A Unified Theory of Nonlinear Wave Propagation in Two-Layer Fluid Systems

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  • Unified Theory of Nonlinear Wave Propag

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A unified theory is presented which describes nonlinear wave propagation in two-layer inviscid and incompressible fluid of arbitrary depth. We consider the two-dimensional systems, in which a layer of lighter fluid overlies a layer of heavier one resting on a flat bottom. The two cases of rigid and free upper boundaries are dealt with separately. We derive approximate nonlinear evolution equations (NEEs) for interfacial and free surface elevations on the basis of a systematic perturbation method with respect to the steepness parameter. We also discuss on NEEs arising from various limiting cases of fluid depth and compare them with existing NEEs. It is found that our theory includes almost all existing nonlinear theories as special cases.

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