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Instability of a periodic flow in geostrophic and hydrostatic balance. (English) Zbl 1390.76087

Summary: Instability of a flow in geostrophic and hydrostatic balance is investigated using numerical simulations of the fully nonlinear, rotating, stratified Boussinesq equations. Burger numbers less than one and small aspect ratio are considered. Although the model we consider has continuous stratification in the vertical, in terms of phenomenology, the large scale baroclinic instability we find is most closely related to that found in the classical setting of E. T. Eady [“Long waves and cyclone waves”, Tellus 1, No. 3, 33–52 (1949; doi:10.1111/j.2153-3490.1949.tb01265.x)]. Indeed, the growth rate and scale of the most unstable mode scale similarly. The advantage of the model we consider lies in being able to use it in studies of unbalanced processes. Preliminary experimentation suggests that there is a small scale instability at small values of Burger number. This instability is initiated in anticyclonic regions, is likely imbalanced, and likely leads to small scale dissipation. By considering two measures of balance – one based on a wave-vortex decomposition and another based on the quasi-geostrophic omega equation – we study the dependence of imbalance on Rossby number. We, however, find that kinetic energy spectra display slopes consistent with quasi-geostrophic turbulence, with no break in slope at high wavenumbers.

MSC:

76E20 Stability and instability of geophysical and astrophysical flows
76U05 General theory of rotating fluids
86A05 Hydrology, hydrography, oceanography
86A10 Meteorology and atmospheric physics

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