Skip to Main content Skip to Navigation
Journal articles

Instabilities of buoyancy driven coastal currents and their nonlinear evolution in the two-layer rotating shallow water model. Part II. Active lower layer

Abstract : The present paper is the second part of the work on linear and nonlinear stability of buoyancy-driven coastal currents. Part I was presented in the companion paper Gula & Zeitlin (2010). In this part we use a fully baroclinic two-layer model, with active lower layer. We revisit the linear stability problem for coastal currents and study the nonlinear evolution of the instabilities with the help of high-resolution DNS. We show how nonlinear saturation of the ageostrophic instabilities leads to reorganization of the mean flow and emergence of coherent vortices. We follow the same lines as in Part I and, first, perform a complete linear stability analysis of the baroclinic coastal currents for various depths and density ratios. We then study the nonlinear evolution of the unstable modes with the help of the recent efficient two-layer generalization of the one-layer well-balanced finite-volume scheme for rotating shallow water equations, which allows to treat outcropping and loss of hyperbolicity associated to shear, Kelvin-Helmholtz type, instabilities. The previous single-layer results are recovered in the limit of large depth ratios. For depth ratios of order one new baroclinic long-wave instabilities come into play due to the resonances among Rossby and frontal or coastal trapped waves. These instabilities saturate by forming coherent baroclinic vortices, and lead to a complete reorganization of the initial current. As in Part I, Kelvin fronts play an important role in this process. For even smaller depth ratios short-wave shear instabilities with large growth rates rapidly develop. We show that at nonlinear stage they produce short-wave meanders with enhanced dissipation. However, they do not change, globally, the structure of the mean flow which undergoes secondary large-scale instabilities leading to coherent vortex formation and cut-off.
Complete list of metadatas

https://hal-upec-upem.archives-ouvertes.fr/hal-00724549
Contributor : François Bouchut <>
Submitted on : Tuesday, August 21, 2012 - 3:15:15 PM
Last modification on : Wednesday, October 14, 2020 - 3:56:36 AM

Links full text

Identifiers

Citation

Jonathan Gula, Vladimir Zeitlin, François Bouchut. Instabilities of buoyancy driven coastal currents and their nonlinear evolution in the two-layer rotating shallow water model. Part II. Active lower layer. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2010, 665 (none), pp.209-237. ⟨10.1017/S0022112010003903⟩. ⟨hal-00724549⟩

Share

Metrics

Record views

833