First-order irrotationality in Gerstner's trochoidal waves
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The exact equations expressing a possible form of gravity wave motion, given byGerstner in 1802, are more of a curiosity than a cornerstone of the hydrodynamic theory of surface waves. The reason is that the motion is not strictly irrotational while physically meaningful waves do possess this property-and no suitable measure of rotationality has been available to permit the extent of the deficiency to be assessed. The Lagrangian method of flow description is shown to provide the required measure, introducing the concepts of first-order irrotationality as well as a ‘displacement potential’. In this manner the gulf that separates Gerstner's unique and important wave solution from the larger body of wave theory is bridged.
KeywordsSurface Wave Large Body Wave Solution Gravity Wave Wave Motion
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