TURBULENT EQUIPARTITIONS IN 2-DIMENSIONAL DRIFT CONVECTION

Unlike the thermodynamic equipartition of energy in conservative syste ms, turbulent equipartitions (TEP) describe strongly nonequilibrium sy stems such as turbulent plasmas. In turbulent systems, energy is no lo nger a good invariant, but one can utilize the conservation of other q uantities such as adiabatic invariants, frozen-in magnetic flux, entro py, or combination thereof, in order to derive new, turbulent quasi-eq ulibria. These TEP equilibria assume various forms, but in general the y sustain spatially inhomogeneous distributions of the usual thermodyn amic quantities such as density or temperature. This mechanism explain s the effects of particle and energy pinch in tokamaks. The analysis o f the relaxed states caused by turbulent mixing is based on the existe nce of Lagrangian invariants (quantities constant along fluid-particle or other orbits). A turbulent equipartition corresponds to the spatia lly uniform distribution of relevant Lagrangian invariants. The existe nce of such turbulent equilibria is demonstrated in the simple model o f two-dimensional electrostatically turbulent plasma in an inhomogeneo us magnetic held. The turbulence is prescribed, and the turbulent tran sport is assumed to be much stronger than the classical collisional tr ansport. The simplicity of the model makes it possible to derive the e quations describing the relaxation to the TEP state in several limits.