On the origin of the ‘surface current’ in turbulent free-surface flows

Abstract

In this study, the interaction with a free surface of an initially axisymmetric jet issuing beneath and parallel to the surface was examined. The purpose was to determine the origin of the ‘surface current’ – the large outward velocity which exists in a thin layer adjacent to the surface. Using the equations of mean motion, it is shown that near the surface, outward acceleration results from the balance between a positive contribution from the lateral Reynolds-stress gradients and a negative contribution from the lateral pressure gradient. The local pressure field near the free surface is shown to be largely determined by the local Reynolds-stress field. Combining these results shows that the lateral acceleration which results in the surface current is related to the Reynolds-stress anisotropy near the surface. The results indicate that there should be roughly a three-fold increase in the lateral growth rate of the jet near the free surface and a similar increase in the outward velocity, when compared to a deep jet. Comparison to available experimental data showed that the maximum outward velocity was consistent with the theory, and that the lateral scale of the surface-current layer was roughly double that of the deep jet, slightly smaller than expected. The near-surface stress anisotropy was shown to be related to the interaction of vorticity with the free surface. This indicates that the results of this study are consistent with earlier explanations of the surface current in terms of vortex/free-surface interaction.