This paper examines the theory of the interaction of sound with a slit-perforated screen in the presence of a uniform, subsonic tangential mean flow on both sides of the screen. The sound induces vortex shedding from sharp edges of the screen. The coupling of this vorticity with the mean flow leads to a significant modification in the predicted acoustic properties as compared with those predicted by the classical treatments of Rayleigh (1897) and Lamb (1932). In particular a considerable portion of the incident acoustic energy can be lost during the interaction, and is convected away in the mean flow in the form of localized vortical disturbances. The analytical results provide theoretical support for the use of perforated plates to inhibit the onset of cavity resonances in, for example, cross-flow heat exchangers.

The behaviour of dilute polymer solutions in sink flow, viz., radial flow toward a point, was investigated experimentally and theoretically. Solutions of polyethylene oxide, in the drag-reducing concentration range, were pushed through a 60° conical channel at Reynolds numbers of order 102. Preliminary studies revealed a range of flow conditions in which the flow was free of secondary motion yet non-Newtonian effects were significant. Measurements of pressure differential between two radial positions yielded the non-Newtonian normal stress developed in the radial direction; the magnitude was the same order as the Newtonian stress, i.e., as the dynamic pressure ½ρV2.

Several fluid models were analysed to determine the stress generated by each in sink flow. It was found that a solution of Rouse–Zimm flexible macromolecules produces a stress which is three orders of magnitude below the observed level, and that macro-molecules with finite extension fall short by two orders. A suspension of elongated particles, of the type analysed by Batchelor, was also considered, but application to the present case was difficult because of the small scale required by the theory. Consequently, the theory was extended to include particles the size of the flow field, and an order-of-magnitude analysis revealed that for such particles to produce the desired stress, the aspect ratio must be $O(10^{\frac{7}{2}})$, and the cross dimension is likely O(0·1)μm. Electron micrographs of freeze-dried samples of the polymer solutions showed the solute in the form of an irregular network of apparently undissolved strands, with diameters in the O(0·1)μm range.

Heat-transfer rates from a non-equilibrium hypersonic air flow to flat plates at zero and 12° incidence have been measured in a free piston shock tunnel at stagnation enthalpy levels up to 51 MJ kg−1. Nozzle flow conditions resulted in test section velocities up to 8·1 km 8−1 and in an experimental regime in which the free stream was chemically frozen and the flat-plate boundary layer was laminar. Estimates of the gas-phase and surface-reaction Damkohler numbers have been made and the heat-transfer results are discussed in this context. At the highest test-section densities non-equilibrium endothermic gas phase reactions involving oxygen atoms in the boundary layer are suggested as a possible mechanism for the observed low heattransfer rates.

The classical problem of water waves on an incompressible irrotational flow is considered. By introducing an appropriate non-dimensionalization, we derive four Korteweg–de Vries equations: two expressed in Cartesian co-ordinates and two in plane polars. The equations are: the classical (plane) KdV equation, the two-dimensional ‘nearly-plane’ equation, the concentric equation and a new ‘nearly-concentric’ equation. On the basis of the underlying water-wave equations, it is seen that two simple transformations exist between these KdV equations.

By constructing appropriate asymptotic regions defined in terms of the relevant small parameters, we show how various initial value problems give rise to certain solutions of the KdV equations. In particular, the generation of the similarity solutions is examined in detail and it is found that these solutions must eventually match to a solution of the full water-wave equations in a neighbourhood of the origin.

Water waves that propagate over a non-rigid bed are attenuated as a result of energy dissipation within the bed. This paper describes the analysis, from the basis of small-amplitude wave theory, of the coupled interaction between the bed, which responds in both an elastic and viscous manner, and an overlying layer of inviscid fluid. A dispersion relation is derived, from which rates of wave attenuation and sea bed deflexions are calculated.

