Length Scale of Vortices and Mode Competition in Quasi 2D Shear Flows

  • D. Yu. Manin
Conference paper
Part of the Springer Series in Nonlinear Dynamics book series (SSNONLINEAR)


Strictly 2D flows constitute a broad and useful class of Navier—Stokes solutions, but in practice they are quickly destroyed by 3D instability. A class of quasi two-dimensional (Q2D) flows can be defined1 in physical terms as flows whose approximate two-dimensionality is due to the presence of flat boundaries (bottom and/or top) so that vertical velocity component is negligible. However the vertical dependence of horizontal velocity is essential in that it provides most of the dissipation. This results in the Rayleigh friction term, −λΔΨ in the governing Q2D equation for stream function Ψ
$$\frac{\partial }{{\partial t}}\vartriangle \Psi + \left[ {\vartriangle \Psi ,\Psi } \right] = \nu {\vartriangle ^2}\Psi - \lambda \vartriangle \Psi + F$$
where F is the forcing, and the specific expression for λ depends on the physical situation1. In particular, large-scale atmospheric flows can be regarded Q2D with λ being the inverse Ekman time scale.




  1. 1.
    Dolzhanskii, F.V. et al. Soy. Phys. Uspekhi, 1990, 7 (30), 495.ADSCrossRefGoogle Scholar
  2. 2.
    Manin, D.Yu. Preprint No. 6, Inst. Atmos. Phys., Moscow, 1989.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • D. Yu. Manin
    • 1
  1. 1.Institute of Atmospheric PhysicsMoscowRussia

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