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Abstract
A renormalized theory of drift wave turbulence in sheared geometry is formulated with the use of a systematic renormalization procedure: Kraichnan's direct-interaction approximation. Emphasis is laid on the need for a renormalized theory to preserve the energy conservation properties satisfied by the exact dynamical equations. The relation of energy conservation in a statistical theory to symmetries of the renormalized equations is discussed. Upon simplifying the direct-interaction approximation applied to a kinetic description of the electron dynamics, a simple Markovian renormalized theory is found which does satisfy the relevant form of energy conservation. The comparison with a previous non-energy-conserving theory shows that the latter overestimated the effect of turbulent destabilization.
We derive and argue for a fluid-like description of the ion dynamics, which generalizes the Hasegawa-Mima equations by including finite gyro-radius effects and, more importantly, by containing appropriate energy sources (the resonant electrons coupled to the ions by the quasineutrality condition) and sinks (ion Landau damping, modelled by a parallel viscosity). The use of physically and empirically motivated approximations (e.g., the short correlation length approximation) on the fluid equations renormalized with the direct-interaction approximation, leads to a closed system of equations for calculating the evolution of the spectral intensity and the relaxation rate of the correlation function. This final formulation of the problem is suitable for numerical computation.
