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On the two-point correlation of potential vorticity in rotating and stratified turbulence

Published online by Cambridge University Press:  11 May 2006

SUSAN KURIEN ,
LESLIE SMITH  and
BETH WINGATE
SUSAN KURIEN
Affiliation:
Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
LESLIE SMITH
Affiliation:
Departments of Mathematics and Engineering Physics, University of Wisconsin, Madison, WI 53706, USA
BETH WINGATE
Affiliation:
Computer and Computational Sciences Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
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Abstract

A framework is developed to describe the two-point statistics of potential vorticity in rotating and stratified turbulence as described by the Boussinesq equations. The Kármán–Howarth equation for the dynamics of the two-point correlation function of potential vorticity reveals the possibility of inertial-range dynamics in certain regimes in the Rossby, Froude, Prandtl and Reynolds number parameters. For the case of large Rossby and Froude numbers, and for the case of quasi-geostrophic dynamics, a linear scaling law with 2/3 prefactor is derived for the third-order mixed correlation between potential vorticity and velocity, a result that is analogous to the Kolmogorov 4/5-law for the third-order velocity structure function in turbulence theory.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 555 , 25 May 2006 , pp. 131 - 140
Copyright
© 2006 Cambridge University Press

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