Potential Flow Over a Wavy Bed: A Persistent Errorby H. M. Pantin, Univ of Leeds, United Kingdom,
Abstract: The standard small-amplitude theory of potential flow over a wavy bed is briefly discussed, together with the three special values of the Froude Number which define four different flow regimes. The situation F2 = tanh (kD) / [kD] is a well-known singularity, corresponding to a shift in the free-surface wave from out-of-phase to in-phase with the bed wave. The situation F2 = coth (kD) / [kD] corresponds to a zero value of the velocity perturbation near the bed, whereas the situation F2 = sinh (kD) / [kD.(cosh(kD)-1)] corresponds to the amplitude of the in-phase surface wave being equal to that of the bed wave. In certain review articles, the situation F2 = coth (kD) / [kD] is presented, wrongly, as corresponding to the equal-amplitude situation. This error is worth noting, since the potential-flow model is still a useful basis for understanding later, more sophisticated models.
Subject Headings: Surface waves | Potential flow | Wave velocity | Errors (statistics) | Froude number | Fluid flow | Free surfaces
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