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A two-layer uid system separated by a pycnocline in the form of an internal wave is considered. The lower layer is infinitely deep, with a higher density than the upper layer which is bounded above by a at surface. The uids are incompressible and inviscid. A Hamiltonian formulation for the dynamics in the presence of a depth-varying current is presented and it is shown that an appropriate scaling leads to the integrable Benjamin-Ono equation.
Compelli, A., Ivanov, R. (2019). Benjamin-Ono Model of an Internal Wave Under a Flat Surface. Discrete and Continuous Dynamical Systems, 39(8), pp.4519-4532. doi:0.3934/dcds.2019185