89 research outputs found

    Wave patterns generated by an axisymmetric obstacle in a two-layer flow

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    Gravity waves generated by a moving obstacle in a two-layer stratified fluid are investigated. The experimental configuration is three-dimensional with an axisymmetric obstacle which is towed in one of the two layers. The experimental method used in the present study is based on a stereoscopic technique allowing the 3D reconstruction of the interface between the two layers. Investigation into the wave pattern as a function of the Froude number, Fr, based on the relative density of the fluid layers and the velocity of the towed obstacle is presented. Specific attention is paid to the transcritical regime for which Fr is close to one. Potential energy trapped in the wave field patterns is also extracted from the experimental results and is analyzed as a function of both the Froude number, Fr, and the transcritical similarity parameter Γ. In particular, a remarkable increase in the potential energy around Fr = 1 is observed and a scaling allowing to assemble data resulting from different experimental parameters is proposed

    Free surface flow past topography : a beyond-all-orders approach

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    The problem of steady subcritical free surface flow past a submerged inclined step is considered. The asymptotic limit of small Froude number is treated, with particular emphasis on the effect that changing the angle of the step face has on the surface waves. As demonstrated by Chapman & Vanden-Broeck (2006), the divergence of a power series expansion in powers of the square of the Froude number is caused by singularities in the analytic continuation of the free surface; for an inclined step, these singularities may correspond to either the corners or stagnation points of the step, or both, depending on the angle of incline. Stokes lines emanate from these singularities, and exponentially small waves are switched on at the point the Stokes lines intersect with the free surface. Our results suggest that for a certain range of step angles, two wavetrains are switched on, but the exponentially subdominant one is switched on first, leading to an intermediate wavetrain not previously noted. We extend these ideas to the problem of flow over a submerged bump or trench, again with inclined sides. This time there may be two, three or four active Stokes lines, depending on the inclination angles. We demonstrate how to construct a base topography such that wave contributions from separate Stokes lines are of equal magnitude but opposite phase, thus cancelling out. Our asymptotic results are complemented by numerical solutions to the fully nonlinear equations
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