The unstable and neutral modes of a compressible boundary-layer flow past an insulated flat plate are discussed in the limit of infinite Mach number. These modes have been documented by Mack and many of the asymptotic results derived here are becoming evident in his computations at finite values of the Mach number. Of particular interest is the existence of a vorticity mode for which the wavenumber is a discontinuous function of Mach number at finite Mach number but is continuous in the limit M∞ → ∞. At large Mach number this is the most unstable mode, and is expected to have relevance also in the hypersonic limit when the flow field is no longer shock-free.

Expressions are derived for the amplitudes of the second-harmonic waves generated when a uniform wave train is normally incident upon a two-dimensional body, submerged in water of infinite depth. These amplitudes are given in terms of integrals over the free surface of products of first-order quantities. For a submerged, circular cylinder, it is shown analytically that there is no second-order reflected wave at any frequency. This extends the classical result that there is no reflection at first-order for this body.

A simple model is proposed to describe the molecular mixing characteristics of a two-dimensional turbulent jet that is discharged into a confined volume. The model, which is based on similarity and physical considerations of only the large-scale motions, derives the characteristic time for the problem and identifies the regime for which the mixing will be most rapid. Results are reported for experiments where helium and helium/argon mixtures were injected into a cylindrical volume initially containing air. Using an aspirating probe that measured transient helium concentrations in the volume, the mixing time was determined as a function of the size of the confining volume and the injection parameters. The experimental results are in general accord with the model, and validate the use of the model for the determination of the minimum mixing time.

The effect of torsion on fully developed laminar flow in a twisted pipe is considered in the low-Reynolds-number regime. The flow in a pipe of elliptical cross-section whose axis is straight but which is twisted about that axis is examined and the secondary flow pattern found. The helical pipe of circular cross-section is also revisited; in this case, the first-order torsional effect on the streamtubes is verified, and previous conclusions that such an effect would be of higher order are explained.

The natural-convection boundary-layer flow over a semi-infinite heated plate of arbitrary inclination is studied by first identifying a set of combined boundary-layer variables and then casting the governing equations into a universal form. The generalized problem yields the existing similarity solutions for the limiting cases of horizontal and vertical plates, and describes the gradual transition of the flow pattern between these two limits at distances from the leading edge which depend on the inclination angle. Near the leading edge the buoyancy force acting normal to the plate causes an ‘impulsive’ driving force to the fluid motion along the plate, while the ‘regular’ driving force exerted by the tangential buoyancy force becomes dominating downstream. Both the exact and the locally-similar solutions are obtained and are found to agree well with each other.

We consider the effects of strong critical-layer nonlinearity on the spatial evolution of an initially linear ‘acoustic mode’ instability wave on a hypersonic flat-plate boundary layer. Our analysis shows that nonlinearity, which is initially confined to a thin critical layer, first becomes important when the amplitude of the pressure fluctuations becomes O(1/M4InM2), where M is the free-stream Mach number. The flow outside the critical layer is still determined by linear dynamics and therefore takes the form of a linear instability wave — but with its amplitude completely determined by the flow within the critical layer. The latter flow is determined by a coupled set of nonlinear equations, which we had to solve numerically.

It is shown how the St Andrew's cross-wave in a density-stratified fluid is modified by a horizontal shear above the level of the source. Ray theory is used to develop the equations for the phase configuration and it is shown that, for the special case when the background natural frequency is constant and the shear is linear, the wave crests are straight lines passing through the source. The waves corresponding to outgoing energy have phase velocities directed towards the horizontal level of the source and the waves which have undergone a reflection have phase velocities directed towards the vertical. It is shown that the ray theory predictions compare well with experiment and with finite-difference calculations.

The present paper reports an experimental study of the development of plane monochromatic waves in the boundary layer on a flat plate at Mach number M = 2.0. The wave characteristics of the plane waves are obtained. Three-dimensional disturbances with an angle of the wave vector to the flow χ = 50–70° are found to be the most unstable. It is shown that the disturbances, consisting of vortical and compressible modes, are engendered in a supersonic boundary layer by a local source of artificial disturbances. It is found that an increase in the bluntness of the leading edge of a plate stabilizes three-dimensional disturbances of a vortical mode.

The linear excitation of straight-crested, capillary–gravity waves on the surface (x > 0) of a deep, viscous liquid in response to the sinusoidal, vertical motion of a hydrophilic wall at x = 0 is calculated on the assumptions that: (i) the dynamical variation of the contact angle is proportional to (but not necessarily in phase with) the velocity of the contact line relative to the wall; (ii) the relative tangential velocity (slip) of the fluid below the contact line is proportional to the shear at the wall, (iii) k0lv [Lt ] 1 and k0lc = O(1), where k0 is the wavenumber, lv is the boundary-layer thickness, and lc is the capillary length. The contact-angle and slip coefficients are complex functions of frequency that are found to be linearly related. Physical considerations suggest that the slip length ls (≡ slip velocity ÷ shear at wall) should be small compared with lv, which, in turn, implies that the motion of the contact line must be small in that parametric domain in which linearization provides a viable description of the wave motion near the wall; however, the analysis proceeds from (i) and (ii), qua phenomenological hypotheses, without a priori restrictions on the contact-line and slip coefficients. The present results include those of Wilson & Jones (1973), who assume that the amplitude and phase of the wave slope at the wall are prescribed, and those of Hocking (1987a), who assumes that the variation of the wave slope at the wall is in phase with the contact-line velocity and neglects viscosity. They also include a correction for the dynamical effects of the static meniscus, which is necessarily present for any static contact angle other than ½π but is neglected in the previous analyses, and have counterparts for the closely related problem (cf. Hocking 1987b) of the reflection of a plane wave from a stationary wall.

A formula is derived for the longitudinal shear dispersion coefficient of a solute in a laminar flow along and around a rotating cylindrical axle in an off-centre closely fitting shaft. The rotation drives a circulation which augments diffusive mixing around the axle and reduces the eventual rate of longitudinal spreading. A simple approximation is shown to give accurate results for the important special case of a cylindrical shaft.