A series of experiments has been undertaken in which three major properties of a surface tension-gravity wave system have been examined. The results of these experiments have been compared with existing theories. The three properties are: (i) viscous decay in the absence of mean flow, the relevant theory being given in Lamb (1932, § 348); (ii) propagation velocities in the presence and absence of flow (Lamb 1932, § 267), and (iii) the change of wave energy on crossing a stable Couette shear flow. The measurements in the last case were compared with two theories, one obtained from the Navier–Stokes equations including terms up to second order in wave slope, the other, following previous authors, obtained on the assumption that any direct interaction of the waves with the shear flow is negligible. According to the theory obtained from the Navier–Stokes equations, the divergence of surface wave energy is equal to the rate of change of wave energy due to the interaction between the mean flow and the wave system plus the rate of change of wave energy due to viscous decay.

An optical system was used to measure the maximum wave slopes, the wave-numbers and the shear velocities.

Results indicate that an anomalous region of wave properties exists for wave-numbers near 2.7 cm−1. For a set of data in which the wave-numbers were always less than 1.8 cm−1, it was found that the viscous decay rate and the propagation laws agree with theory to within the experimental error, and the interaction measurements fit the theory with the non-linear term included rather than the traditional theories.

Electrical power of 0·32MW has been extracted for a period of 100 μsec from a plasma of shock-ionized argon travelling at 4×105cm per sec through a magnetic field of 10,000 G. Currents of more than 10,000amp are drawn and the resulting modification of the applied field is considered.

Maximum power is obtained when the external load is matched to the plasma generator which has an internal impedance equivalent to its own electrical resistance in series with a resistance arising from its behaviour as a compressible fluid.

Values of the electrical conductivity of the plasma obtained in these experiments (about 3 × 103mho per metre) show that the plasma resistance is controlled by electron motion and these values are in good agreement with those found by other methods.

Linearized methods developed in earlier papers (Spence 1956, 1961) are used to discuss the non-stationary flow of a wing with a jet-flap. We consider a thin twodimensional wing at zero incidence in a steady stream of speed U, with a thin jet emerging parallel to the chord at the trailing edge, and study the motion following an instantaneous deflexion of the jet through an angle τ0. If the momentum-flux coefficient CJ of the jet is [Lt ] 4, the governing equations can be put in a form in which CJ does not appear explicitly, and a similarity solution then gives the shape of the jet at small times t from the start of the motion as a function of $(x -c)\mu ^{-\frac {1}{3}}t^{-\frac {2}{3}}$, where x= c is the trailing edge and $\mu = \frac{1}{2}C_J$. The solution is obtained from a certain third-order integro-differential equation, by constructing the Mellin transform of the non-dimensional shape. When t is large the jet near the wing approaches the shape given by the known results for steady flow, but its shape at distances of the order of Ut downstream changes diffusively under the action of the starting vortex. A similarity solution is also found for the flow in this region in terms of $(x -c)\mu ^{-\frac {1}{3}}t^{-\frac {2}{3}}$, without restriction to small μ. Expressions for the lift coefficient at small and large times are found, and the case of an oscillating deflexion angle is treated by the same methods.

The common assumption that the energy of waves on a non-uniform current U is propagated with a velocity (U + c) where cg is the group-velocity, and that no further interaction takes place, is shown in this paper to be incorrect. In fact the current does additional work on the waves at a rate γijSij where γij is the symmetric rate-of-strain tensor associated with the current, and Sij is the radiation stress tensor introduced earlier (Longuet-Higgins & Stewart 1960).

In the present paper we first obtain an asymptotic solution for the combined velocity potential in the simple case (1) when the non-uniform current U is in the direction of wave propagation and the horizontal variation of U is compensated by a vertical upwelling from below. The change in wave amplitude is shown to be such as would be found by inclusion of the radiation stress term.

In a second example (2) the current on the x-axis is assumed to be as in (1), but the horizontal variation in U is compensated by a small horizontal inflow from the sides. It is found that in that case the wave amplitude is also affected by the horizontal advection of wave energy from the sides.

From cases (1) and (2) the general law of interaction between short waves and non-uniform currents is inferred. This is then applied to a third example (3) when waves encounter a current with vertical axis of shear, at an oblique angle. The change in wave amplitude is shown to differ somewhat from the previously accepted value.

