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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 9, issue 5/6
Nonlin. Processes Geophys., 9, 487–496, 2002
https://doi.org/10.5194/npg-9-487-2002
© Author(s) 2002. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.
Nonlin. Processes Geophys., 9, 487–496, 2002
https://doi.org/10.5194/npg-9-487-2002
© Author(s) 2002. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

  31 Dec 2002

31 Dec 2002

Baroclinic instability of a symmetric, rotating, stratified flow: a study of the nonlinear stabilisation mechanisms in the presence of viscosity

R. Mantovani1,* and A. Speranza1 R. Mantovani and A. Speranza
  • 1Mathematics Department, University of Camerino, Via Madonna delle Carceri, 62032 Camerino (MC), Italy
  • *presently: ESRIN, European Space Agency, Via Galileo Galilei, 00044 Frascati, Italy

Abstract. This paper presents the analysis of symmetric circulations of a rotating baroclinic flow, forced by a steady thermal wind and dissipated by Laplacian friction. The analysis is performed with numerical time-integration. Symmetric flows, vertically bound by horizontal walls and subject to either periodic or vertical wall lateral boundary conditions, are investigated in the region of parameter-space where unstable small amplitude modes evolve into stable stationary nonlinear solutions. The distribution of solutions in parameter-space is analysed up to the threshold of chaotic behaviour and the physical nature of the nonlinear interaction operating on the finite amplitude unstable modes is investigated. In particular, analysis of time-dependent energy-conversions allows understanding of the physical mechanisms operating from the initial phase of linear instability to the finite amplitude stable state. Vertical shear of the basic flow is shown to play a direct role in injecting energy into symmetric flow since the stage of linear growth. Dissipation proves essential not only in limiting the energy of linearly unstable modes, but also in selecting their dominant space-scales in the finite amplitude stage.

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