Baroclinic instability in a long wave environment. Part II: Ageostrophic energy conversions

Abstract

AbstractA linear, quasi‐geostrophic, numerical, spectral, initial value, model is used to examine the stability properties of two long wave flows on a mid‐latitude β plane. In the ‘barotropic case’ the long wave amplitude is independent of height; in the ‘baroclinic case’ the long wave amplitude varies from zero at the bottom and top to a maximum near the model's ‘tropopause’. The initial structure of the unstable short waves incorporates the eigenfunctions for a similar, straight‐flow version of this problem. The solutions rapidly converge to a repeatable structure.This report emphasizes the eddy energetics and especially its horizontal variation due to the long wave. In deriving the eddy energy equation three ‘ageostrophic’ conversions are found along with the two quasigeostrophic conversions. While the ageostrophic conversions vanish on a volume average, they are locally important; they redistribute the eddy properties in each of the three directions; none are described by any previous author. The vertical ageostrophic conversion is the difference between the conversion terms shared by the eddy available potential and eddy kinetic energy equations. The horizontal ageostrophic conversions steer the eddies along storm tracks which would not be anticipated on the basis of the basic flow's direction or vertical shear. These conversions create significant cross‐isobaric motion of eddies even though the long wave amplitude is modest compared with the zonal mean flow. This motion is not reproduced in a standard barotropic model wherein the ageostrophic conversions are all identically zero. On a global average the eddies are baroclinically growing; the barotropic conversion is small and damping.