4.6 Article

Highly nonlinear internal solitary waves with a free surface

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Summary: This paper investigates high-order strongly nonlinear long wave models and finds that the system for the bottom velocity is stable to all disturbances at any order of approximation. However, systems for other velocities can be unstable or even ill-posed. A new third-order solitary wave solution of the Euler equations is obtained using the high-order strongly nonlinear system and is expanded in an amplitude parameter. The paper shows the importance of using a more accurate spatial discretization scheme for numerical computations and successfully solves the strongly nonlinear systems for the propagation of solitary waves and their collision.

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