Royal Society Publishing

Vertical jets from standing waves

Michael S Longuet-Higgins


When a shallow‐water wave meets a steep cliff or harbour wall, a jet is sometimes thrown upwards with very high initial acceleration. In the present work it is shown that a similar phenomenon can occur in a standing wave in deep water, provided that the initial shape of the trough is narrow and an almost circular arc. During collapse of the trough, vertical accelerations exceeding 10g are found, with subsequent vertical velocities exceeding 1.7c, where c is the phase‐speed of a small‐amplitude progressive wave. The vertical acceleration, plotted as a function of the time, is shown to be very sensitive to the initial shape of the wave trough. The presence of a much shorter wave superposed on the initial wave profile can further increase the maximum acceleration and velocity.

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