Two-dimensional turbulence in inviscid fluids or guiding center plasmas

Numerical tests of the inviscid equilibrium theory of Kraichnan (1975) are described. The mathematical description applies equally well to the two-dimensional electrostatic guiding center plasma and to the two-dimensional inviscid Navier-Stokes fluid. The predictions of this analytic theory are discussed. A pair of coupled equations are derived for the two-time vorticity autocorrelation in Fourier space and the infinitesimal unit response function G of Kraichnan in the so-called Eulerian direct interaction approximation. Kraichnan's assertion that thermodynamic limits exist for the negative temperature states is questioned.