Abstract
On the basis of the transformed Eulerian-mean equation which includes Eliassen-Palm flux divergence or quasi-geostrophic potential vorticity transport for large-scale extratropical motions, a transformed energy conversion equation is derived for further understanding of the wave-zonal flow interaction. The transformed mean energy conversion equation is readily derived from the transformed mean equation. In order to obtain the transformed eddy energy conversion equation consistent with the transformed mean energy conversion equation, an attempt is made to transform the eddy equation, and the transformed energy conversion equation is constructed for both mean motion and eddy motion. It is shown that there is no conversion between the mean available potential energy and the eddy available potential energy formally in the transformed energetics.
The transformed energy conversion equation is applied to some theoretical problems such as Eady's baroclinic instability, upward propagating stationary planetary wave incident on a critical level and upward propagating planetary wave packet. For Eady's problem, the transformed energetics explicitly describes the significance of the existence of horizontal boundaries which is known to be essential to baroclinic instability. The behavior of energy conversion is simpler in the transformed energetics than in the ordinary energetics for the critical level problem and the wave packet problem since the transformed energy conversion equation does not include originally the term irrelevant to the net influence on the budget of energy in the result.
The new form based on the transformed equation is useful to understand the circumstances that the wave-mean flow interactions occur although there are some limitations in the energetics itself.
