It is argued that the heat transfer between a roughened surface and a stream of incompressible fluid flowing over it is dependent on both the viscosity and thermal conductivity of the fluid even when the roughness is large enough for viscosity to have ceased to affect the skin friction.

Concentrating on closely spaced roughness, sufficiently large for the skin friction to be independent of Reynolds number, a simple model is constructed of the flow near the surface. It consists of horseshoe eddies which wrap themselves round the individual excrescences and trail unsteadily downstream; the eddies are imagined to scour the surface and thereby to transport heat between the surface and the more vigorous flow in the neighbourhood of the roughness crests. Taken in conjunction with Reynolds analogy between temperature and velocity distributions in the fluid away from the surface, the model leads to an expression for the rate of heat transfer which contains a function of the roughness Reynolds number and the Prandtl number of the fluid whose detailed form is found by appeal to the limited experimental data available. An order-of-magnitude argument suggests that the functional form established empirically is consistent with the assumed model of the flow close to the surface.

The object of the work is to establish a basis for the analysis of experimental data and for their extrapolation with respect to Reynolds number and Prandtl number.

The previously established criterion for the stability of a vortex sheet with respect to two-dimensional disturbances in a compressible fluid is extended to three-dimensional disturbances, and it is shown that disturbances travelling at sufficiently oblique angles with respect to the undisturbed flow are unstable. Slip-line instability downstream of a Mach reflexion is discussed briefly.

Measurements in the mixing region of a 1 in. diameter cold air jet are described for Mach numbers ranging from 0.2 to 0.55. The statistical characteristics of the turbulence in the first few diameters of the flow may be expressed in terms of simple kinematic similarity relationships. These are based on the jet diameter and the distance downstream from the jet orifice as length-scales, and the inverse of the local shear as a time-scale. The experiments show that the integral time scale of the turbulence in a frame convected with the maximum energy of the turbulent motion is inversely proportional to the local shear.

The most interesting result obtained is that the local intensity of the turbulence is equal to 0.2 times the shear velocity. This velocity is defined as the product of the local integral length-scale of the turbulence with the local shear. The local intensity is defined as the R.M.S. value of the local velocity fluctuations divided by the jet efflux velocity. It was found that the length-scale is proportional to the distance from the jet orifice, while the maximum shear is also related to this distance as well as to the jet efflux velocity. These two similarity relations break down close to the jet orifice and change beyond the first six or so diameters downstream. The convection velocity is not equal to the local mean velocity but varies slowly over the region of maximum shear when it is just over half the jet efflux velocity. The measurements of other observers fit the relationships obtained quite well. From these relationships it is possible to calculate the noise generated by the mixing region of a given jet directly, using expressions derived by Lilley (1958).

The mean velocity distribution in a low-speed three-dimensional turbulent boundary-layer flow was investigated experimentally. The experiments were performed on a large-scale model which consisted of a flat plate on which secondary flow was generated by the pressure field introduced by a circular cylinder standing on the plate. The Reynolds number based on distance from the leading edge of the plate was about 6 x 106.

It was found that the wall-wake model of Coles does not apply for flow of this kind and the model breaks down in the case of conically divergent flow with rising pressure, for example, in the results of Kehl (1943). The triangular model for the yawed turbulent boundary layer proposed by Johnston (1960) was confirmed with good correlation. However, the value of yuτ/v which occurs at the vertex of the triangle was found to range up to 150 whereas Johnston gives the highest value as about 16 and hence assumes that the peak lies within the viscous sublayer. Much of his analysis is based on this assumption.

The dimensionless velocity-defect profile was found to lie in a fairly narrow band when plotted against y/δ for a wide variation of other parameters including the pressure gradient. The law of the wall was found to apply in the same form as for two-dimensional flow but for a more limited range of y.

The energy transfer due to non-linear interactions between the components of a gravity-wave spectrum discussed in Parts 1 and 2 of this paper is evaluated for a fully and partially developed Neumann spectrum with various spreading factors. The characteristic time scales of the energy transfer are found to be typically of the order of a few hours. In all cases the high frequencies and the low-frequency peak are found to gain energy from an intermediate range of frequencies. The transfer of energy to very low frequencies and to waves travelling at large angles to the main propagation direction of the spectrum is negligible. Computations are presented also for the rate of decay of swell interacting with local wind-generated seas (represented by a Neumann spectrum). An appreciable decay is found only for swell frequencies in the same range as those of the local sea.

The present paper discusses the hydrodynamics and propulsive properties when a jet of fluid is ejected from the opening of a tube. Formulas for the calculation of the thrust are provided and the basic equations for the horizontal rectilinear motion of a rigid torpedo-like body are studied in some detail. The results may be applied to investigate in an elementary way the locomotion of certain aquatic animals.

The effect of harmonic oscillations in the magnitude of the surface temperature on the free-convection laminar velocity and temperature boundary layers on a flat plate is analysed. Low-and high-frequency solutions are developed separately. The results obtained are in striking contrast to the corresponding results for forced-convection flows.

The motion of a viscous, electrically conducting fluid past a finite two-dimensional obstacle is investigated. The magnetic field is assumed to be uniform and parallel to the velocity at infinity. By means of a perturbation technique, approximations valid for large values of the Hartmann number M are derived. It is found that, over any finite region, the flow field is characterized by the presence of shear layers fore and aft of the body. The limit attained over the exterior region represents the two-dimensional counterpart of the axially symmetric solution given by Chester (1961). Attention is focused on a number of nominally ‘higher-order’ effects, including the presence of two distinct boundary layers. The results hold only when M [Gt ] Re; Re = Reynolds number. However, a generalization of the procedure, in which the last assumption is relaxed, is suggested.

Blunt-body solutions for suspersonic flow usually concern closed body surfaces. This paper reports on an experimental investigation of a two-layer shock cap and indicates the existence of a predictable contact surface separating the layers. The inner layer was generated by injecting air through a contoured axisymmetric channel on a blunt body so as to simulate a hemispherical contact surface in a Mach number 4.8 flow.

Results show the existence of the contact surface and the influence of a range of mass-injection rates upon the displacement of the bow shock and contact surface from the body.

The general character of the magnetohydrodynamic flow past a non-conducting flat plate in the presence of transverse magnetic fields is analysed in some detail. The appropriate extension of the Rayleigh problem to the magnetohydrodynamic case is shown to yield solutions which correctly predict some features of the steady flow past a semi-infinite flat plate; in addition, it is shown that the knowledge of these significant features permits an easy evaluation of their magnitudes in other extensions of the Rayleigh problem. The flow past a semi-infinite flat plate is analysed by two methods. First, by linearizing the governing equations and incorporating the assumption of a low ratio of viscous to magnetic diffusivity, the results for skin friction and the normal component of magnetic field at the plate are obtained and are shown to be useful in interpreting the character of these low conductivity flows. Secondly, the complete set of governing equations is formulated as a finite difference problem and solved numerically on a digital computer. The results obtained, in addition to demonstrating feasibility of the numerical calculations, show that the disturbance produced by the plate is no longer confined to a thin viscous layer if the ratio of viscous to magnetic diffusivity is greater than 10−2, but that an appreciable Alfvén type disturbance is excited.