Russian Journal of Earth Sciences Russian Journal of Earth Sciences Russian Journal of Earth Sciences 1681-1208 46527 10.2205/2020ES000731 ОРИГИНАЛЬНЫЕ СТАТЬИ ORIGINAL ARTICLES ОРИГИНАЛЬНЫЕ СТАТЬИ An interesting oddity in the theory of large amplitude internal solitary waves An interesting oddity in the theory of large amplitude internal solitary waves Stastna Marek Stastna Marek mmstastna@uwaterloo.ca Lamb Kevin G Lamb Kevin G University of Waterloo ru University of Waterloo ru University of Waterloo ru University of Waterloo ru 20 4 29 10 2021 https://rjes.ru/en/nauka/article/46527/view

In the theory of internal waves in the coastal ocean, linear stratification plays an exceptional role. This is because the nonlinearity coefficient in KdV theory vanishes, and in the case of large amplitude waves, the DJL theory linearizes and fails to give solitary wave solutions. We consider small, physically consistent perturbations of a linearly stratified fluid that would result from a localized mixing near a particular depth. We demonstrate that the DJL equation does yield exact internal solitary waves in this case. These waves are long due to the weak nonlinearity, and we explore how this weak nonlinearity manifests during shoaling.

In the theory of internal waves in the coastal ocean, linear stratification plays an exceptional role. This is because the nonlinearity coefficient in KdV theory vanishes, and in the case of large amplitude waves, the DJL theory linearizes and fails to give solitary wave solutions. We consider small, physically consistent perturbations of a linearly stratified fluid that would result from a localized mixing near a particular depth. We demonstrate that the DJL equation does yield exact internal solitary waves in this case. These waves are long due to the weak nonlinearity, and we explore how this weak nonlinearity manifests during shoaling.

 Internal waves DJL theory shoaling nearly linear stratification Internal waves DJL theory shoaling nearly linear stratification

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