A wake model for the free-streamline theory is proposed to treat the two-dimensional flow past an obstacle with a wake or cavity formation. In this model the wake flow is approximately described in the large by an equivalent potential flow such that along the wake boundary the pressure first assumes a prescribed constant under-pressure in a region downstream of the separation points (called the near-wake) and then increases continuously from this under-pressure to the given free-stream value in an infinite wake strip of finite width (the far-wake). Application of this wake model provides a rather smooth continuous transition of the hydrodynamic forces from the fully developed wake flow to the fully wetted flow as the wake disappears. When applied to the wake flow past an inclined flat plate, this model yields the exact solution in a closed form for the whole range of the wake under-pressure coefficient.

In a recent work Longuet-Higgins & Stewart (1961) have studied the changes in wavelength and amplitude of progressive waves of constant frequency as they are propagated into regions of surface divergence or convergence. In the work here described the complementary conditions are assumed. Standing waves of uniform wavelength, λ, exist in an area of uniform surface divergence. Changes in amplitude and wavelength are studied. These changes depend on the existence of the radiation stress which was discovered by Longuet-Higgins & Stewart but the physical interpretation of this stress is simpler for standing than for progressive waves. Three different ways of obtaining the same rate of strain in the direction of the current caused the amplitude to vary as $\lambda|^{-{\frac {1}{4}}}, \lambda|^{-{\frac {3}{4}}}$ and $\lambda|^{-{\frac {5}{4}}}$, respectively.

Experiments in which free-standing waves were generated in a tank one wave-length wide which was then made narrower verified the conclusion that contraction does not alter the periodic character of the waves, even though the ratio of amplitude to wavelength becomes so great that they can no longer be treated mathematically by the usual linearized approximation. The shape of the profile then appears to agree well with calculations of Penney & Price (1952).

In a recent paper Tadjbakhsh & Keller (1960) have predicted that two-dimensional finite standing gravity waves in a rectangular container will have lower frequency than infinitesimal standing waves in deep water but have higher frequency below a certain mean depth to wavelength ratio. This is in strong contrast to the frequency results for finite progressive waves obtained by many investigators. Experimental confirmation of this prediction is reported together with estimates of the magnitude of the frequency effects at several depths. The frequency effect reversal appears to occur at a depth ratio of 0·14, somewhat less than the predicted ratio of 0·17.

The density distribution in the relaxation regions of shock waves in carbon dioxide were determined in the Mach number range 1·4 to 4·0 using an interferometer. The over-all density ratios were found to agree with the theoretical final equilibrium values. Detailed analysis of the relaxation regions showed that the simple relaxation equation is inadequate, the relaxation frequency depending on departures from equilibrium as well as on temperature.

Vibrational relaxation effects are examined for hypersonic nozzle air flows. A simple method of estimating the distribution of vibrational temperature along a nozzle is described and higher-order approximations discussed. Results are presented for hyperbolic axisymmetric nozzles with reservoir conditions 1000 ≤ p0 ≤ 4000 p.s.i., 1000 ≤ T0 ≤ 3000 °K. Vibrational freezing is shown to occur and to cause significant changes in the nozzle exit flow conditions.

The probe of a hot-film flowmeter was towed in directions approximately normal to the direction of a tidal stream. The one-dimensional spectra are found to be proportional to $k|^{-{\frac {5}{3}}}$ in the inertial subrange.

The laminar sublayer and ‘transition zone’ are shown to be the region where the turbulent velocity fluctuations are directly dissipated by viscosity. A simplified linearized from of the equations of motion for the turbulent fluctuations is used to describe the turbulent field between the wall and the fully turbulent part of the flow. The mean flow in the viscous sublayer and the turbulent field outside the sublayer are assumed to be known from experiment. The thickness of the sublayer arises naturally in the theory and is directly analogous to the inner viscous region for the fluctuations in a laminar flow. It is shown that the large-scale fluctuations containing most of the turbulent energy are convected downstream with a velocity characteristic of the middle of the boundary layer. Thus Taylor's hypothesis does not apply to these large-scale fluctuations near the wall. The convective velocity found in the measurements of pressure fluctuations at the boundaries of turbulent flows is in accord with the theory. Calculations are given for the energy spectra and u′ fluctuation level in the sublayer and other aspects of the fluctuation field are discussed. The linear pressure fluctuation field at the edge of the sublayer is calculated and found to be much larger than the nonlinear field. Examining the effect of strong free-stream turbulence on laminar boundary-layer transition, it appears that the physical model underlying Taylor's parameter is incorrect.

This paper investigates the perturbation modes of the steady parallel flow of a compressible fluid of finite constant viscosity and electrical conductivity in a uniform arbitrarily oriented magnetic field. In particular, in addition to the classical fast and slow sound and Alfvén modes, one obtains some waves whose amplitude is finite whenever the diffusive coefficients are finite and which resemble the diffusion of vorticity from stream surfaces in classical hydrodynamics. The paper also re-interprets upward-facing MHD waves and upstream wakes in a new way.

This paper modifies and refines earlier work of Palm (1960) concerning the finiteamplitude steady state of cellular convective motion attained when a horizontal layer of fluid becomes unstable as a result of being heated from below. The two non-linear ordinary differential equations to which the problem was reduced by Palm (under certain conditions) are given in a corrected form, and are then analysed in some detail. The principal conclusions are that, for the model considered, hexagonal convection cell may be the stable equilibrium state only if the variation of kinematic viscosity with temperature is sufficiently great. Under the same circumstances a two-dimensional roll cell is also possible, the initial conditions determining which state actually occurs. Although further work is indicated, it seems probable that in an actual experiment with sufficiently large kinematic-viscosity variation, the hexagonal cells are more likely to appear. The analysis enables conclusions to be drawn concerning the flow direction at the cell centre, and also shows that a disturbance of sufficient magnitude may grow even though the situation is a stable one by linearized theory. Comparison with experiment is discussed.

It is often supposed that the mean velocity indicated by a yawed hot-wire anemometer is the component of the stream velocity normal to the wire. Experiments have been performed which show that a better approximation is obtained by taking the velocity as the resultant of the normal component of the mean stream and 0.2 times the component parallel to the wire.