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 ε (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 ε, namely, M ≡ ( A + ε)/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.