Large-Amplitude Solitary Waves in Two-Layer Density Stratified Water
Abstract
We present a large-amplitude existence theory for two-dimensional solitary waves propagating through a two layer body of water. The domain of the fluid is bounded below by an impermeable flat ocean floor and above by a free boundary at constant pressure. For any piecewise smooth upstream density distribution and laminar background current, we construct a global curve of solutions. This curve bifurcates from the background current and, following along the curve, we find waves that are arbitrarily close to having horizontal stagnation points. The small-amplitude waves are constructed using a center manifold reduction technique. The large-amplitude theory is obtained through analytical global bifurcation together with refined qualitative properties of the waves.
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Information & Authors
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Published In
SIAM Journal on Mathematical Analysis
Pages: 4812 - 4864
DOI: 10.1137/20M1383537
ISSN (online): 1095-7154
Copyright
© 2021, Society for Industrial and Applied Mathematics.
History
Submitted: 1 December 2020
Accepted: 27 April 2021
Published online: 30 August 2021
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National Science Foundation https://doi.org/10.13039/100000001 : DMS-1812436
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