A Relationship between Energy and Angular Momentum Conservation in Dynamical Models

Abstract

In Newtonian particle dynamics the covariance of the kinetic energy equation to transformation between different inertial frames may he demonstrated only if the correct momentum equation is applied. A similar relation exists between the angular momentum equation and covariance of the kinetic energy equation to transformation between frames rotating with different angular velocities. Lagrangian and global versions hold for fluid motion. Analogous relations are implied by the hydrostatic primitive equations on a sphere (for the class of coaxial transformations, at least) when changes of the apparent vertical are properly allowed for. Repercussions for numerical forecasting and climate simulation models are discussed, the suggestion being that the importance of finite analogues of angular momentum conservation principles has been underestimated.