The phenomenon of steady cellular convection in a rotating fluid in which the stratification is statically unstable is well known. If the temperature field also varies in the horizontal direction a thermal wind is generated which can diminish the amplitude of the cells, or if inertial effects are strong enough, confine them to a narrow vertical band. On the other hand, in an enclosed container resonance can occur which increases the amplitude of the cells beyond the scope of a linear theory.

A model for particle propulsion by an instantaneous heat discharge is presented. The flow is driven by a gravity-independent transient fluid dilatation, engendered by an unsteady temperature field which corresponds to heat emission from a localized source located within the particle. We focus on the highly eccentric case, where the heat is released in proximity to the particle surface. Solution of the Stokes equations and subsequent evaluation of the resulting hydrodynamic thrust yields a nonlinear non-autonomous ordinary differential equation governing the evolution of particle position with time. This equation depends upon a single parameter which represents the relative effects of heating magnitude and initial geometry.

The axisymmetric boundary-layer separation of an incompressible impulsively started flow in a wavy-walled tube is analysed at moderate to high values of the Reynolds number. The investigation is carried out by numerical integration of either the Navier–Stokes equations or Prandtl's asymptotic formulation of the boundary-layer problem. The presence of an adverse pressure gradient induces reverse flow at the tube wall independently of the Reynolds number; its occurrence can be predicted by a timescale analysis. Following that, the viscous calculations show different dynamics depending on the Reynolds number. As the Reynolds number increases, the boundary layer has in a well-defined internal structure where longitudinal lengthscales become comparable with the viscous one. Thus the boundary-layer scaling fails locally, with a minimum of pressure inside the boundary layer itself. The formation of the primary recirculation is well captured by the asymptotic model which, however, is not able to describe the roll-up of the vortex structure inside the recirculating region. This inadequacy appears well before the flow evolves to the characteristic terminal singularity usually assumed as foreshadowing the vortex shedding phenomenon. The outcomes are compared with the existing results of analogous problems giving an overall agreement but improving, in some cases, the physical picture.

Euromech Colloquium 353, held at the University of Karlsruhe, Germany, 1–3 April 1996 brought together scientists working in the field of localized disturbances of flows in order to discuss new developments and the potential for application. The colloquium attracted a total of 56 participants from nine European countries, i.e. France, Germany, The Netherlands, Poland, Russia, Sweden, Switzerland, Ukraine and United Kingdom as well as from the US and Israel.

This paper describes an experiment in which a uniformly sheared turbulence was subjected to simultaneous streamwise flow curvature and rotation about the streamwise axis. The distortion of the turbulence is complex but well defined and may serve as a test case for turbulence model development. The uniformly sheared turbulence was developed in a straight wind tunnel and then passed into a curved tunnel section. At the start of the curved section the plane of the mean shear was normal to the plane of curvature so as to create a three-dimensional or ‘out of plane’ curvature configuration. On entering the curved tunnel, the flow developed a streamwise mean vorticity that rotated the mean shear about the tunnel centreline through approximately 70°, so that the shear was nearly in the plane of curvature and oriented so as to have a stabilizing effect on the turbulence. Hot wire measurements of the mean velocity, mean vorticity, mean rate of strain and Reynolds stress anisotropy development along the wind tunnel centreline are reported. The observed effect of the mean shear rotation on the turbulence was to diminish the shear stress in the plane normal to the plane of curvature while generating non-zero values of the shear stress in the plane of curvature. A rotating frame was identified for which the measured mean velocity field took the form of a simple shear flow. The turbulence anisotropy was transformed to this frame to estimate the effects of frame rotation on the structure of sheared turbulence.

A class of exact solutions of the Navier–Stokes equations is derived. Each of them represents the velocity field v=U+u of a thin vortical layer (a planar jet) under a uniform strain velocity field U in three-dimensional infinite space, and provides a simple flow model in which nonlinear coupling between small eddies plays a key role in small-scale vortex dynamics. The small-scale structure of the velocity field is studied by numerically analysing the Fourier spectrum of u. It is shown that the Fourier spectrum of u falls off exponentially with wavenumber k for large k. The Taylor expansion in powers of the coordinate (say y) in the direction perpendicular to the vortical layer suggests that the solution may be well approximated by a function with certain poles in the complex y-plane. The Fourier spectrum based on the singularities is in good agreement with that obtained numerically, where the exponential decay rate is given by the distance of the poles from the real axis of y.

