An Analytical Study on the Feedback between Large- and Small-Scale Eddies

Abstract

The feedback between large-scale stationary Rossby waves and small-scale high-frequency eddies is computed analytically in the framework of a barotropic and frictionless model atmosphere. The Rossby wave is meant to model blocking situations characterized by high-over-low dipoles and flow splitting, while the eddies represent synoptic disturbances propagating in the deformation field of the blocking pattern. Apart from a westward contribution to the phase speed of the large-scale pattern, the eddy forcing (Reynolds stress), averaged in time, turns out to be a nonlinear function of the large-scale streamfunction amplitude. It is shown that the eddy forcing always determines, in the time average, a steepening of the flow split associated with the block and (possibly) multiple large-scale amplitudes. A comparison between these results and previous studies about eddy forcing of blocking situations is attempted.