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Mathematical modelling of long ocean waves with a discontinuous density gradient

type de publication      article dans une revue internationale avec comité de lecture
date de publication 2001
auteur(s) Ouahsine Abdellatif; Bois Pierre-Antoine
journal Journal of Engineering Mathematics
volume (numéro) 40 (2)
pages 141 – 158
résumé A mathematical model for studying the propagation of long internal ocean waves of finite amplitude is proposed. The vertical structure of the pressure perturbation is investigated and reduced to a Sturm–Liouville eigenvalue problem. In the continuous stratification case, the pattern of this vertical structure depends on the choice of the characteristic scale of a varying stratification parameter, denoted by δ. As this parameter asymptotically approaches a critical value (i.e. δδcri), the amplitudes of the solution's normal modes increase considerably. The internal waves break and produce an unstable interface, which degenerates into a turbulent mixed layer. These conditions correspond to the critical state of wave existence. When δcri a three-layer discontinuous gradient model is proposed to resolve the problem. It consists in specifying one solution within a thin intermediary layer and two solutions on either side of this layer. The results show that the use of appropriately matching interfacial conditions allows to obtain generally matching solutions, even for small values of the nonconstant stratification parameter δ.
mots clés long waves, stratification, frontogenesis, density gradient, matched asymptotics
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