Analytical Solutions of Transversely Propagating Rossby Waves

Abstract

In the horizontally 2-dimensional quasi-geostrophic system, we construct analytical solutions of transversely propagating Rossby waves across the basic zonal flow. On the assumption that the basic potential vorticity is piece-wise constant in the meridional direction, the solution with a meridionally localized initial disturbance can be obtained analytically. The analytical solutions show, for example, the following. In the case of a uniform basic zonal flow, the Rossby wave propagates diagonally due to the planetary potential vorticity gradient. In the case of a jet-like basic zonal flow, the oscillating Rossby wave is almost trapped along the jet-axis. However, for the growing Rossby wave, the amplitudes on the jet-axis and on the jet-flanks eventually become comparable.