The conclusion that non-linear interactions affect the amplification of the waves has some bearing on the theoretical efficiency of hydraulic and pneumatic breakwaters.

Sphere drag has been measured in a low-density supersonic wind tunnel by a simple displacement technique. A conical nozzle of fixed geometry, operated at a constant supply temperature of about 300 °K was used. Test section Mach numbers ranged between 3.8 and 4.3 depending on supply pressure. The Reynolds number and Knudsen number range, based on free-stream conditions and sphere diameter, were 50 < Re∞ < 1000 and 0·106 < Kn∞ < 0·006, respectively. This range was achieved by varying sphere size and supply pressure. The drag coefficient was found to increase from a value of CD = 1·17 at Re∞ = 1000 to CD = 1·73 at Re∞ = 50.

The paper gives the result of a study on the efflux of gases through circular apertures. The problem is considered as an example of a transition from the gasdynamic to the gaskinetic régime.

The mass flow of helium, argon and nitrogen was measured for a range of upstream pressures corresponding to (mean free path)/(aperture diameter) from about 50 to 5 × 10−3; within this range the transition from molecular effusion to inviscid, transonic flow takes place. The theory for the two asymptotic limits is discussed and first-order corrections to the free molecular and inviscid limit formulae are given.

The present paper is concerned with the conditions of flow in tanks containing stirred fluids. An attempt is made to apply the theoretical concepts of local isotropy to explain the behaviour of liquid in liquid dispersions, subjected to turbulent agitation. Relations describing quantitatively the influence of turbulence on both break-up and coalescence of individual droplets are derived and are compared with experimental evidence. A special type of dispersion is described in which droplet size is controlled by the prevention of coalescence due to turbulence. The dependence of droplet size on energy dissipation per unit mass, as predicted by the theory of local isotropy, is put to an experimental test using geometrically similar vessels of different sizes.

Though the results are not entirely conclusive, experimental evidence suggests that the hypothesis of locally isotropic flow may be applicable to the flow conditions described in the paper, and that statistical theories of turbulence can be of practical value in estimating droplet sizes in agitated dispersions.

On the basis of results from a previous paper, expressions are found for the phase velocity and amplification rate of a wave travelling obliquely to the direction of flow. This wave comprises the general harmonic component of three-dimensional small disturbances, and accordingly a double Fourier integral is introduced to represent a bounded disturbance whose initial distribution over the free surface may be arbitrarily prescribed. Hence an asymptotic approximation is derived for a disturbance which is initially concentrated around a point on the free surface. Several distinctive properties of a localized unstable disturbance are noted: for instance, it lies mainly within an elliptical region whose area increases linearly with time as it moves downstream and which is modulated by long-crested waves. An experimental observation of a growing disturbance on an unstable film is recorded, and its main features are seen to be in agreement with the theory.

In so far as linearized perturbation theory remains applicable, the effects investigated are common to a wide class of parallel and nearly parallel laminar flows. In the final part of the paper the method used to analyse the instability of a film is generalized in order to reveal the connexion between this and other problems; this aim is achieved by demonstrating collective properties of the complete class of flows in question, but particular reference is made to the example of laminary boundary layers and Poiseuille flow between parallel planes.

It is shown that for appropriately posed problems, the solutions of the linearized Navier–Stokes equations approach those of the linearized Euler equations as the viscosity tends to zero.

A study of the stability of a plane laminar flame front is made. The effects of disturbances on the flame structure are investigated by a small perturbations technique, taking into account the mechanism of diffusion, heat conduction and unsteady combustion. By use of a simplified model of the flame structure, and the assumption that the flame thickness is small compared with the wavelength of disturbances, a formula for the perturbation of the flame propagation velocity is derived. The flame velocity is shown to depend on the curvature of the flame, and on the rates of change of fluid velocities at the flame boundary. From stability analysis it then follows that properties of the mixture, as expressed in terms of the coefficient of heat conductivity and various coefficients of diffusion, play an important role in determining the stability picture. For some estimated values of these parameters the theoretical results are shown to agree with the general trend of the experimentally observed behaviour.

The motion of drops of liquid through an immiscible field liquid has been observed and drag coefficients have been measured at Reynolds numbers from 0.01 to 1500. Several kinds of motion have been distinguished and it has been noticed that a change in the motion is always preceded by an increase in the drag coefficient and is usually followed by a return to the drag coefficient for solid spheres. When the drop is deformed, the drag coefficient and the form of the motion is not determined solely by the Reynolds number. The effect of the walls of a containing vessel on the motion is computed for low Reynolds numbers.

