Abstract
The flow produced by water waves in the laminar boundary layer above a two-dimensional rough bed is studied analytically. At low Reynolds numbers the fluid drifts in closed recirculating cells, without dispersion. At high Reynolds numbers, vortex formation occurs for large-scale roughness and sudden jets of fluid are produced at a certain point in each half wave cycle with small-scale roughness. In both cases there is vigorous mixing close to the bed. The similarity between this mixing and that described by other authors in this field as turbulence suggests that the results of this study may be applied to the problem of transition in oscillatory boundary layers. The measurements made by LI and Manohar are reexamined and new curves proposed. The results of other authors are found to be in reasonable agreement with the new curves. An explanation is provided for the formation of tongues of dye.
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