Stationary Rossby-wave ray envelope ($(x-Ut{)}^2+y^2\le (Ut{)}^2$)

For a uniform eastward current $U>0$ on a beta plane with $\beta >0$, stationary nondivergent Rossby waves have $k^2+l^2=\beta /U$. Their ground-frame group velocity is $2U(k^2,kl)/(k^2+l^2)$, tracing a circle centered at $(U,0)$ with radius $U$. Packets emitted by a localized source throughout $0<s<t$ occupy the disk shown in geometrical ray theory. This envelope is distinct from the full balanced near field. A westward current has no nontrivial stationary propagating branch in this model.