This paper is concerned with the boundary layer on a semi-infinite flat plate in a uniform stream of conducting fluid, with a magnetic field in the stream direction such that the Alfvén speed is less than the undisturbed fluid speed. Series solutions are derived which are applicable for large and small values of the electrical conductivity, and which give a guide as to the validity and limitations of theories which assume the fluid to have infinite or zero conductivity.

Simple ideas of dimensional analysis and of limiting cases are used to elucidate the stability characteristics of a steady basic parallel flow of a viscous incompressible fluid. The principal result is that the stability characteristics of a smoothly varying velocity profile for wave disturbances of small wave-number can be found by use of a discontinuous velocity profile. The boundary conditions for a disturbance at a discontinuity of the basic flow are derived, and are used to find the stability characteristics of broken-line representations of the hal-jet and jet. These findings are in agreement with previous ones.

By applying the method of initial values to the theory of stability of shear flows, Case has recently found certain results which are in apparent conflict with those obtained by the theory of normal modes. It is shown how these differences may be reconciled. Some new features in the theory of normal modes are also brought out. The relative merits of the two theories are compared.

Many salient features of fully developed turbulent jets, plumes and wakes with steady mean flow are shown clearly by the relationship between the momentum flux and the mass flux in the column of moving fluid. Using a simple model for the flows, this relationship can be found from the solution of a single ordinary differential equation and the character of many related flows can be represented immediately (except for actual distribution in space) on a single momentummass flux diagram.

In this note some approximate solutions based on dimensional arguments are outlined briefly for cases of buoyant and non-buoyant wakes and jets directed along the axis of a uniform main stream, and momentum-mass flux curves are presented.

An I.B.M. 704 electronic computer was used to integrate the differential equations, which determine the shock singularity, when the velocity after the shock on a body is subsonic. The results are given in twenty-two cases corresponding to three different bodies; the procedure followed was outlined in a previous paper (Cabannes 1952).

Scorer (1950) has described an extension of the method of stationary phase. This method is used to derive an approximation to the wave pattern at large distances from the ship in a simple manner. The approximation is valid in the vicinity of the critical angle and the nature of the disturbance in this region is readily seen. The divergent and transverse wave systems in a critical region are shown, together with their variation of amplitude and phase.

An investigation has been carried out on the behaviour of a thin sheet of liquid in connexion with the new method of lacquer application known as ’curtain coating’. A method is described for measuring the velocity of the sheet and an equation deduced for calculating this for a liquid of any viscosity. The minimum liquid flow rate required to maintain a stable sheet is discussed, and some effects of the impingement of the sheet on a rapidly moving surface are described.

Recent work by Hall and Vinen has established that mutual friction between the normal and superfluid components of liquid helium II is caused by interactions between quantized vortex-lines and the normal fluid. If the mean separation of the vortex-lines is small compared with the channel width, the general character of the flow may not depend on the discrete nature of the lines except in so far as this is the cause of the mutual friction. Equations of motion are developed which refer to components of the velocity field with a scale large compared with the line separation, and these are used to discuss the nature of possible turbulent motions. Reasons are given for believing that isothermal flow is very similar to that of a Newtonian fluid, and the theory is developed for turbulent pressure flow along a channel and a circular pipe. The predicted variation of flow rate with pressure gradient is in good agreement with experimental measurements for Reynolds numbers (based on tube diameter and normal fluid viscosity) above 1400, and it is likely that turbulent flow can exist only above this critical Reynolds number. For Reynolds numbers which are not too small, the equations of motion apply to steady ’laminar’ flow and these lead to a relation between flow rate and pressure gradient in reasonable agreement with experiment.

In this paper steady flows of an incompressible, viscous, electrically conducting fluid are constructed from fundamental solutions of magnetohydrodynamics in which the applied magnetic field is parallel to the velocity at infinity. The flat plate and the sphere are considered as examples, and approximate solutions are presented for the limiting cases of large and small Reynolds and magnetic Reynolds numbers. The effects of currents in the body are also considered, and it is found that unless the magnetic Prandtl number is larger than unity, currents in the body have negligible effect on the flow.