  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.
