Mathematical modelling of long ocean waves with a discontinuous density gradient

摘要: A mathematical model for studying the propagation of long internal ocean waves finite amplitude is proposed. The vertical structure pressure perturbation investigated and reduced to a Sturm–Liouville eigenvalue problem. In continuous stratification case, pattern this depends on choice characteristic scale varying parameter, denoted by δ. As parameter asymptotically approaches critical value (i.e. δ → δcri), amplitudes solution's normal modes increase considerably. break produce an unstable interface, which degenerates into turbulent mixed layer. These conditions correspond state wave existence. When < δcri three-layer discontinuous gradient proposed resolve It consists in specifying one solution within thin intermediary layer two solutions either side results show that use appropriately matching interfacial allows obtain generally solutions, even small values nonconstant