On the Two-point Correlation of Potential Vorticity in Rotating and Stratified Turbulence

Details On the Two-point Correlation of Potential Vorticity in Rotating and Stratified Turbulence On the Two-point Correlation of Potential Vorticity in Rotating and Stratified Turbulence

2005-07-15

arxiv.org/abs/nlin/0507034v2

Nonlinear Sciences

Chaotic Dynamics

10 pages, to appear in Journal of Fluid Mechanics (2006)

Scientific paper

10.1017/S0022112006009116

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 Karman-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.

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