The Evolution of a Rossby-Wave Packet in a Three-Dimensional Baroclinic Atmosphere

Abstract

The development of an individual quasi-geostrophic disturbance in a three-dimensional baroclinic atmosphere is investigated by using a wave-packet representation and the WKB method. The results obtained indicate that the development of a Rossby-wave packet in the upper level of the atmosphere depends on the packet's structure and location with respect to the zonal flow, whether the zonal flow is stable or not. The wave packet develops (decays) if the three-dimensional rays are indirect up-gradient (down-gradient) in the zonal flow. All characteristics of the wave packet are changing with time. The spatial scale or the three-dimensional wavelength of the developing (decaying) wave packet increases (decreases). The tilt of barotropic decaying (developing) trough line away from the meridian increases (decreases), while the vertical tilt of the baroclinic decaying (developing) trough line increases (decreases). The maximum amplitude of the developing (decaying) Rossby-wave packet moves toward (out from) the jet region, if the zonal flow is stable. Unlike a single normal mode, most wave packets cause considerable divergence of momentum and heat flux; hence there exists strong interaction between a Rossby-wave packet and the zonal flow.