Summary
The waves generated by a steadily moving two-dimensional pressure distribution are examined using non-linear shallow water theory. The applied pressure is zero ahead of the disturbance, that is in the downstream direction, and is a constantP 0 in the upstream direction, these regions being joined smoothly by a cubic function.
We consider here only the case of supercritical flow in both regions, the solution representing an asymmetric solitary wave travelling with the disturbance. The wave profiles are determined by an iterative method previously employed for non-linear waves. Wave amplitudes and profiles, and the wave drag, associated with each system are computed for various values ofP 0/Q g h, whereh is the undisturbed depth of water ahead of the wave.
The solution obtained reduces to the classical solitary wave of finite amplitude when the applied pressure is everywhere zero.
Résumé
Nous avons calculé les expressions des profils d'ondes solitaires produites par une pression, qui se propagent sur la surface d'une couche d'eau peu profonde avec une vitesseU plus grande que (g h)1/2. La pression appliquée est nulle en avant de l'onde, elle est une constanteP 0 en arrière, et entre ces deux régions elle est representée par une fonction cubique. Les profils sont calculés par une methode iterative déjà employée pour des ondes non-linéaires. L'amplitude, le profil et la force ont été evalués pour diverses valeurs deP 0/Q g h, ouh est la profondeur en avant de l'onde.
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Division of Numerical and Applied Mathematics, National Physical Laboratory.
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Hunt, J.N., Tanner, D.A. On solitary waves generated by a moving pressure field. PAGEOPH 85, 309–323 (1971). https://doi.org/10.1007/BF00875418
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DOI: https://doi.org/10.1007/BF00875418