Three-dimensional wave patterns generated by moving disturbances at transcritical speeds

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Abstract
Disturbances in the form of pressure fields, source distributions and time-dependent bottom topographies are discussed and found to produce similar wave patterns. Results obtained for wide channels are discussed in the light of the features of soliton reflection at a wall. Comparison with experiments shows excellent agreement. The introduction of radiation conditions enables long-time simulation of the development of wave patterns in infinite and semi-infinite fluids. A stationary wave pattern is also found to emerge for slightly supercritical Froude numbers, but contrary to linear results the leading divergent waves may originate ahead of the disturbance. This behaviour is due to nonlinear interactions similar to those governing collisions between solitons. This study on wave generation by a moving disturbance is based on numerical solutions of Boussinesq-type equations. The equations in their most general form are integrated by an implicit difference method. Strongly supercritical cases are described by a simplified set of equations which is solved by a semi-implicit difference scheme.

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