The flow field about a small, slowly sedimenting particle in a centrifuge is examined using matched asymptotic expansions. The near field is dominated by Stokes flow while in the far field a non-axisymmetric cubical conical structure (a viscously modified Taylor column) is found. This far field induces a Coriolis modification in the near field leading to Coriolis corrections to the Stokes drag law. The Coriolis modification of the predicted molecular weight (if the particle were a molecule) of a small particle is calculated. The analysis is applied to an unbounded fluid as well as to a fluid bounded between parallel plates oriented normal to the rotation vector. In the latter case the governing equations for the rotating fluid are posed as a self-adjoint system of partial differential equations and solved using (symmetric) Green's matrices.

The internal-wave system is calculated for a body oscillating transversely, and translating uniformly, through an infinite stratified fluid of constant Brunt-Väisälä frequency. A linearized, time-dependent analysis is used, in which the vertical displacement of a fluid element is the basic dependent variable. Axisym-metric slender-body theory for a homogeneous fluid is used to determine the time-dependent source and dipole distributions required to represent the motion of the body for excitation of the internal waves. The equations are solved by Fourier-transform techniques; and the internal-wave amplitude is evaluated in the far field by the method of stationary phase. The surfaces of constant phase are found to change character as the ratio of the oscillation frequency ω of the body to the Brunt-Väisälä frequency N varies through unity. Along preferred directions, the amplitude of the internal waves is found to decay inversely with distance to the $\frac{5}{6}$ power, whereas, for uniform translation, the amplitude of the internal waves falls off inversely with distance from the body. An asymptotic expression for the amplitude in preferred directions is calculated for several values of the ratio ω/N.

Interactions between laminar thermal natural convection plumes generated by line and concentrated heat sources were experimentally investigated with a Mach-Zehnder interferometer. Adjacent plane plumes were found to interact more strongly than axisymmetric plumes a t the same spacing. These flows with nominally free boundaries were also found to be affected by nearby surfaces which interfered with the supply of entrainment fluid. Several types of interference with plume entrainment were investigated. The nature of the interacting flows suggests a model which is successful in interpreting the mechanism. An application of the effects of plume interaction is discussed.

In this paper we present a theoretical model which permits the conservation equations of fluid dynamics to be conditioned in a fashion analogous to the experimentalist's technique of ‘conditioned sampling’. The detailed analysis refers to the best-known sampling condition, outer-edge intermittency; but the model equation may be applicable to other flow situations, wherein condition- ing exposes details of the physical phenomena. The analysis results in predic- tions of the flow variables within the turbulent flow and of the intermittency. Comparison is made with two sets of experimental results for the two-dimensional mixing layer and with a boundary layer.

The rate of entrainment of ambient fluid across a turbulent interface has been defined as the mean rate of increase of turbulent fluid in the flow direction. Experiments to measure this quantity by conditional sampling in a two-dimen- sional wall jet are described. Further, estimates of this entrainment rate were made for the turbulent boundary layer, two-dimensional wake, two-dimensional jet and round jet and the results are discussed.

The rate of entrainment through the end of a plume or jet which impinges on a density interface has been determined in the laboratory, where the interface was produced by layers of fresh and salt water and the plume by a salt-water source. Observations of the impingement area indicated that entrainment was confined to a region about the size of the plume cross-section. It was thus concluded that the entrainment flux into the plume must be a function of the local width, velocity and buoyancy difference, and these can be combined into a single para- meter, the Froude number. Measurements of the volume flux showed it to be proportional to the cube of the Froude number. The flux of buoyancy from the salt-to fresh-water volumes is consequently proportional to the Froude number. In the second part of the study the density distribution in the initially fresh layer was derived and is verified by the experiments. This distribution has direct applications in the analysis of convective motions in the atmosphere and the ocean.

Observations made in a well-developed, thermally stratified, horizontal, flat- plate boundary layer are used to study the effects of buoyancy on the mean flow and turbulence structure. These are represented in a similarity framework obtained from the concept of local equilibrium in a fully developed turbulent flow. Mean velocity and temperature profiles in both the inner and outer layers are strongly dependent on the thermal stratification, the former suggesting an increase in the thickness of the viscous sublayer with increasing stability. The coefficients of skin friction and heat transfer, on the other hand, decrease with increasing stability.

