A consistent algorithm for quasigeostrophic energy and energy flux analysis

The energy flux vector is familiar to geophysical fluid dynamics, but only in the abstract. Equations for computing the energy balance and the energy flux vector (S) for a quasigeostrophic numerical ocean model are provided in both analytic and finite difference form. The multilayer model includes wind, lateral and bottom friction, and bathymetry. The finite difference approximation to the analytic energy balance is consistent with the finite difference approximation to the quasigeostrophic potential vorticity equation. An application of the algorithms to a simple steady ocean gyre illustrates their use. This choice of the flux vector (from an infinity of possibilities) has several advantages: it is computationally convenient; it is capable of field measurement; it has nice mathematical properties in the limit of small amplitude motion; and it facilitates intuition about the dynamics.