On the Direction of the Eddy Momentum Flux in Baroclinic Instability

Isaac M. Held Geophysical Fluid Dynamics Laboratory/N0AA, Princeton University, Princeton, NJ 08340

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David G. Andrews Department of Atmospheric Physics, Clarendon Laboratory, Word University, Oxford, England

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Abstract

The direction of the vertically-integrated horizontal eddy flux of momentum in linear baroclinically unstable modes is investigated in a number of cases where the basic flow contains horizontal, as well as vertical, shear. A general result is presented for slowly-growing modes on a flow with weak horizontal shear. Some special cases are described in which standard baroclinic instabilities of finite growth rate (for an internal jet, Eady's model, and a two-layer model) are perturbed by weak horizontal shear, and some computations for flows with large horizontal shear are also mentioned. A general rule emerging from these calculations is that for flows with horizontal jet structure of broader scale than the radius of deformation, the vertically-integrated momentum flux tends to be into the jet (or upgradient); while for jets narrower than the radius of deformation, momentum fluxes tend to be out of the jet (downgradient), even when the contribution of horizontal curvature to the basic state potential vorticity gradient is negligible. However. some exceptions to this general rule exist.

Abstract

The direction of the vertically-integrated horizontal eddy flux of momentum in linear baroclinically unstable modes is investigated in a number of cases where the basic flow contains horizontal, as well as vertical, shear. A general result is presented for slowly-growing modes on a flow with weak horizontal shear. Some special cases are described in which standard baroclinic instabilities of finite growth rate (for an internal jet, Eady's model, and a two-layer model) are perturbed by weak horizontal shear, and some computations for flows with large horizontal shear are also mentioned. A general rule emerging from these calculations is that for flows with horizontal jet structure of broader scale than the radius of deformation, the vertically-integrated momentum flux tends to be into the jet (or upgradient); while for jets narrower than the radius of deformation, momentum fluxes tend to be out of the jet (downgradient), even when the contribution of horizontal curvature to the basic state potential vorticity gradient is negligible. However. some exceptions to this general rule exist.

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