Interaction Between Long Internal Waves and Free Surface Waves in Deep Water
Kairzhan A. Kennedy C. Sulem C.
November 2024Birkhauser
Water Waves
2024#6Issue 3477 - 520 pp.
We consider a density-stratified fluid composed of two immiscible layers separated by a sharp interface. We study the regime of long internal waves interacting with modulated surface wave packets and describe their resonant interaction by a system of equations where the internal wave solves a high-order Benjamin–Ono (BO) equation coupled to a linear Schrödinger equation for the envelope of the free surface. The perturbation methods are based on the Hamiltonian formulation for the original system of irrotational Euler’s equations as described in Benjamin–Bridges (J Fluid Mech 333:301–325, 1997) and Craig et al. (Pure Appl Math 58:1587–1641, 2005). We also establish a local well-posedness result for a reduced BO–Schrödinger system using an approach developed by Linares et al. (J Diff Eqs 250:450–475, 2011).
Hamiltonian systems , Internal waves , Surface waves
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Department of Mathematics, Nazarbayev University, Astana, 010000, Kazakhstan
Department of Mathematics and Statistics, Queen’s University, Kingston, K7L 3N6, ON, Canada
Department of Mathematics, University of Toronto, Toronto, M5S 2E4, ON, Canada
Department of Mathematics
Department of Mathematics and Statistics
Department of Mathematics
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