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February  2004, 10(1&2): 165-176. doi: 10.3934/dcds.2004.10.165

Transport in rotating fluids

Peter Constantin 1,

1. 

Department of Mathematics, The University of Chicago, Chicago, Il 60637, United States

Received  August 2001 Revised  May 2002 Published  October 2003

We consider uniformly rotating incompressible Euler and Navier-Stokes equations. We study the suppression of vertical gradients of Lagrangian displacement ("vertical" refers to the direction of the rotation axis). We employ a formalism that relates the total vorticity to the gradient of the back-to-labels map (the inverse Lagrangian map, for inviscid flows, a diffusive analogue for viscous flows). We obtain bounds for the vertical gradients of the Lagrangian displacement that vanish linearly with the maximal local Rossby number. Consequently, the change in vertical separation between fluid masses carried by the flow vanishes linearly with the maximal local Rossby number.
Keywords: Euler and Navier-Stokes equations, Lagrangian displacement.
Mathematics Subject Classification: 35Q30.
Citation: Peter Constantin. Transport in rotating fluids. Discrete & Continuous Dynamical Systems, 2004, 10 (1&2) : 165-176. doi: 10.3934/dcds.2004.10.165
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