hide
Free keywords:
-
Abstract:
Many processes in the atmosphere involved interactions over a wide range of length and time scales. One of the most important of these is the upscale growth of small errors that limit predictability. Multiscale asymptotic analysis is an attractive tool for understanding these interactions, since it enables the consistent derivation of approximate equations for each of the relevant scales, and of the interactions between scales. We consider motions where the leading order dynamics on the mesoscale is the weak temperature gradient approximation, and on the synoptic scale, quasigeostrophic theory. The dominant downscale interaction term is advection of mesoscale features by the synoptic-scale wind. In the upscale direction, the interactions take the form of eddy correlation terms, leading to a horizontal diffusion, but also transport of horizontal momentum by diabatically-driven vertical motions. The approximate equations are validated using high resolution numerical simulations, with appropriate filtering to separate the two scales of motion. The results confirm the leading-order dynamics on both scales, and allow a quantitative evaluation of the contributions of different scale interaction terms.
