Energy budgets in Charney-Hasegawa-Mima and surface quasigeostrophic turbulence.

We study energy transfer in unbounded Charney-Hasegawa-Mima and surface quasigeostrophic turbulence. The possible inverse-cascading quantities in these systems are, respectively, I identical with integral ( infinity )(0)k(-2)E(k) dk and J identical with integral ( infinity )(0)k(-1)E(k) dk, where E(k) is the kinetic energy spectrum. The supposed direct-cascading quantities for both surface quasigeostrophic and Navier-Stokes turbulence are shown to be bounded. We derive a constraint on E(k) for the surface quasigeostrophic system.