Abstract
The generation of instability in inviscid, non-diffusive geophysical flows is generically caused by a resonan ce between two wave modes. The weakly nonlinear unfolding of this situation is described in the long-wave regime, using a particular two-layer quasi- geostrophic model as an illust rative example. The outcome is a system of two coupled Korteweg-de Vries equations. This system contains a very rich solution set, consisting typically of solit ary wave interactions. We will describe some numerical solutions of the coupled Korteweg-de Vries equations, supplemented by perturbation analyses. We also report on some preliminary analogous numerical simulations of the full two-layer quasi-geostrophic system.
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Grimshaw, R., Gottwald, G. (2001). Models for Instability in Geophysical Flows. In: Hodnett, P.F. (eds) IUTAM Symposium on Advances in Mathematical Modelling of Atmosphere and Ocean Dynamics. Fluid Mechanics and Its Applications, vol 61. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0792-4_18
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DOI: https://doi.org/10.1007/978-94-010-0792-4_18
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