Theoretical basis for stationary Rossby wave propagation
1 Classic theory on zonal basic flow
The classical Rossby wave propagation theory (Hoskins and Karoly 1981) begin with a nondivergent barotropic vorticity equation linearized about
where
is the meridional gradient of the absolute vorticity in the Mercator projection.
The dispersion relation is
where
The stationary waves can propagate if the flow is westerly (
Please refer to and Hoskins and Ambrizzi (1993) for the details.
Hoskins and Ambrizzi (1993) suggested that the classic theory for zonally averaged flow can be applied to a realistic longitudinally varying flow by considering the local latitudinal zonal wind profile; i.e., by replacing
Many interhemispheric teleconnections cannot be understood via the classic stationary Rossby wave theory (see discussions in Zhao et al. 2015).
2 Rossby wave theory on a horizontally non-uniform flow
The dispersion relation describing the propagation characteristics of perturbations can be derived from the linearized barotropic non-divergent vorticity equation on a time-mean slowly varying basic state with the WKB approximation (Karoly 1983, Li and Nathan 1997, Li et al. 2015, Zhao et al. 2015) as
where
Using the dispersion relation and kinematic wave theory (Whitham 1960; Bühler 2009) gives the following ray tracing equations
See Li et al. (2015) and Zhao et al. (2015) for details of Rossby wave propagation behaviors on a horizontally non-uniform flow.