Thermodynamic Potential in Local Turbulence Simulations

For the reduced local equations customary in, e.g., the computation of turbulence in tokamaks the energy is still a conserved quantity. However, kinetic and magnetic energy do not appear in the reduced energy functional and thus are not constrained by it, since they are ordered small compared to the fluctuations of internal energy in the reduction process. Constraints on velocity and field fluctuations can be derived using instead the generalized grand canonical potential, which is conserved in reversible processes. This is exemplified for the Boltzmann, gyrokinetic, and fluid equations.