We derive an integral expression for the flux of a single-phase fluid through a porous medium with prescribed boundary conditions. Taking variations with respect to the parameters of a given permeability model yields an integral expression for the sensitivity of the flux. We then extend the method to consider linear changes in permeability. This yields a linearised flux expression which is independent of changes in the pressure field that result from the changes in the permeability. For demonstration purposes, we first consider an idealised layered porous medium with a point source and point sink. We show how the effects of changes in permeability are affected by the position of the source and sink relative to the layered structure as well as the layer height and orientation of the layered structure. The results demonstrate that, even in a simple porous system, flux estimates are sensitive to the way in which the permeability is represented. We derive relationships between the statistical moments of the flux and of the permeability parameters which are modelled as random variables. This allows us to estimate the number of permeability parameters that should be varied in a fully nonlinear calculation to determine the variance of the flux. We demonstrate application of the methods to permeability fields generated through fast Fourier transform and kriging methods. We show that the linear estimates for the variability in flux show good agreement with fully nonlinear calculations for sufficiently small standard deviations in the underlying permeability.

When a laminar diffusion flame is established over a spinning, thermoplastic, polymer fuel disc in a quiescent, oxidizing environment, the polymer melts and flows radially outwards, causing some fuel to be lost and not transported to the diffusion flame. The viscosity of the liquid in the melt layer retards the radial flow, thereby determining the amount of fuel lost. The melt layer is analysed here for two limiting cases, namely one in which the liquid viscosity depends strongly on temperature, leading to an asymptotic analysis involving two zones in the liquid, and one in which the liquid viscosity is constant, independent of temperature, so that there is only one zone in the liquid. The utility of these two limits is assessed by comparing their predictions with those of full numerical integrations for poly(methyl methacrylate) (PMMA) discs burning in air at atmospheric pressure.

The time development of small three-dimensional disturbances in plane Poiseuille flow of helium II is considered. The study is conducted by considering the interaction of a normal fluid field and a superfluid field. The interaction is caused by a mutual friction forcing between the two flow fields. Specifically, the stability of the normal fluid affected by the mutual forcing is considered. Compared to the ordinary fluid case where the mutual forcing is not present, the presence of the mutual forcing implies a substantial increase of the transient growth of the disturbances. The increase of the transient growth occurs because the mutual forcing reduces the damping of the disturbances. The phase of transient growth becomes thereby more prolonged and higher levels of amplification are reached. There is also a minor effect on the transient growth caused by the modification of the mean flow owing to the mutual forcing. The strongest transient growth occurs for streamwise elongated disturbances, i.e. disturbances with streamwise wavenumber α = 0. When α increases beyond zero, the transient amplification quickly becomes reduced. Striking differences compared to the ordinary fluid case are that the largest transient amplification does not occur when the spanwise wavenumber (β) is close to two and that the peak level of the disturbance energy density amplification does not depend on the square of the Reynolds number.

Convection driven by radial and normal gravity forces in a rotating, horizontal cylinder is examined. The cylinder is subjected to uniform volumetric heating and constant-temperature wall cooling. The parameters are the radial-gravity and normal-gravity Rayleigh numbers, Rar and Rag (with Rar, Rag ≤ 106), the rotational Reynolds number, Re = 2Ω r02/v (0 ≤ Re ≤ 250), and the Prandtl number (Pr = 7). Critical conditions for the radial-gravity rest state correspond to a two-cell flow in the azimuthal plane with Rar,c = 13738. Finite-amplitude transient and steady flows are obtained with a Galerkin finite element method for Rayleigh number ratios in the range 0.1 ≤ Rar/Rag ≤ 100. When radial gravity dominates the flows tend to be multicellular and, during transients, initial high-wavenumber forms evolve to lower-wavenumber forms. When normal gravity dominates the flows are bicellular. When radial and normal gravity forces are comparable, in the presence of rotation, complex time-dependent motions occur and the largest rates of fluid circulation and heat transfer are observed.

James Lighthill died on 17 July 1998, at the end of a ten-hour swim round the Channel Island of Sark. He had earlier, at age 49, been the first person ever to do this, and he was carrying out the swim for the seventh time when the exertion revealed a mitral valve weakness which had never been diagnosed, and which led to his sudden death in the water. The swim was one of many long ‘adventure swims’ which Lighthill liked to take, all characterized by strong tidal currents and often heavy seas. And Lighthill took much pleasure through exercising his comprehensive understanding of fluid mechanics first in preparing for them through study of local conditions and then in adapting his performance when, as often, he found that in practice the currents were not as charted and, in fact, often more treacherous.

Many obituary notices have already appeared in the national press in the UK and USA, and now in the newsletters and journals of learned societies; and extensive conspectuses of Lighthill's contributions to fluid mechanics and applied mathematics, and to science generally and to the administration of science, will be published in Annual Review of Fluid Mechanics (2000), and in Biographical Memoirs of Fellows of the Royal Society (2000). The reader will learn, from those accounts, of the unique range and depth of Lighthill's contributions; and virtually all readers should expect to be surprised and impressed to read of facets of Lighthill's work of which they were previously totally unaware.