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Does Ekman Friction Suppress Baroclinic Instability?

Shian-Jiann LinGeophysics Fluid Dynamics Program, Princeton University, Princeton, New Jersey

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Raymond T. PierrehumbertGeophysical Fluid Dynamics Laboratory/N0AA, Princeton University, Princeton, New Jersey

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Abstract

The effect of Ekman friction on baroclinic instability is reexamined in order to address questions raised by Farrell concerning the existence of normal mode instability in the atmosphere. As the degree of meridional confinement is central to the result, a linearized two-dimensional (latitude-height) quasi-geostrophic model is used to obviate the arbitrariness inherent in choosing a channel width in one-dimensional (vertical shear only) models. The two-dimensional eigenvalue problem was solved by pseudospectral method using rational Chebyshev expansions in both vertical and meridional directions. It is concluded that the instability can be eliminated only by the combination of strong Ekman friction with weak large-scale wind shear. Estimates of Ekman friction based on a realistic boundary-layer model indicate that such conditions can prevail over land when the boundary layer is neutrally stratified. For values of Ekman friction appropriate to the open ocean, friction can reduce the growth rate of the most unstable mode by at most a factor of two but cannot eliminate the instability.

By reducing the growth rate and shifting the most unstable mode to lower zonal wavenumbers, viscous effects make the heat and momentum fluxes of the most unstable mode deeper and less meridionally confined than in the inviscid case. Nevertheless, linear theory still underestimates the penetration depth of the momentum fluxes, as compared to observations and nonlinear numerical models.

Abstract

The effect of Ekman friction on baroclinic instability is reexamined in order to address questions raised by Farrell concerning the existence of normal mode instability in the atmosphere. As the degree of meridional confinement is central to the result, a linearized two-dimensional (latitude-height) quasi-geostrophic model is used to obviate the arbitrariness inherent in choosing a channel width in one-dimensional (vertical shear only) models. The two-dimensional eigenvalue problem was solved by pseudospectral method using rational Chebyshev expansions in both vertical and meridional directions. It is concluded that the instability can be eliminated only by the combination of strong Ekman friction with weak large-scale wind shear. Estimates of Ekman friction based on a realistic boundary-layer model indicate that such conditions can prevail over land when the boundary layer is neutrally stratified. For values of Ekman friction appropriate to the open ocean, friction can reduce the growth rate of the most unstable mode by at most a factor of two but cannot eliminate the instability.

By reducing the growth rate and shifting the most unstable mode to lower zonal wavenumbers, viscous effects make the heat and momentum fluxes of the most unstable mode deeper and less meridionally confined than in the inviscid case. Nevertheless, linear theory still underestimates the penetration depth of the momentum fluxes, as compared to observations and nonlinear numerical models.

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