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Momentum Flux, Flow Symmetry, and the Nonlinear Barotropic Governor

Noboru NakamuraProgram in Atmospheric and Oceanic Sciences, Princeton University, Princeton, New Jersey

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Abstract

A number of idealized life-cycle simulations of baroclinically unstable waves are systematically analyzed to study the effects of eddy momentum flux and of zonal mean horizontal shear on the finite-amplitude evolution of the waves. Twenty-level quasigeostrophic and primitive equation models with channel geometry are numerically integrated with the most unstable linear normal mode as an initial condition. The flows are inviscid except for weak second-order horizontal diffusion.

It is found that the finite-amplitude baroclinic waves are sensitively influenced by the vertically integrated eddy momentum flux of the normal mode via the large barotropic shear it spins up in the mean flow. This “barotropic governor” mechanism prevents the eddy from attaining all the available potential energy stored in the domain, leading to irreversible barotropic decay. Only in the purely baroclinic, f-plane, quasigeostrophic problem, where the vertically integrated eddy momentum flux identically vanishes due to symmetry, is the growth of baroclinic waves unaffected by the barotropic governor and bounded solely by the total available potential energy. Barotropic shear in the basic flow, the earth's spherical geometry, and nonquasigeostrophic motion all introduce spatial asymmetry into the normal mode, whose nonlinear evolution therefore rapidly departs from the purely baroclinic solution. The details of the departure depend sensitively on the shape of the initial asymmetry, however.

The results suggest the natural tendency of baroclinic waves toward barotropic decay in nearly inviscid atmospheres.

Abstract

A number of idealized life-cycle simulations of baroclinically unstable waves are systematically analyzed to study the effects of eddy momentum flux and of zonal mean horizontal shear on the finite-amplitude evolution of the waves. Twenty-level quasigeostrophic and primitive equation models with channel geometry are numerically integrated with the most unstable linear normal mode as an initial condition. The flows are inviscid except for weak second-order horizontal diffusion.

It is found that the finite-amplitude baroclinic waves are sensitively influenced by the vertically integrated eddy momentum flux of the normal mode via the large barotropic shear it spins up in the mean flow. This “barotropic governor” mechanism prevents the eddy from attaining all the available potential energy stored in the domain, leading to irreversible barotropic decay. Only in the purely baroclinic, f-plane, quasigeostrophic problem, where the vertically integrated eddy momentum flux identically vanishes due to symmetry, is the growth of baroclinic waves unaffected by the barotropic governor and bounded solely by the total available potential energy. Barotropic shear in the basic flow, the earth's spherical geometry, and nonquasigeostrophic motion all introduce spatial asymmetry into the normal mode, whose nonlinear evolution therefore rapidly departs from the purely baroclinic solution. The details of the departure depend sensitively on the shape of the initial asymmetry, however.

The results suggest the natural tendency of baroclinic waves toward barotropic decay in nearly inviscid atmospheres.

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