It has been shown experimentally that quite large departures occur from the universal inner-law velocity distribution in the presence of severe favourable pressure gradients in turbulent boundary layers and that these departures are associated with the tendency for the turbulent boundary layer to revert to a laminar state. From the measurements a criterion for the onset of reverse transition has been deduced in terms of the mean shear-stress gradient in the wall region of the flow. Experiments in fully developed pipe and channel flows suggest that the proposed criterion may be quite generally applicable to all fully turbulent shear flows.

Based on a dimensional consideration, the ‘−3 power law’ on the spatial spectrum of sand waves formed by flowing water Sηη(k) is derived for a large wave-number equilibrium subrange, \[ S_{\eta\eta}(k)\sim \alpha k^{-3}, \] where α is a constant depending on the angle of repose of sand particles and k denotes the wave-number.

Likewise, the frequency spectrum is shown to have the ‘−3 power law’ range for higher frequencies as well as the ‘−2 power law’ range for frequencies near a spectral peak.

These spectra are shown to agree with experimental data from various sources.

High-frequency plane sound waves in ideal gases with internal dissipation are discussed. Particular applications to dissociating diatomic gases and gases displaying vibrational relaxation are considered. A criterion in the form of an inequality is derived for the validity of the high-frequency approximation and an asymptotic analysis is developed.

The scattering of a gravity wave of wave number k by a circular dock of radius a and draft d – h in water of depth d is calculated through a variational approximation. The total and differential scattering cross-sections, the peripheral displacement, and the lateral force on the dock are presented as functions of ka with d/a and h/d as parameters and compared with the classical results for a circular cylinder (h = 0). A pronounced resonance is found near ka = 2 for certain values of d/a and h/d.

The work that follows considers the velocity profiles within the boundary layer at the wall of an arbitrarily converging funnel. The occurrence of super-velocities, i.e. components of velocity within the boundary layer exceeding their corresponding free stream component, is investigated and the relevance of such a phenomenon to the efficiency of discharge discussed.

The hydrodynamic stability is examined of liquids in which the viscosity varies with distance below a free surface. It is assumed that the viscosity becomes indefinitely large with distance from the surface, and that there is an ‘effective depth’ within which most of the motion occurs; but, otherwise, the viscosity distribution is arbitrary. The particular cases of wave-generation by a concurrent air flow at a horizontal liquid surface, and the stability of inclined flow under gravity are treated. It is shown that instabilities may occur which are similar to those known for thin uniform liquid films.

It is shown that as a result of their non-linear interactions, internal gravity waves in an unbounded fluid can be trapped to a layer of finite depth by periodic small variations in either the density gradient or in a weak horizontal steady current. This trapping occurs when the vertical component of the wave-number is half that of the density gradient or of the current variations. The energy density of the wave motion trapped near the ocean surface decreases exponentially with depth over a distance that is inversely proportional to the magnitude of the variations in density gradient or in horizontal current speed.

It has been found experimentally that the turbulent pipe flow through a mitred, right-angle bend produces a downstream secondary circulation which does not conform to the twin-circulatory flow usually to be found in pipe bends. The secondary flow is dominated by a single circulation about the axis in either a clockwise or an anticlockwise sense, between which it switches abruptly at a low, random frequency. The phenomenon is explained in terms of the asymmetry of the inner wall separation and the turbulent axial circulation generated in the upstream flow.

Laminar flow of a stably stratified fluid with uniform upstream velocity and density gradient past a flat plate is investigated experimentally and theoretically. In the experimental study, the flat plate, parallel to the direction of motion, is towed horizontally at uniform speeds in a tank of stratified salt water at uniform density gradients. The horizontal velocity in front of, above, and behind the flat plate is measured with a flow visualization technique. One of the striking phenomena is the strong upstream influence (the upstream wake) of an obstacle in a flow of stably stratified fluid when the gravity effect is comparable to, or more than the inertial effect. The velocity profiles of the upstream wake and boundary layer above the flat plate are wavy and found to be governed by the ratio of Reynolds number Be to Richardson number Ri. The problem is also analysed theoretically with Boussinesq's approximation and two-parameter perturbation expansions for the upstream wake and the boundary layer. The solutions for the upstream wake and for the boundary layer are compared with measurements.

A numerical examination has been made of the reflectivity of critical levels with low Richardson number to internal gravity waves propagating in stratified fluids with shear. At sufficiently low positive Richardson numbers the reflected wave may actually be stronger than the incident.

The normal mode instabilities of three simple models have also been computed. The results are presented in three dimensions: Richardson number, horizontal wave scale and real wave frequency.

The velocities, accelerations and drag forces experienced by two equal spheres falling along their line of centres in a viscous fluid were determined for three groups of Reynolds numbers R in the range where it is commonly assumed that Stokes's approximation applies. For all groups, with R ranging between 0·060 and 0·216, both spheres continually acclerated as they fell, and the upper sphere fell faster and accelerated more than the lower one. In contrast to Stimson & Jeffery's (1926) theory, which is based on the Stokes approximation, and to most earlier experimenters, the drag-force coefficients of the upper sphere computed from the experiments were significantly smaller than those for the lower sphere. Oseen's theory for this case agreed with the experiments in some respects, but contrary to it the drag-force coefficient varied with R for the upper sphere as well as the lower sphere.