A shallow three-dimensional hump disturbs the two-dimensional incompressible boundary layer developed on an otherwise flat surface. The steady laminar flow is studied by means of a three-dimensional extension of triple-deck theory, so that there is the prospect of separation in the nonlinear motion. As a first step, however, a linearized analysis valid for certain shallow obstacles gives some insight into the flow properties. The most striking features then are the reversal of the secondary vortex motions and the emergence of a ‘corridor’ in the wake of the hump. The corridor stays of constant width downstream and within it the boundary-layer displacement and skin-friction perturbation are much greater than outside. Extending outside the corridor, there is a zone where the surface fluid is accelerated, in contrast with the deceleration near the centre of the corridor. The downstream decay (e.g. of displacement) here is much slower than in two-dimensional flows.

SUMMARYAn experimental study has been made of the shear flow of stratified fluid of characteristic buoyancy frequency ,Y with characteristic speed @ past a three-dimensional obstacle of height I; when the Froude number, Fr = d % / . N / T , is much smaller than one. It is already known that in the limit Fr+O the inviscid equations of motion may be expanded in powers of Fr* and that the lowest-order solution is a flow confined to horizontal planes, passing around the obstacle rather than over it. This theory breaks down within a distance #/Jf from the level of the top of the obstacle.The experiments were carried out ih a closed-circuit stratified water channel with a hemisphere, a cone and a truncated cylinder for Fr between 0 0 3 and 0.3 at Reynolds numbers between 100 and IOOO. The qualitative features have been determined by flow visualization with dye. The flows are found to be nearly in horizontal planes except near the tops of the obstacles. Also there are revealed two other prominent features which the theory cannot predict. In the lee of the obstacles at the level of the top, a cowhorn-shaped eddy with horizontal axis is observed for high enough Fr; it combines the characteristics of rotors and of horseshoe vortices. Below this lev&, there is a separated wake flow in each horizontal plane. Vortices are shed provided the Reynolds number is large enough and provided Fr is less than about 0.15. The shedding frequency is the same at all heights.Attention is drawn to atmospheric situations of which these features may be ingredients.

A complete description is sought for the two-dimensional laminar flow response of an incompressible boundary layer encountering a hump on an otherwise smooth boundary. Given that the typical Reynolds number Re (based on the development length L* of the boundary layer) is large, the flow characteristics depend on only two parameters, the non-dimensional length and height scales l, h of the obstacle. For short humps of length less than the familiar O(Re−⅜) triple-deck size the critical height scale, which produces a nonlinear interaction and hence the prospect of separation, is of order $Re^{-\frac{1}{2}}l^{\frac{1}{3}}$. For long humps whose length is greater than the triple-deck size the corresponding critical height scale is much bigger, of order $l^{\frac{5}{3}}$. Height scales below critical produce only a weak flow response while height scales above critical force relatively large-scale separated motions to occur. In the paper the flow structures and typical solutions produced by two representative cases, a short obstacle of length comparable with the oncoming boundary-layer thickness and a long obstacle of height comparable with the boundary-layer thickness, are mainly considered. The former case is controlled by the unknown pressure force induced locally in the flow near the hump and by two length scales, that of the hump itself and that of the longer triple deck. The latter case is governed mainly by the inviscid externally produced pressure force. Alternatively, however, all the dominant flow properties in both cases can be obtained as special or limiting solutions of the triple-deck problem. Comparisons between the cases studied are also presented.