A formulation of a wave-activity flux for stationary Rossby waves on a zonally varying basic flow

A new formulation of an approximate conservation relation is proposed for stationary Rossby waves on a zonally varying basic flow, utilizing that A (proportional to wave enstrophy:) and E (proportional to wave energy) are both. related to the wave activity pseudomomentum. For stationary Rossby waves, it is shown in the limit of a small-amplitude: plane wave on a slowly varying: unforced non-zonal flow that a particular linear combination of A and E, namely: M equivalent to (A + E)/2. is independent of the wave phase. even if unaveraged, and is conserved under steady unforced and nondissipative conditions. It is also shown. that the three-dimensional flux of M is parallel to the local group velocity in the WKB limit. The flux could be a useful diagnostic tool, as shown in an example that presents a ''snapshot'' of the three-dimensional propagation of a stationary Rossby wavetrain in the real atmosphere. Our conservation relation is a generalization of that for stationary Rossby waves on a zonally-uniform basic flow derived by Plumb.