A theory is initiated for the generation of waves upon a water surface, originally at rest, by a random distribution of normal pressure associated with the onset of a turbulent wind. Corrlations between air and water motions are neglected and the water is assumed to be inviscid, so that the motion of the water, starting from rest, is irrotational. It is found that waves develop most rapidly by means of a resonance mechanism which occurs when a component of the surface pressure distribution moves at the same speed as the free surface wave with the same wave-number.

The development of the waves is conveniently considered in two stages, in which the time elapsed is respectively less or greater than the time of development of the pressure fluctuations. An expression is given for the wave spectrum in the initial stage of development (§ 3.2), and it is shown that the most prominent waves are ripples of wavelength λcr = 1·7 cm, corresponding to the minimum phase velocity c = (4gT/ρ)1/4 and moving in directions cos-1(c/Uc) to that of the mean wind, where Uc is the ‘convection velocity’ of the surface pressure fluctuations of length scale λcr or approximately the mean wind speed at a height λcr above the surface. Observations by Roll (1951) have shown the existence under appropriate conditions, of waves qualitatively similar to those predicted by the theory.

Most of the growth of gravity waves occurs in the second, or principal stage of development, which continues until the waves grow so high that non-linear effects become important. An expression for the wave spectrum is derived (§ 4.1), from which follows the result $\overline {\xi ^2} \sim \frac {\overline{p^2}t} {2 \surd 2\rho ^2 U_c g},$ where $\overline {\xi ^2}$ is the mean square surface displacement, $\overline {p ^2}$ the mean square turbulent pressure on the water surface, t the elapsed time, Uc the convection speed of the surface pressure fluctuations, and ρ the water density. This prediction is consistent with published oceanographic measurements (§ 4.3).

It is suggested that this resonance mechanism is more effective than those suggested by Jeffreys (1924, 1925) and Eckart (1953), and may provide the principal means whereby energy is transferred from the wind to the waves.

In the Munk-Jones cross-flow theory for slender bodies of revolution (Munk 1924; Jones 1946), the cross force on an inclined body is obtained by replacing the three-dimensional flow by a non-steady two-dimensional flow, and by equating the cross-force to the rate of change of cross-flow momentum on a transverse lamina moving past the body with the free stream velocity U0. The result obtained for the lift force L on an element of the body is, for small angles of attack α, $dL|dx = \frac {1}{2} \rho U^2_0(dA|dx)2 \alpha$ where A is the cross-sectional area of the body, and, by integration $L = \frac {1}{2} \rho U^2_0 A_B 2 \alpha$ where AB is the base area of the body.

For flows of jet type, the assumption of a coefficient of eddy kinematic viscosity in turbulent flow leads to the possibility of combining in one the equations for laminar and turbulent motion. An approximation to the solution of these equations is found for the flow of compressible fluid issuing from a narrow slit, far from the slit. The stream function is expanded in a power series in squares of the Mach number. Bickley's solution (1937) for the corresponding problem in incompressible flow is used to start the iterative process by which successive terms of the power series are obtained. In order to find an analytical form for the second term of the series, it has been assumed that the Prandtl number is unity, that the viscosity varies as the nth power of the absolute temperature, and that the stagnation temperature of the jet is the same as that of the surrounding gas. The solution found differs only slightly from that of Howarth (1948) and Illingworth (1949) when laminar flow is considered; only the ‘change of scale’ effect (arising from a distortion of the coordinates in Bickley's solution) is of importance. In turbulent flow the effect of the second term of the series is as important as the ‘change of scale’ effect. The effect of compressibility on the width of the mixing region is discussed for both laminar and turbulent jet flow far from the orifice.

In the first part of the paper the dimensional laws governing the processes of heat and momentum transport from an infinite rough plane are assembled and their consequences set out. In the second part, the detailed equations for the turbulent energy, the mean square temperature fluctuation and the covariance of temperature and vertical velocity are used, together with some speculative assumptions concerning the dissipative action of the turbulence, to derive a series of relations between the turbulent intensities and the Austausch coefficients. One of these relations indicates that the flux form of the Richardson number cannot exceed a critical value which is about 0·15. It follows that in highly stable conditions the buoyancy forces have little direct effect on the turbulent energy balance, their action being primarily to cause a reduction in the scale of the motion and some change in its structure.