The results are relevant wherever the sea bed, in its response to water waves, is non-rigid, as is often the case in coastal waters. Depending on the elasticity and viscosity of the sea bed, the wave attenuation can be of the same or of a larger order of magnitude than that due to bottom friction or percolation in a permeable bed. Where waves propagate over a soft viscous bed, for example as is the case at certain mud flats off the south-west coast of India, exceptionally high rates of attenuation are possible whereby waves are almost completely damped within several wavelengths.

A theoretical investigation is made of turbulent thermal convection in a horizontally infinite layer of fluid confined between a rigid isothermal upper plate and a rigid adiabatic lower plate, driven by a temperature difference between the plates that is totally induced by volumetric heating of the layer. The dependence of upper surface Nusselt number, Nu, on both Prandtl number, Pr, and internal Rayleigh number, RaI, is obtained from considerations of the Boussinesq equations of motion. Also obtained is the dependence of various turbulence quantities upon distance from the upper plate. At a sufficiently high Rayleigh number, the present theory gives $Nu \sim Ra^{\frac{1}{4}}_I$ for large Pr and Nu ∼ Pr¼Ra¼I for small Pr. At lower Rayleigh numbers, however, the Nusselt number is found to vary according to $Nu \sim (a-b\,Ra^{-\frac{1}{12}}_I)^{-1} Ra^{\frac{1}{4}}_I$, where a and b are coefficients dependent upon Pr. The asymptotic $Ra^{\frac{1}{4}}_I$ law tends to support the boundary layer instability model of Howard (1966), although significant deviation from the model is predicted by the present theory over the range of Rayleigh numbers explored experimentally (Kulacki & Nagle 1975; Kulacki & Emara 1977). Based upon the results of this study the empirical power-law representation of Nu is critically examined and found to be adequate within finite ranges of RaI. Comparison of the present flow situation is made with the corresponding case of turbulent Bénard convection.

Numerical solutions are presented for the unsteady irrotational flow generated by the movement of the stern of a two-dimensional semi-infinite body at the free surface of an incompressible fluid. When separation occurs other than at a sharp trailing edge, the location of the separation point is computed as part of the solution. Linear and nonlinear results are compared. It is shown that for draught-based Froude numbers greater than 3 the nonlinear effects are negligible for most practical purposes while for Froude numbers less than three these effects can be significant.

The lateral extent of the large-scale features of a high-Reynolds-number, turbulent mixing layer are studied by means of an array of twelve hot wires placed across the span of the wind tunnel. Correlation measurements show that the large-scale structure rapidly approaches an asymptotic state, in which the lateral correlation length becomes proportional to the local mixing-layer thickness. Visualizations of the instantaneous hot-wire outputs show the large structure to extend across the wind tunnel, but to contain spanwise irregularities. It is argued that these spanwise irregularities are produced by the pairing interactions between adjacent vortices.

Periodic wave trains propagating over water which varies in depth in the direction of wave propagation are studied by using accurate solutions for wave trains in constant depth of water. The accurate solutions are (i) Cokelet's (1977) extension of Stokes’ approximation and, for the longer waves, (ii) a solution for trains of solitary waves using the solitary-wave solution of Longuet-Higgins & Fenton (1974).

A representative selection of results is shown in diagrams. A feature which arises from the use of these accurate solutions is that near the highest wave two solutions are possible for a given incoming wave. Although the solutions cannot describe waves that break, it is shown that as depth is decreased a point is reached beyond which no solution can be found. This is taken to indicate the region in which waves break.

The limitations of the theory are discussed and analysed. Comparisons with experimental measurements of Hansen & Svendsen (1979) are included.

Axisymmetric steady motion of an inhomogeneous rotating fluid is considered. A system of equations, with appropriate boundary conditions, controlling the smooth interior fields is derived under the assumption of small dissipation and small side-boundary conductance. It is argued that this system, being derived without linearization of the equations, might form the basis of valuable numerical analysis. Assuming sufficiently weak forcing, i.e. high insulation of the non-horizontal boundaries, a linear system is derived. An explicit solution is presented and discussed for a particularly simple and important case.