Long-Range Order and Deformation Radius Effects in 2-D Turbulence

Abstract

The most prominent feature of a 2-D flow excited at a small scale l _f is an inverse cascade, i.e. creation of large-scale motions from small-scale eddies. While in an infinite system with no external fields this process lasts forever, in a finite system of size L ≫ l _f , energy eventually starts accumulating at L (“condensation”) and the energy spectrum becomes steeper, thus slowing down the inverse cascade. For a flow in an external field (including rotation, stratification, and magnetic fields), where a substantial part of the energy goes into waves, the inverse cascade often slows down after waves of the scale of the deformation radius L _R , determined by the external field, are created. In these systems the energy spectrum first steepens at scale O(L _R ), and then slowly larger motions are generated due to energy leakage through the “shield” at L _R . The basic questions are: What are the dominant structures in this phenomenon? If structures exist, how are they distributed in physical space? Can the flow achieve a stable or a quasistationary configuration? We attempt to give at least partial answers to these questions.