This paper deals with an experimental investigation of a turbulent low-speed jet of air spreading out radially over a flat smooth plate: a flow which has been discussed by Glauert (1956) in his theory of the wall jet.

The aim of the experiments has been to determine the mean velocity distribution and rate of growth of the jet. It is found, within the experimental range and accuracy, that the velocity profiles are similar and that the rate of change of velocity and width of the jet can be expressed by simple power-laws.

Detailed measurements have been made of the temperature field in natural convection above a heated horizontal surface in air, with and without a cold upper boudary. The object was to provide experimental material for the testing of existing theories of convection and the development of new ones. Using a variety of experimental techniques, it was possible to measure the heat transfer, the mean temperature profiles, mean squares of the temperature fluctuations and the autocorrelation functions of the temperature fluctuations. These results are considered in relation with the ‘similarity’ theory of Priestley and the ‘neutral stability’ theory of Malkus. Both these theories lead to the conclusion that, for convection between parallel planes at high Rayleigh numbers, nearly the whole of the mean temperature variation occurs in comparatively thin surface layers whose mutual interaction is small. The present experiments confirm this in some detail, but the exact form of the variation of mean temperature cannot be completely reconciled with either of the theories.

In an earlier paper the uniform shear flow past a sphere was studied, by investigating how vortex lines are deformed by the ‘primary flow’ (flow in the absence of shear), and deducing the ‘secondary’ vorticity field (first approximation for small shear). In another paper the image system associated with each element of secondary vorticity was found, whence the Biot-Savart law can be used to determine the secondary flow field by integration. The integration is here carried out for the ‘downwash’ (secondary flow component perpendicular to the undisturbed flow, down the velocity gradient) on the dividing streamline. Difficulties due to the infinite domain of integration and singularities of the integrand are overcome by selecting variables of integration carefully and using known analytical properties of the secondary vorticity. From the computation of downwash is inferred the first approximation (for small shear A) to the ‘displacement’ δ (displacement of the dividing streamline, up the velocity gradient, far upstream of the sphere). If U is the upstream flow velocity and a the radius of the sphere, the computed value of lim (Uδ/Aa2) is 0·9. $A \rightarrow 0$ Details of the calculation show that the secondary trailing vorticity is not an important contributor to the displacement, The downwash is due almost entirely to vorticity upstream of the sphere (Hall's earlier simplified theory gave good results, e.g., 1.24 instead of 0.9, because it concentrated on the effect of local vorticity in producing downwash); further, this produces displacement principally through its image vorticity.

The relation between theories for a sphere and experimental results on Pitot tubes (beginning with Young & Maas 1936) is discussed. Theoretical evidence on tertiary- and quartary-flow effects is used here in the light of recent work which renders the successive-approximation sequence uniformly valid at infinity. The conclusion is that the theories, taken together, are not inconsistent with the experimental evidence that (i) at values of the ‘shear parameter’ Aa/U at which the displacement is measurable the ratio δ/a seems to have asymptoted to an approximately constant value, and (ii) displacement is greatly reduced in supersonic flow (Johannesen & Mair 1952) or when ‘sharp-lipped’ tubes are used (Livesey 1956).

With the increasing popularity of combustion driving in strong shock tube experiments, the possibility of detonation must be considered seriously. In addition to the extreme and relatively well-known conditions associated with a detonation, there exists a phase during the transition from a flame to a detonation during which pressures and velocities of propagation can exist which are higher than those associated with the fully formed detonation. This has been discussed theoretically by Oppenheim (1952) and has been shown experimentally by several workers. A luminous front having a higher than detonation velocity has been observed by Bone, Fraser & Wheeler (1936) and others. J. B. Smith (1949), using calibrated burst diaphragms at the end of a pipe, has observed reflected pressures in fuel gas-air, acetylene-air, and hydrogen-air mixtures which were approximately four times greater than those associated with a reflected normal detonation. Turin & Huebler (1951), using quartz pressure transducers in the side of a tube, observed pressures during this transition process about three and a half times higher than those at a later time when detonation was fully developed. They worked with Toledo natural gas. Mooradian & Gordon (1951) also have clear indications of this phenomenon with hydrogen-air mixtures.