Energy and potential enstrophy flux constraints in the two-layer quasi-geostrophic model

Details Energy and potential enstrophy flux constraints in the two-layer quasi-geostrophic model Energy and potential enstrophy flux constraints in the two-layer quasi-geostrophic model

2012-01-03

arxiv.org/abs/1201.0567v1

Nonlinear Sciences

Chaotic Dynamics

23 pages; submitted to J. Fluid Mech

Scientific paper

We investigate an inequality constraining the energy and potential enstrophy flux in the two-layer quasi-geostrophic model. This flux inequality is unconditionally satisfied for the case of two-dimensional Navier-stokes turbulence. However, it is not obvious that it remains valid under the multi-layer quasi-geostrophic model. We derive the general form of the energy and potential enstrophy dissipation rate spectra for a generalized multi-layer model. We then specialize these results for the case of the two-layer quasi-geostrophic model under dissipation configurations in which the dissipation terms for each layer are dependent only on the streamfunction or potential vorticity of that layer. We derive sufficient conditions for satisfying the flux inequality and discuss the possibility of violating it under different conditions.

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