Exact third-order structure functions for two-dimensional rotating stratified turbulence

We apply Kolmogorov's isotropic turbulence theory to the two-dimensional isotropic rotating stratified turbulence in a vertical plane with equal Coriolis and buoyancy frequencies. Contrary to the two-dimensional turbulence, a downscale total energy flux is discovered, explained and justified by numerical simulations in different parameter regimes depending on the relative sizes of Ozmidov (Zeman) and forcing scales. Based on the Karman-Howarth-Monin equation, exact expressions for the third-order structure functions, which are uniformly valid across the entire non-dissipative range including the forcing scales, are derived by assuming a statistical balance between external random forcing and small-scale dissipation, and they show good agreements with numerical results. In addition, potential applications to interpreting measured geophysical fluid data are discussed.