The Evolution of a Stratospheric Wave Packet

This work examines the extent to which a few basic concepts that apply to plane waves, for example, the refraction of waves up the gradient of the index of refraction, apply to stratospheric planetary waves. This is done by studying the relation between group velocity (Cg) and the wave activity velocity, which is defined as the Eliassen–Palm flux divided by the wave activity density (Va 5 F/A). It is shown that although in the limit of plane waves Va equals Cg, the two velocities are not equal for stratospheric waves, because of reflection, tunneling, and superposition. The use of conservation of wave activity to understand the spatial variations of wave structure is explored. This is done by defining a wave activity packet as part of the wave that moves with Va. Integral lines of Va are then used to keep track of the wave packet location and volume. In the idealized case of an almost-plane wave, conservation of wave activity leads to variations in the amplitude of the wave when it is refracted by the slowly varying basic state. This effect is related to changes in wave packet volume. The wave activity packet framework is used to examine the importance of the ‘‘volume effect’’ for explaining the spatial variations of stratospheric waves. The wave packet formulation is also used to study the evolution of a wave propagating from the troposphere to the stratosphere. It is shown that the consequence of the polar night jet being a leaky waveguide is that perturbations initially concentrate up into the waveguide and only later leak out to the equatorial region. This can explain the observed stratospheric wave life cycle of baroclinic growth followed by a barotropic stage. Finally, integral lines of Va are used to estimate vertical propagation timescales of an observed wave, and it is shown that this estimate is consistent with linear wave dynamics.