Algebraic disturbances, a non-modal component of the linear perturbation fields, are shown to be an essential feature of stratified shear flows. We find that they must be included even in situations where the modes form a complete set, for such completeness does not extend to the space of these ill-behaved functions.

If the Richardson number Ri is less than ¼ anywhere in the flow, the algebraic disturbances are very generally instabilities of the system, growing without limit as time t → ∞.

Both of these results are in direct contradiction with the currently accepted viewpoint. We examine the previous research in this field to locate the source of this discrepancy.

The algebraic instabilities are not form preserving, and display extreme distortion as they evolve. In the asymptotic limit they appear as quasi-horizontal flow fields, with a vertical ‘wavelength’ that tends to zero. As such, they must be expected to induce secondary shear instabilities and cascade into motions of smaller (horizontal) scale.

The closing mechanism of the natural aortic valve is investigated experimentally in a two-dimensional analogue. The interaction between the sinus content and the aortic flow when the latter is decelerating is studied for different Strouhal numbers: for high Strouhal numbers the sinus content rotates virtually as a rigid mass around the centreline whereas for low Strouhal numbers, corresponding to the human situation, the cusp remains straight and slowly rotates around its point of attachment. Simple theoretical models based on the phenomena observed are proposed. Acceptable agreement between theory and experiment is found.

A detailed description of radiative interactions in laminar compressible boundary layers for moderate Mach numbers is presented by way of asymptotic analysis and supporting solutions. The radiation field is described by the differential approximation. While the asymptotic analysis is valid for large N (the ratio of photon mean free path to molecular mean free path) and arbitrary Boltzmann number, Bo (the ratio of convective heat flux to radiation heat flux), the solutions are obtained for Bo [Lt ] 1, the case of strong radiative interactions.

The asymptotic analysis shows the existence of an optically thin boundary layer for large N and all Bo. For Bo [Lt ] 1, two outer regions are observed — one optically thin (at short distances from the leading edge) and the other optically thick (at large distances from the leading edge). An interesting feature not pointed out in the previous literature is the existence of a wall layer at large distances from the leading edge where convective heat flux can be ignored to the leading order of approximation. The radiation field in all cases can be very well approximated by a one-dimensional description.

The solutions have been constructed using the ideas of matched asymptotic expansions by approximate analytical procedures and numerical methods. It is shown that, to the leading order of approximation, the radiation slip method yields exactly the same result as the more complicated matching procedure. Both the cases of linear and nonlinear radiation have been considered, the former being of interest in developing approximate methods which are subsequently generalized to handle the nonlinear problem. Detailed results are presented for both cases.

The effect of uniform wall suction on the structure of turbulence in a fully established turbulent pipe flow has been measured, with special attention to the critical layers close to the wall. Uniform suction was introduced into a pipe flow with a Reynolds number of 17250 by means of a porous-walled section 2·2 diameters in length with very fine perforations. The effect of suction on the turbulent energy balance was then measured over the entire cross-section at four axial locations. The results indicate the following.

1. The amplitudes of the three principal velocity fluctuation components are reduced by suction, but to differing degrees. Moreover, the effects of suction on the amplitudes of these fluctuations develop at differing rates such that the x-wise components are first affected, then the r-wise and lastly the ϕ-wise components.

2. The suction-induced perturbation in the turbulent structure propagates from the wall to the pipe centre-line with a velocity approximately equal to the friction velocity Uτ.

3. Even with very small rates of fluid extraction the maxima of the terms in the turbulent energy balance occurring close to the wall are drastically reduced. Nevertheless there is no tendency for the location of these maxima to move towards the wall.

4. The general reduction of the level of turbulent energy across the entire section is due to transport of this energy by the augmented mean radial velocity towards the wall, where it is dissipated since the boundary condition inhibits the passage of turbulent energy through the wall.

