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

  • N. N. Kukharkin
  • S. A. Orszag
  • V. Yakhot
Conference paper
Part of the Fluid Mechanics and its Applications book series (FMIA, volume 36)


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.


External Field Rossby Wave Potential Vorticity Giant Planet Scalar Nonlinearity 
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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • N. N. Kukharkin
    • 1
  • S. A. Orszag
    • 1
  • V. Yakhot
    • 1
  1. 1.Fluid Dynamics Research CenterPrinceton UniversityPrincetonUSA

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