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A New Class of Equations for Rotationally Constrained Flows

  • Keith Julien
  • Edgar Knobloch
  • Joseph Werne

Abstract:

The incompressible Navier–Stokes equation is considered in the limit of rapid rotation (small Ekman number). The analysis is limited to horizontal scales small enough so that both horizontal and vertical velocities are comparable, but the horizontal velocity components are still in geostrophic balance. Asymptotic analysis leads to a pair of nonlinear equations for the vertical velocity and vertical vorticity coupled by vertical stretching. Statistically stationary states are maintained against viscous dissipation by boundary forcing or energy injection at larger scales. For thermal forcing direct numerical simulation of the reduced equations reveals the presence of intense vortical structures spanning the layer depth, in excellent agreement with simulations of the Boussinesq equations for rotating convection by Julien et al. (1996).

Keywords

Convection Vorticity Velocity Component Stokes Equation Vertical Velocity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Keith Julien
    • 1
  • Edgar Knobloch
    • 2
  • Joseph Werne
    • 3
  1. 1.Department of Applied Mathematics, University of Colorado, Boulder, CO 80309, U.S.A.US
  2. 2.JILA, University of Colorado, Boulder, CO 80309, U.S.A.US
  3. 3.JILA, University of Colorado, Boulder, CO 80309, U.S.A.US

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