Flow visualization, laser-Doppler anemometry and pressure measurements have been used to identify and delineate the regimes of vortex breakdown in a rotating cavity with a central axial flow of air. For the particular cavity tested (where the ratio of the outer to the inner radius was ten and the ratio of the axial width to the inner radius was approximately five), spiral breakdown and axisymmetric breakdown occur in both laminar and turbulent flow. Rossby numbers ε characterizing the boundaries between the breakdown modes were established from visual observations of flow behaviour, from discontinuities in velocity components and in the pressure drop across the cavity, and from changes in the velocity spectra. In laminar flow, spiral breakdown occurs for 1·6 [lsim ] ε [lsim ] 3·2 and axisymmetric breakdown occurs for 0·8 [lsim ] ε [lsim ] 1·5. In turbulent flow, spiral breakdown occurs for 21 [lsim ] ε [lsim ] 100 and 1·5 [lsim ] ε [lsim ] 2·6, and axisymmetric breakdown occurs for 2·6 [lsim ] ε [lsim ] 21 and 0·8 [lsim ] ε [lsim ] 1·5. At the higher Rossby numbers, the flow under laminar conditions is significantly different to that under turbulent conditions; at the lower Rossby numbers, it was found to be impossible to distinguish between laminar and turbulent flow.

The formation of singularities in two-dimensional magnetohydrodynamic flow is investigated by direct numerical simulation. It is shown that two-dimensional magnetohydrodynamic turbulence is not as singular as three-dimensional hydrodynamic turbulence (in the sense that it has a less highly excited small-scale structure) but that it is more singular than two-dimensional hydrodynamic turbulence.

This analysis demonstrates theoretically that a lateral bending wave propagating along the walls of a two-dimensional channel filled with a viscous incompressible fluid will induce a mean flow. In addition to this ‘pure’ bending wave, another possible condition is investigated: that of the superposition of an area contraction wave propagating with the same speed as the lateral bending wave. This second condition, called complex wave motion, takes into account the slight occlusion which occurs naturally at the amplitude peaks when a finite amplitude bending wave propagates along the walls of a container. A perturbation solution is found which satisfies Navier—Stokes equations for the case in which wave amplitude/wavelength is ‘small’. However the wave amplitude is finite, in the sense that it is of the same order as the channel width. Under these conditions, the occlusion at the amplitude peaks is allowed to be of the same order as the channel width. For the case of a pure bending wave the motion induced by the peristaltis is found to be of second order in the perturbation parameter, whereas in the more realistic case a first-order pumping effect is obtained.

A Helmholtz velocity profile with velocity discontinuity 2U is embedded in an infinite continuously stratified Boussinesq fluid with constant Brunt—Väisälä frequency N. Linear theory shows that this system can support resonant over-reflexion, i.e. the existence of neutral modes consisting of outgoing internal gravity waves, whenever the horizontal wavenumber is less than N/2½U. This paper examines the weakly nonlinear theory of these modes. An equation governing the evolution of the amplitude of the interface displacement is derived. The time scale for this evolution is α−2, where α is a measure of the magnitude of the interface displacement, which is excited by an incident wave of magnitude O(α3). It is shown that the mode which is symmetrical with respect to the interface (and has a horizontal phase speed equal to the mean of the basic velocity discontinuity) remains neutral, with a finite amplitude wave on the interface. However, the other modes, which are not symmetrical with respect to the interface, become unstable owing to the self-interaction of the primary mode with its second harmonic. The interface displacement develops a singularity in a finite time.

Short-crested wave systems, as produced by two progressive waves propagating at an oblique angle to each other, have an extremely important effect on a sedimentary bed. The complex water-particle motions are conducive to lifting material into suspension and sustaining it in motion. In order to study this phenomenon rigorously, the variables of this wave system are derived to a third-order approximation by a perturbation method. The case of waves reflecting obliquely from a vertical wall is examined under the assumptions of full reflexion, uniform finite depth and an inviscid incompressible fluid. The new formulation reduces to standing or Stokes waves at the limiting angles of approach. Expressions for kinematic quantities are also presented.

It is well known that vortex sheets are diffused by viscosity. For a plane sheet this diffusion is described by a linear diffusion equation. Here we consider a rolled vortex sheet, and show that the viscous diffusion of the vorticity concentrated at the turns of the sheet, when they are very closely spaced, can also be described by a linear equation, in appropriately transformed variables.