Chang and Orlanski have presented significant observational andcomputational evidence for downstream development of mid-latitude stormtracks from regions of enhanced baroclinicity in contrast to global modal development. They have made the important suggestion that the precursor waves generating this downstream development might be much more predictable than the details of the trailing storm track. Swanson and Pierrehumbert recognized that the velocity and spatial profile of the downstream leading edge is given by the "linear marginal stability velocity" and its associated (complex) wavenumber. These predictions are given by a linear theory, which greatly simplifies the dynamics.
We have developed a general theory for the modulation of downstream developing leading edges in the presence of an unstable and weakly variable medium. We derive simplified equations for the evolution of the envelope of such a wave. We apply this general theory to several systems, including a two-layer system of quasigeostrophic equations on the F-plane and the complex Ginzburg-Landau equations. If we allow the medium to have a slow variation in the direction transverse to the direction of propagation, we find in some cases interesting anisotropic dispersion-diffusion equations. These simplified equations are then tested against numerical solutions of the full equations and a good agreement is found.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics