Atmospheric Local Energetics and Energy Interactions between Mean and Eddy Fields. Part I: Theory

A new diagnostic scheme for the atmospheric local energetics is proposed. In contrast to conventional schemes, this scheme correctly represents the local features of the Lorenz energy cycle for time-mean and transient-eddy fields. The key point is that the energy equation is divided not into two but into three parts consisting of the mean, eddy, and interaction energy equations, when basic variables are divided into mean and eddy fields. The interaction energy itself vanishes when appropriate averaging is taken. However, the equation for interaction energy does not vanish and gives a relationship between the interaction energy flux and the two types of energy conversion terms. These three quantities give the complete information for the energy interactions between mean and eddy fields. The Lorenz energy diagram is reconstructed to include a representation of this relationship. A brief discussion about the relationship with wave activity analysis is also given.