Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Transport in rotating fluids

Pages: 165 - 176, Volume 10, Issue 1/2, January/February 2004      doi:10.3934/dcds.2004.10.165

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Peter Constantin - Department of Mathematics, The University of Chicago, Chicago, Il 60637, United States (email)

Abstract: 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

Received: August 2001;      Revised: May 2002;      Available Online: October 2003.