Measurements of mean-pressure distributions and boundary-layer development on rough-walled circular cylinders in a uniform stream are described. Five sizes of distributed sandpaper roughness have been tested over the Reynolds-number range 7 × 104 to 5·5 × 105. The results are examined together with those of previous investigators, and the observed roughness effects are discussed in the light of boundary-layer theory. It is found that there is a significant influence of surface roughness on the mean-pressure distribution even at very large Reynolds numbers. This observation is supported by an extension of the Stratford–Townsend theory of turbulent boundary-layer separation to the case of circular cylinders with distributed roughness. The pressure rise to separation is shown to be closely related, as expected, to the characteristics of the boundary layer, smaller pressure rises being associated with thicker boundary layers with greater momentum deficits. Larger roughness gives rise to a thicker and more retarded boundary layer which separates earlier and with a smaller pressure recovery.

Results are presented of a simplified description of the seasonal and spring–neap tidal dependence of the axial dispersion coefficients in the Severn Estuary. The coefficients are derived from salt budget calculations, which are based on 29 sets of observations of the axial salinity distributions in the estuary during 1971–1976. Regression analyses of the salinity distributions determine simple linear and logarithmic relationships for the dispersion coefficients in terms of tidal range and the total rate of input of fresh water to the estuary, the appropriate averaging periods for the freshwater inputs being computed as part of the analyses.

The results show that the coefficients generally increase with increasing run-off, and, away from the mouth, depend upon the tidal range, showing a small decrease with increasing tidal range in the seaward part of the estuary, and a large increase with increasing tidal range towards the head. The yearly averaged coefficients lie in the order-of-magnitude range 102–103 m2s−1, with the larger values occurring near the head.

The computed dispersion coefficients are applied to calculations of the seasonal dependence of residence times, the results being expressed as functions of axial distance along the estuary. It is shown that the residence time of the whole estuary varies from roughly 100 days during winter conditions to 200 days during summer conditions, and that the residence time landward of a particular section decreases rapidly as the section taken approaches the head of the estuary.

Considered below is the plane, high-Reynolds-number (Re), flow of an incompressible fluid through a channel suffering a severe non-symmetric constriction, ‘severe’ meaning ‘of typical dimensions comparable with the channel width a*’. The (mainly inviscid) flow description is governed by free streamline theory, to be consistent with the viscous incompressible separation from the constriction surface and with a relatively slow eddy motion beyond. Separation also occurs far ahead of the constriction, at a distance $O(Re^{\frac{1}{7}} a^{*})$ upstream. Attention is given primarily to the flow features for a particular class of slowly varying severe constrictions, from which however the features for the probably more useful classes of slender (i.e. of large length but O(a*) height) and moderately severe (i.e. of O(a*) length but small height) constriction follow, as do those for curved or cornered channel flows. In all these cases a long-scale flow response is induced upstream and downstream and in many cases remarkably simple universal formulae for the separation and reattachment positions result. The corresponding O(a*) corrections to the upstream separation distance above are also derived.

The stability boundary of a density-stratified fluid contained in an inclined slot subjected to a lateral temperature gradient was determined experimentally. The initial stratification due to salt was stable and linear in the vertical direction. Experiments were conducted in a 1·0 × 11.1 × 25·7 cm slot with the inclination angle θ from the vertical varying from −75° to + 75°. A positive angle denotes heating from the lower wall while a negative angle denotes heating from the upper wall. The temperature difference across the slot was increased slowly until the onset of instability was observed by means of a shadowgraph. The critical thermal Rayleigh number was found to be non-symmetrical with respect to θ = 0°, with heating of the upper wall less stable than heating of the lower wall. This is because there is a larger vertical solute gradient in the steady-state regime prior to the onset of instabilities when the lower wall is heated. The secondary flow consisting of horizontal convecting layers was very stable θ < 0° cases because of the stabilizing temperature effect. The motion of the layers when θ > 0° was quite vigorous. At θ = +75°, the secondary flow became unstable in a rather dramatic manner not observed heretofore.

Linear stability analysis is applied to the problem of a density-stratified fluid contained in an inclined slot being subjected to a lateral temperature gradient. Stability equations are solved using the Galerkin technique with 12 terms in the truncated expansion series. Within the range of θ considered, |θ| < 75°, critical instability was found to be of the stationary type. Results of critical thermal Rayleigh numbers and wavenumbers at all inclination angles are in good agreement with the experimental results obtained earlier (Paliwal & Chen 1980). Contrary to intuition, these results show that the system is more stable when the lower wall is heated. This is shown to be the result of the increased vertical solute gradient in the steady state prior to the onset of instabilities when the heating is from below.

In order to determine the heat transfer inside a TIG (tungsten/inert gas) weld pool, it is necessary to have a good understanding of the flow patterns of the liquid metal. The principal force driving the fluid motion is the electromagnetic j × B force due to the current from the welding arc and its self-magnetic field. In this paper we consider the flow of a viscous incompressible conducting fluid in a hemispherical container due to various distributions of the electric current. The problem is posed as a time-dependent problem and is solved numerically using the Du Fort–Frankel leap-frog method. Results are presented for currents of 100 A flowing through the weld pool. This is a typical current for TIG welding, and corresponds to a Reynolds number in the range 200 < Re < 600. Previous solutions of the problem were restricted to low Reynolds numbers, i.e. low currents.

An extension of the analytical results of Kaup & Newell (1978) concerning the effect of a perturbation on a solitary wave of the Korteweg–de Vries equation is given and numerical studies are conducted to verify the conclusions. In all cases, the numerical results agree with the results predicted by the theory. The most striking feature of the perturbed flow is the presence of a shelf in the lee of the solitary wave whose role is to absorb (provide) the extra mass which is created (depleted) by the perturbation.

Numerical solutions have been obtained for steady viscous flow past a circular cylinder at Reynolds numbers up to 300. A new technique is proposed for the boundary condition at large distances and an iteration scheme has been developed, based on Newton's method, which circumvents the numerical difficulties previously encountered around and beyond a Reynolds number of 100. Some new trends are observed in the solution shortly before a Reynolds number of 300. As vorticity starts to recirculate back from the end of the wake region, this region becomes wider and shorter. Other flow quantities like position of separation point, drag, pressure and vorticity distributions on the body surface appear to be quite unaffected by this reversal of trends.