The paper examines the role of heat diffusion as an internal noise source in aeroengines and as a source of noise in the mixing of hot jets. We consider a number of model problems and find that the sound induced by unsteady heat transfer can show an unusually weak dependence on the mean flow velocity U, the intensity scaling as U3 in three dimensions. At low enough velocities diffusion effects will overwhelm other noise sources, but we have failed in our search for a significant practical situation in which we can prove that sound generated by diffusion clearly dominates over that excited by unsteady aerodynamic forces; they are sometimes comparable.

We examine the possibility that diffusive monopole sources feature in the noise of hot jets using model problems in the linear case and using dimensional analysis in the nonlinear case, and conclude that no significant monopole exists when the specific heats are constant. But they are not constant at low frequencies when, for example, heat flows into and out of vibrational energy modes; then an important monopole source is present. This source shows an unusually complicated scale effect.

Formal expressions are derived for the effective thermal conductivity Kij of randomly dispersed suspensions undergoing shear. These are then evaluated for the cases of dilute suspensions of cylinders and of spheres when the bulk motion is a simple shear, the Péclet number Pe is large, and the particle Reynolds number is small enough for inertia effects to be negligible. It is shown that as Pe → ∞ the presence of shear can significantly affect the O(ϕ) contribution to Kij (ϕ being the volume fraction of the solids), which becomes independent of k, the thermal conductivity of the suspended material. This results from the presence of regions of closed streamlines surrounding each particle which, for sufficiently large Pe, attain an isothermal state and therefore act as regions of infinite conductivity.

The unsteady laminar flow due to the penetration of a horizontal jet of constant density into a stratified fluid is considered. A numerical solution of the Navier–Stokes equations under the Boussinesq approximation is obtained by means of an implicit finite-difference method. Results for different values of the Reynolds and internal Froude numbers are given and discussed.

The mass, momentum and energy-transfer equations are solved to determine the response of a rectangular enclosure to a fire or other high-temperature heat source. The effects of non-participating radiation, wall heat conduction, and laminar natural convection are examined. The results indicate that radiation dominates the heat transfer in the enclosure and alters the convective flow patterns significantly. At a dimensionless time of 5·0 the surface of the wall opposite a vertical heated wall has achieved over 99% of the hot-wall temperature when radiation is included but has yet to change from the initial temperature for pure convection in the enclosure. At the same time the air at the centre of the enclosure achieves 33% and 13% of the hot-wall temperature with and without radiation, respectively. For a hot upper wall the convection velocities are not only opposite in direction but an order of magnitude larger when radiation transfer between the walls is included.

A mathematical model for the unsteady fluid-dynamic response of the semicircular canals is developed. The endolymph is assumed to be an incompressible Newtonian fluid and the presence and effects of both the utricle and the cupula are specifically accounted for. A first approximate solution is obtained using a singular perturbation method. It is shown that the canal can be modelled as a heavily damped, second-order system which behaves as an angular-velocity meter. A comparison of the model response with experimental results is made; fairly good agreement is found.

A finite-difference numerical method for the solution of the unsteady flow of a viscous incompressible fluid through axisymmetric circular ducts of variable axial geometry is developed and applied to the flow in a spherical-cavity geometry approximating the human aortic valve. The presence and motion of the valve leaflets are considered only as long as they can be assumed to present negligible impedance to the flow. The numerical solution is based on the vorticity/streamfunction approach, and is carried out for the systolic acceleration phase of the heart beat. A hybrid-mesh design consisting of a fine cell structure in the region close to the solid walls and a coarser grid in the core region is used. An experimental flow-visualization study in an acrylic model of the spherical cavity shows good agreement with the numerical simulation. An early separation of flow occurs at the entrance to the cavity, and an annular eddy grows in the wake until it occupies most of the cavity. The use of the hybrid mesh also makes possible the simulation of fine secondary-flow features in the cavity under peak-flow conditions.

In a turbulent two-dimensional flow enstrophy systematically cascades to very small scales, at which it is dissipated. The kinetic energy, on the other hand, remains at large scales and the total kinetic energy is constant. Above random topography an initially turbulent flow tends to a steady state with streamlines parallel to contours of constant depth, anticyclonic around a bump. A numerical experiment verifies this prediction. In a closed basin on a beta-plane the solution with minimum enstrophy implies a westward flow in the interior, returning in narrow boundary layers to the north and south. This result is interpreted using a parameterization of the effects of the eddies on the large-scale flow. The numerical solution is in qualitative agreement, but corresponds to a minimum of a more complex measure of the total enstrophy than the usual quadratic integral.

The turbulence generated by a vertically oscillating grid in a water tank and the entrainment across a salinity interface caused by this turbulence have been investigated experimentally. Measurements were carried out in a homogeneous layer of fluid as well as a two-layered fluid, which permitted us to determine the decay law of this turbulence and the way in which the structure of the turbulence depends on the mesh size and on the frequency and amplitude of the grid oscillation. It was found that the turbulent kinetic energy decays with distance from the grid according to a power law $\overline{q^2}\propto z^{-n}$, with n close to 2, and that the turbulent Reynolds number remains approximately constant during decay. The linear dependence of the r.m.s. turbulent velocity on the grid oscillation frequency found by Thompson & Turner (1975) in the case of a square-bar grid has been confirmed. It is shown here that this linear relation remains valid when an interface is present and consequently the dependence of the entrainment velocity on the local Richardson number is of the form $u_e/u \propto Ri^{-\frac{3}{2}}$, the Péclet number being high. While the bearing of these results on the problem of the thermocline or an inversion is clear we wish to emphasize that the spatial decay of turbulence is interesting in itself.

An analysis is presented of the creeping motion around a flow-oriented slender particle in a material medium subject to a uniaxial extension in the far field. A general quasi-steady rheological model is adopted, of a kind representing isotropic (Noll) fluids subject to time-independent velocity gradients, or isotropic solids subject to time-independent strain fields. The analysis is based on the premise of a shear-dominated motion in the near field, which is joined asymptotically to the extension-dominated motion in the far field. For axisymmetric particles, and to the order of terms in slenderness considered here, the far-field perturbation due to the particle can be represented as a distributed coaxial line force in a transversely isotropic medium whose strength is governed by the structure of the near-field rheology.

On the basis of the results for a single particle, a formula is derived for the stress contribution due to the presence of oriented slender fibres in dilute suspension in a non-Newtonian fluid. For certain simple rheological models exhibiting a strong shear-thinning behaviour, the particle contribution to tensile stress is greatly diminished relative to the Newtonian case, as was predicted by an earlier rudimentary treatment (Goddard 1975). The present analysis is thought to be highly promising for applications to general composite materials.