωt, with coefficients that are functions of a similarity variable. The first four equations for velocity coefficient functions are solved exactly in closed form, and the next six by numerical integration. This gives four terms in the series for the primary flow and three terms in each series for the secondary flow.

The results indicate that the asymptotic steady state is approached after about 2 radians of the disk's motion and that it can be approximately obtained from the initial-value, time-dependent analysis. Furthermore, the non-steady flow has three phases, the first two of which are accurately and fully described with the terms computed. During the first-half radian (phase 1), the velocity field is essentially similar in time, with boundary-layer thickening the only significant effect. For 0·5 [lsim ] Ωt [lsim ] 1·5 (phase 2), boundary-layer growth continues at a slower rate, but simultaneously the velocity profiles adjust towards the shape of the ultimate steady-state profiles. At about Ωt = 1·5, some flow quantities overshoot the steady-state values by small amounts. In analogy with the ‘Greenspan-Howard problem’ (1963) it is believed that the third phase (Ωt > 1·5) consists of a small amplitude decaying oscillation about the steady-state solution.

The present paper proposes a theory for the mechanical behaviour of a fluid with a rigid microstructure. The microstructure is described by a director frame of three vectors and a second-order tensor W and its gradient are proposed as measures of the kinematics of this frame. When the frame is spinning without deforming, W reduces to the director spin velocity. Postulating the existence of a couple stress in addition to the classical Cauchy stress, the linear constitutive equations for such a structured fluid are derived and then specialized to the case of transverse isotropy.

These equations are used to study rectilinear shearing flow. When [dtri ]W = 0, the condition for a non-interacting substructure, the results of the theory are shown to be in agreement with the work of Jeffery and of Ericksen. For mutually interacting substructure particles, [dtri ]W ≠ 0, a geometric analysis of the non-linear differential equations is performed in order to exhibit the effects of particle concentration on the flow kinematics.

Numerical solutions of the equations of steady free convection in a vertical slot have been obtained by a procedure which relies solely on an iterative solution of Poisson's equation. With a mesh spacing of $\frac{1}{40}$ the solutions are stable up to a Rayleigh number of order 105. The numerical experiments are comparable to the author's laboratory experiments (Elder 1965) and to the experiments of Eckert & Carlson (1961). The growth of the boundary layers and the uniform vertical temperature gradient are well described. It is tentatively suggested that certain unstable motions found prior to the divergence of the numerical solution are comparable to the secondary flows found by the author.