Two basins maintained at different densities are connected by a relatively shallow strait. If the strait is short, the flow is such that the Froude number is unity. The thickness of the intermediate layer, between the outflow and the inflow, is controlled by the requirement that the Richardson number be critical; this thickness is always about one-fifth of the total depth, both in these experiments and in the Strait of Gibraltar. If the strait is long, the Froude number is less than unity in the interior but increases to unity at each end. A strait may be considered short when its length is less than a few hundred times the sill depth.

This paper is a theoretical and experimental investigation of the onset of the buoyancydriven longitudinal roll cells that occur when a liquid layer flows over a heated horizontal plate. Linear stability theory is applied under the assumption that the spatially developing temperature profile can be treated locally, that is at each axial position, as being ‘frozen’. Using the film thickness as the length scaling factor, the critical Rayleigh numbers associated with the onset of longitudinal rolls are found to be considerably lower than measured values. A modified local stability analysis using the thermal boundary-layer thickness as the scaling factor is shown to agree with experiments. Predicted wavenumbers and the position of the onset of cellular convection are in agreement with wavenumbers measured by flow-visualization techniques. The position of the onset of cellular convection is also obtained from heat-transfer measurements at the heated surface. In the asymptotic limit of a linear undisturbed temperature profile the classical solutions of the Rayleigh-Bénard problem for the critical Rayleigh number and wavenumber are recovered, the only effect of the flow being the structure of the secondary flow that occurs when the system is unstable. Amplification theory is also compared with experimental data for the position at which the thermal effects of the convection are detectable and for the wavenumbers measured by flow visualization. The thermal amplification ratio $\overline{Nu}$ and a velocity-disturbance amplification ratio $\overline{w}$ are used to interpret the onset of discernible cellular convection. The data are not consistent with any single amplification ratio over the range of Rayleigh numbers studied (103 < Ra < 3 × 105), and the theoretical and experimental results suggest that a band of wavenumbers rather than a single wavenumber is encountered when cellular convection occurs.

This paper presents an inviscid bluff-body wake model which correctly takes into account the displacement effect of the far wake by means of an appropriate source–sink system located behind the body. The separating streamlines, which in previous inviscid wake models have been regarded as the time-averaged shear layers emanating from the separation points within a small distance downstream of the body, can be interpreted as the displacement surface of the wake throughout the whole region of flow behind the body. The solutions for a normal flat plate, a circular cylinder and a 90° wedge are worked out and compared with experiments, where possible. The theoretical pressure distributions agree fairly well with the experimental ones. The shape of the separating streamlines obtained from the present theory is physically reasonable and compares well with experimental results for a normal plate and a 90° wedge.

This paper treats the steady inertialess flow of an incompressible viscous fluid through an infinite rectangular duct rotating rapidly about an axis (the y axis) perpendicular to its centre-line (the x axis). The prototype considered has parallel sides at z = ± 1 for all x, parallel top and bottom at y = ± a for x < 0 and straight diverging top and bottom at y = ± (a + bx) for x > 0. An earlier paper (Walker 1975) presented solutions for b = ±(1), for which the flow in the diverging part (x > 0) is carried by a thin, highvelocity sheet jet adjacent to the side at z = 1, the flow elsewhere in this part being essentially stagnant. The present paper considers the evolution of the flow as the divergence decreases from O(1) to zero, the flow being fully developed for b = 0. This evolution involves four intermediate stages depending upon the relationship between b and E, the (small) Ekman number. In each successive stage, the flow-carrying side layer in the diverging part becomes thicker, until in the fourth stage, it spans the duct, so that none of the fluid is stagnant.

Swirling flow in an axisymmetric duct can support vorticity waves propagating parallel to the axis of the duct. When the cross-sectional area of the duct changes a portion of the wave energy is scattered into secondary vorticity and sound waves. Thus the swirling flow in the jet pipe of an aeroengine provides a mechanism whereby disturbances produced by unsteady combustion or turbine blading can be propagated along the pipe and subsequently scattered into aerodynamic sound. In this paper a linearized model of this process is examined for low Mach number swirling flow in a duct of infinite extent. It is shown that the amplitude of the scattered acoustic pressure waves is proportional to the product of the characteristic swirl velocity and the perturbation velocity of the vorticity wave. The sound produced in this way may therefore be of more significance than that generated by vorticity fluctuations in the absence of swirl, for which the acoustic pressure is proportional to the square of the perturbation velocity. The results of the analysis are discussed in relation to the problem of excess jet noise.

The effect of helicity on the Lagrangian velocity covariance UL(t) in isotropic, normally distributed turbulence is examined by computer simulation and by a renormalized perturbation expansion for UL(t). The first term of the latter represents Corrsin's (1959) conjecture (extrapolated to all t), which relates UL(t) to the Eulerian covariance and the distribution G(x, t) of fluid-element displacement. Truncation of the expansion at the first term yields the direct-interaction approximation for G(x, t). The expansion suggests that with or without helicity Corrsin's conjecture is valid as t → ∞ and that in either case UL(t) behaves asymptotically like $t^{-(r+\frac{3}{2})}$ if the spectrum of the Eulerian field varies like kr+2 at small wavenumbers. Corrsin's conjecture breaks down at small and moderate t if there is strong helicity while remaining accurate at all t in the mirror-symmetric case. Computer simulations for a frozen Eulerian field with spectrum confined to a thin spherical shell in k space indicate that strong helicity induces an increase in the Lagrangian correlation time by a factor of approximately three. Direct-interaction equations are constructed for the Lagrangian space-time covariance and the resulting prediction for UL(t) is compared with the simulations. The effect of helicity is well represented quantitatively by the direct-interaction equations for small and moderate t but not for large t. These frozen-field results imply good quantitative accuracy at all t in time-varying turbulence whose Eulerian correlation time is of the order of the eddy-circulation time. In turbulence with weak helicity, the directinteraction equations imply that the Lagrangian correlation of vorticity with initial velocity is more persistent than UL(t), by a substantial factor.