On the conversion between mean and eddy components of potential and kinetic energy in isentropic and isopycnic coordinates

Abstract

Equations for the mean and eddy kinetic energy and for the mean and eddy potential energy in isopycnic and isentropic coordinates are derived, and conversion terms between the four energy forms are identified. Contrary to Lorenz' isobaric formulae, a conversion term between mean kinetic and eddy potential energy is found in the isopycnic/isentropic framework; furthermore, no term governing direct conversion between eddy and mean potential energy exists in isopycnic coordinates. The option of “re-routing” some energy conversion processes to eliminate the formal difference between the isopycnic/isentropic and the isobaric viewpoint is discussed. A numerical simulation of baroclinic instability in an isentropic coordinate model is used to illustrate the energy conversion processes.