Equilibration in Nonlinear Baroclinic Instability

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  • 1 Department of Atmospheric Sciences, university of Illinois, Urbana, IL 61801
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Abstract

The influences of wave-wave and wave-zonal flow interactions an the baroclinic instability in a basic quasi-geostrophic two-layer model are investigated. A minimum spectral resolution is used. The evolution of the system obtained with (without) the wave-wave interaction is referred to as the general (special) equilibration.

The special equilibration leads to a steady single wave state. This wave, similar to Pedlosky's finding, has a longer zonal wavelength than that of the most unstable wave according to the linear theory under representative dissipative conditions. In contrast, the general equilibration leads to one of four distinctly different equilibrated states, depending upon the baroclinic forcing and the dissipation parameters. It can be a steady single-wave state, or a steady multiple-wave state, or a triad-limit-cycle or an incoherently fluctuating state. A regime diagram is given to delineate the bifurcations that give rise to such equilibrated states as a function of the forcing and damping parameters.

The triad-limit-cycle is a robust response, prevalent under a wide range of parametric conditions. The most favorable conditions for its existence are intermediate forcing and damping. Its vacillation period is of the order of tens of days under realizable parametric conditions. Furthermore, it modulates considerably higher frequency fluctuations with periods of several days. A diagnosis of the energetics reveals that while such a limit cycle arises from the wave-wave interaction, the embedded higher frequency fluctuations are mainly associated with the wave-zonal flow interaction. It also reveals that the general equilibration tends to barotropize the flow in agreement with basic findings of Rhine and Salmon for geostrophic turbulence.

Abstract

The influences of wave-wave and wave-zonal flow interactions an the baroclinic instability in a basic quasi-geostrophic two-layer model are investigated. A minimum spectral resolution is used. The evolution of the system obtained with (without) the wave-wave interaction is referred to as the general (special) equilibration.

The special equilibration leads to a steady single wave state. This wave, similar to Pedlosky's finding, has a longer zonal wavelength than that of the most unstable wave according to the linear theory under representative dissipative conditions. In contrast, the general equilibration leads to one of four distinctly different equilibrated states, depending upon the baroclinic forcing and the dissipation parameters. It can be a steady single-wave state, or a steady multiple-wave state, or a triad-limit-cycle or an incoherently fluctuating state. A regime diagram is given to delineate the bifurcations that give rise to such equilibrated states as a function of the forcing and damping parameters.

The triad-limit-cycle is a robust response, prevalent under a wide range of parametric conditions. The most favorable conditions for its existence are intermediate forcing and damping. Its vacillation period is of the order of tens of days under realizable parametric conditions. Furthermore, it modulates considerably higher frequency fluctuations with periods of several days. A diagnosis of the energetics reveals that while such a limit cycle arises from the wave-wave interaction, the embedded higher frequency fluctuations are mainly associated with the wave-zonal flow interaction. It also reveals that the general equilibration tends to barotropize the flow in agreement with basic findings of Rhine and Salmon for geostrophic turbulence.

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