Momentum, Vorticity and Transport: Considerations in the Design of a Finite-Volume Dynamical Core

Abstract

This chapter provides an end-to-end discussion of issues related to the design and construction of dynamical cores. The governing equations of motion are derived from basic principles cast in the Lagrangian frame of motion. The Reynolds Transport Theorem is derived so that these conservation statements can be recast in their weak, integral form in the Eulerian reference frame. Special attention is given to the relationship between the momentum equation and vorticity dynamics. The principles of conservation of circulation and vorticity are derived in the continuous system. It is demonstrated that the kinematic principles related to circulation and vorticity can be carried over exactly into the discrete system. The analysis is conducted in an idealized, two-dimensional setting that is meant to serve as a prototype system for the consideration of the full three-dimensional general circulation of the atmosphere and ocean.