Asymptotic Models for Internal Waves
By Jerry L. Bona, David Lannes, Jean-Claude Saut. 2007
176 citations recorded by the source corpus.
We derived here in a systematic way, and for a large class of scaling regimes, asymptotic models for the propagation of internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid assumption and with a flat bottom. The full (Euler) model for this situation is reduced to a system of evolution equations posed spatially on $\R^d$, $d=1,2$, which involve two nonlocal operators. The different asymptotic models are obtained by expanding the nonlocal operators with respect to suitable small parameters that depend variously on the amplitude, wave-lengths and depth ratio of the two layers. We rigorously derive classical models and also some model systems that appear to be new. Furthermore, the consistency of these asymptotic systems with the full Euler equations is established.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Oceanography
View Paper: https://www.semanticscholar.org/paper/2aebe3e489b0b1f7113637c4d21d794a6f626ed7
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In Applied Mathematics
In Computational Theory and Mathematics
In Oceanography
Citations in the corpus
- The Cauchy problem on large time for surface waves Boussinesq systems (2012, methodology): “This technique has previously used by one of the authors [28] to establish the large time well-posedness of some asymptotic models for internal waves (see [9,12]).”