Form-drag instability in a barotropic and a baroclinic atmosphere
We discuss the form-drag instability for a quasi-geostrophic channel flow. We first study the characteristics of this instability in a barotropic flow, considering in detail the influence of the meridional scale and discussing which structure of the perturbation zonal flow must be chosen in order to describe properly this instability.
We then consider a continuous quasi-geostrophic channel model in which the topography enters only through the bottom boundary condition, and we discuss how in this case the effects of the form-drag are felt by the mean zonal flow through the ageostrophic mean meridional circulation. Because the meridional structure of the perturbation zonal flow cannot simply be extended from the barotropic to the continuous case, we show how to modify it properly.
We then study the baroclinic model in the particular case of constant (in the vertical) basic-state zonal flow and show how this case closely resembles the barotropic, demonstrating the barotropic nature of the form-drag instability.
Key wordsForm-drag instability barotropic atmosphere Basoclinic atmosphere
is the partial derivative with respect tot.
is the partial derivative with respect tox.
is the partial derivative with respect toy.
represents the geostrophic stream function.
is the eastward component of the geostrophic wind.
is the northward component of the geostrophic wind.
is the eastward component of the ageostrophic wind.
is the northward component of the ageostrophic wind.
is the vertical component of the wind.
is the Coriolis parameter=2Ω sin ϑ≈fo+βy.
is the Coriolis parameter evaluated at mid-latitude.
is the Brunt-Vaisala frequency.
is the zonal (x) average ofA at constantp andy.
is the horizontal (x andy) average ofA at constantp
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