This paper describes an experimental study of the electromagnetic stirring in a mercury induction furnace. The 200 mm-diameter furnace is supplied with a single-phase electric current of frequency 50–4700 Hz. The flow pattern is measured by means of a special two-wire probe, which tracks the thermal wake behind a hot-film probe. The magnitudes of fluctuating velocities are measured by hot-film anemometry. Attention is focused on the influence on the mean and turbulent motion of the electromagnetic-skin depth, which is determined by the supply frequency. The measurements of the mean motion show that, for a fixed magnetic field, stirring is maximum when the value of the skin depth normalized by the pool radius is about 0.2, in agreement with previous theoretical predictions. Two turbulence regimes may be distinguished for different frequency ranges. At low frequency the various properties of the turbulence, such as the mean-square fluctuations, the integral scales and the turbulent dissipation rate, are almost uniform over the whole bath. However, at high frequency the turbulence is non-uniform; there is an increase in the turbulent fluctuations and dissipation rate and a decrease of the integral scale within the electromagnetic-skin depth near the wall.

An attempt is made in this paper to tackle the problem of nonlinear wave resistance by formulating it in Fourier space and by deriving a nonlinear integral equation for the wave amplitude by an approach similar to the one leading to the Zakharov equation.

The procedure is illustrated for two simple examples of two- and three-dimensional travelling pressure distributions. A regular perturbation solution up to third-order terms in the slenderness parameter shows that the expansion is not uniform for small Froude numbers. A uniform, generalized, expansion is then constructed, with its leading term satisfying a new nonlinear integral equation. This rather simple integral equation, of a Volterra type, is solved numerically. The generalized wave drag is shown to be significantly larger than the one predicted by the regular perturbation expansion at small Froude number. The method adopted here has the advantage of singling out in a systematic manner the terms of the free-surface conditions which cause the small-Froude-number non-uniformity, and it is applicable to both two- and three-dimensional flows. The results are compared with existing approximate methods of computing wave drag at low Froude numbers. It is found that quasilinearized approximations may be quite accurate for the examples considered here.

This is an experimental and theoretical study of the slow translation of a hot sphere through a fluid at rest at infinity. The viscosity depends strongly on temperature, i.e., if ΔT = T0 − T∞ is the applied temperature difference and γ = |(d/dT0) lnμ(T0)|, then the parameter θ = γ ΔT is large: it is about 6.5 in the experiments and is taken as infinite in the theory. The flow is determined by two large parameters, namely the Nusselt number N and the modified viscosity ratio ε−1 = ν∞/(ν0θ3). The qualitative state of the flow is observed to depend on the relation between N and ε. If ε−1 → ∞ (N fixed, possibly large) previous analysis (Morris 1982) shows that all the shear occurs in a thin low-viscosity film coating the sphere; this film and the associated thermal layer separate at the equator, and a separation bubble of low-viscosity fluid trails the sphere. (ii) If N → ∞ (ε−1) large but fixed) even the most viscous fluid deforms, and both the drag and heat losses are found to be controlled by this highly viscous flow. The present work maps the major asymptotic states which separate these two end-states for small ε. The drag and heat-transfer laws are determined experimentally and theoretically: in addition it is shown that separation of the thermal layer ceases when the drag is controlled by the most viscous fluid, even though the heat transfer in this case can be still controlled by the dynamics of the least-viscous fluid. The heat-transfer and drag laws are also given for a sphere moving in a spherical container of finite radius. This model is shown to give a close estimate of wall effects for a sphere moving in a cylindrical container. For state (i) the theory predicts the heat transfer to within 20% and, for the smallest ε, the drag to within 30%. In the experiments ε is small enough for all limiting states to be evident but, apart from state (i), a design flaw prevents a quantitative test of the theory. For the other states, the theory is compared with numerical results from Daly & Raefsky (1985). Although the values of ε in the calculations are not small enough for the limiting states to be achieved, the theory predicts the drag to within 8% and the heat transfer to within 10 %.

The results of tests on an axial-flow compressor stage designed to allow operation at unusually low axial clearances are presented. The axial clearance was varied between 1 and 33 % of the blade chord whilst the compressor was running, and the stage pressure rise showed a peak at a clearance around 4 % of blade chord. The pressure rise was 8 % higher at this clearance than at 33 % of chord, with no significant change in the stage efficiency. In addition, reducing the clearance was found under some conditions to bring the stage from a stalled to a fully unstalled state. The sound output of the stage was measured at all clearances, and the results show a significant increase in the high harmonics of the blade-passing frequency at low axial clearances.

An aortic-valve model is developed, having a quadratic cross-section, two rigid cusps and two wedge-shaped aortic sinuses. The flow through this valve is assumed to be one-dimensional, just as the flow behind the cusps should be one-dimensional. The resulting model equations are two nonlinear ordinary differential equations of second order for the valve opening area as a function of time in two different ranges.

This model allows the size of the aortic sinus to be varied; it also permits a computation of the pressure at both sides of the cusps (unlike previous models of this kind, which consider the flow behind the cusps as stagnant). The computed valve motion due to this pressure difference is in good agreement with experimental results, although no vortex with circular streamlines is postulated in the aortic sinuses. Obviously such vortices trapped in the sinuses are not important for the valve closure, which is controlled solely by the flow deceleration.

A stratified two-layer fluid is brought to solid-body counterclockwise rotation inside a cylindrical tank having a conical bottom with a radial topographic ridge. A stress is then applied to the top surface by means of a clockwise differentially rotating disk. The resulting Ekman-layer flux causes the top layer to spin-down and the interface to rise near the wall and to descend a t the centre of the tank. As this process continues, the interface (front) between the two layers intersects the disk surface, and after that migrates away from the wall and allows the bottom fluid to contact the disk directly. The migration of the front continues until a steady state is reached, the front becomes stationary and the system is in geostrophic balance. The first sign of upwelled flow at the surface always occurs as a high-speed jet-like plume at the bottom topography, and only at a later time does a uniform upwelled flow appear a t the surface upstream of the topography. This plume, which always forms near the downstream edge of the topography, migrates in advance of the upstream front to produce an upwelling maximum at the bottom topography.

The final width of the upstream flow in steady-state conditions is estimated by a simple theoretical model, which is in good agreement with the experimental results. We have an experimental criterion to predict the occurrence of travelling baroclinic waves on the upstream front. On the downstream side of the ridge, large standing waves are observed, with significant upwelling within them. Under some circumstances cyclones pinch-off from the upstream front, the plume on the ridge and the crests of the large downstream standing waves. We present criteria to predict the occurrence of these pinch-off processes.