Normalized turbulent intensities, fluxes and their correlation coefficients also vary with buoyancy. In stable conditions, turbulence becomes rapidly suppressed with increasing stability as more and more energy has to be expended in over- coming buoyancy forces. The buoyancy effects are found to be more dominant in the stress budget than in the turbulent energy budget. The horizontal heat flux is much greater than the vertical heat flux and their ratio increases with stability. The ratio of the eddy diffusivities of heat and momentum, on the other hand, decreases with increasing stability. The spectra of velocity and temperature fluctuations indicate no buoyancy subrange, but the wavenumber corresponding to peak energy is found to increase with increasing stability.

This paper presents a summary of the results of an extensive experimental investigation of the problem considered by Tatsumi (1952a, b) and more recently by Huang & Chen (1974a, b). The results, like the analyses, show that the linear instability is confined to the non-similar inlet region of the pipe.

Three-dimensional convection in a Boussinesq fluid confined between horizontal rigid boundaries is studied in a series of numerical experiments. Convection in air, whose Prandtl number Pr = 0·71, is systematically investigated, together with another model for Pr = 1. Convection with a steadily changing mean temperature is also considered. Two-dimensional rolls over the Rayleigh number range 4500 [les ] Ra [les ] 24000 and three-dimensional flow patterns over the range 26000 [les ] Ra ≤ 32000 are shown to be stable in air when the mean temperature of the layer is constant ($\partial \overline{T}/\partial t = \eta = 0$). Discrete changes in the slope of the heat-flux curve are shown to exist in the ranges \[ 7000\leqslant Ra\leqslant 8000,\quad 12000\leqslant Ra\leqslant 14000\quad{\rm and}\quad 24000\leqslant Ra\leqslant 26000 \] in air. Only the last discrete transition in the heat flux is asSociated with a significant transition in the flow pattern. Two-dimensional rolls with a horizontally asymmetric distribution of upward and downward motions over the range 4500 [les ] Ra [les ] 8000, and three-dimensional flow patterns over the range 10 000 [les ] Ra [les ] 20 000 are shown to be stable when the mean temperature varies with time. The circulation in a three-dimensional cell depends on the sign of the mean temperature change: downward motions occupy the centre of the cell when $\partial\overline{T}/\partial t > 0$, and upward motions when $\partial\overline{T}/\partial t < 0 $. Motions start to be time dependent for Ra > 20000. Transitions in the planform are asSociated with discrete changes in the slope of the heat-flux curve. Transitions in both the heat flux and flow pattern depend quantitatively on the Prandtl number.

The problem of obtaining a numerical solution for the steady flow between two coaxial infinite disks, one fixed and porous, the other rotating, is reduced by von Kámán's hypothesis to solution of a system of nonlinear equations. A Newton-type iteration results in several solutions to these equations, as a number of authors have already indicated. Nevertheless, an interval in which only one solution is found exists for small values of the Reynolds number based on the angular velocity of the rotating disk, the distance between the disks and the kinematic viscosity of the fluid. At large values of this Reynolds number, two solutions appear and have been the subject of intense controversy.

In this paper, both physical and numerical arguments are presented which support a Batchelor-type solution for the flow between infinite disks, in which part of the fluid rotates as a solid body. The other solution, following Stewartson, assumes that the velocity of the fluid outside the boundary layers is entirely axial. This only seems to be verified experimentally when the distance between the disks is large compared with the (finite) radius of the disks.

The effect on an obliquely incident surface wave of a vortex sheet separating two uniform currents is considered. It is shown that the amplitude of the transmitted wave as a function of the angle of incidence and current strength is very close to that obtained by Longuet-Higgins & Stewart on the assumption of small smooth changes in current velocity. The difference is accounted for by a small amount of reflexion of the wave by the vortex sheet. It is suggested that, in the intermediate range where the change in current velocity over a wavelength is comparable with the wave velocity, the wave amplitude of the transmitted wave lies between the curves of Longuet-Higgins & Stewart and those found here.

The linear stability of a rotating contained perfect gas flowing axially is shown to depend on a ‘centrifugal Richardson number’ when the ratio of the axial flow to the peripheral velocity, and the ratio of the peripheral velocity to the sound speed are both small. The Boussinesq approximation is not made. In the limit of infinite sound speed the known incompressible result (unstable, Pedley 1968) is reproduced. Comparison with computational results indicates that the asymptotic theory is pessimistic.

Gans' criterion is shown to be valid for all inviscid non-diffusive flows where the radial velocity is everywhere zero and the physical variables are functions of the radial distance only. That is, a modified form of the Miles-Howard theorem holds for a large class of helical gas flows.