Residual mean circulation

The residual mean circulation is the meridional and vertical circulation used by the transformed Eulerian mean. It combines the Eulerian-mean circulation with an eddy-induced contribution so that mean tracer evolution is advected by a single nondivergent flow.

For constant Coriolis parameter $f_0$ and buoyancy frequency $N$, thermal-wind balance and transformed mean-flow equations givewhere ${\chi }^{\ast }$ is the residual-circulation streamfunction and $\mathbf{F}$ is the Eliassen–Palm flux.