Theoretical and heuristic modelling methods are reviewed for studying turbulence phenomena of fluids and plasmas. Emphasis is placed on understanding of effects on turbulence characteristics due to inhomogeneities of field and plasma parameters. The similarity and dissimilarity between the methods for fluids and plasmas are sought in order to shed light on the properties that are shared or not by fluid and plasma turbulence.

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Turbulence theories and modelling of fluids and plasmas

I present here a review of recent theoretical progress in the possible role of microturbulence in the solar wind. The solar wind is anticipated to excite plasma microinstabilities because of its transition from collision-dominated to collisionless behavior. The applications of linear plasma theory that have been made in this field are extensively reviewed and discussed, along with our present understanding of nonlinear plasma phenomena. The solar wind is an excellent laboratory for studying many aspects of solar and plasma physics and may soon provide some answers to several fundamental questions.

Plasma instabilities in the solar wind: A theoretical review

The authors show that a generalization of the Kraichnan Direct Interaction Approximation for fluid turbulence to the Vlasov or Klimontovich equations for plasmas contains most previously proposed 'strong' turbulence theories with the addition of further ad hoc approximations. This comparison depends on an exact factorization of the DIA into screened and unscreened quantities. The usual perturbed orbit or renormalized weak turbulence corrections to the unscreened Green's function are shown to inadequately account for the self-consistent nature of the turbulent electric fields. A direct prescription for the calculation of the unscreened correlation function which determines the Fokker-Planck friction coefficient is carried through in an approximation which neglects mode coupling effects. No enhanced noise due to phase-space clumps is found; in the discrete particle theory a turbulence renormalized (broadened) expression for the discrete particle noise is obtained.

https://iopscience.iop.org/article/10.1088/0032-1028/20/12/001/pdf

Direct interaction approximation and plasma turbulence theory

Ion cyclotron waves cannot be quasilinearly stabilized in Q-machine experiments because the electron distribution function does not have time to flatten while electrons pass through the plasma volume. We invoke a turbulently dissipative (or ‘resonance broadening’) model to explain the observed steady-state mode saturation. We give a qualitative picture of the important nonlinear features and their implications for plasma heating experiments. We extend the turbulently dissipative model to give nonlinear frequency shifts and a description of the mode linewidths in steady-state experiments. Turbulent resistivity is calculated and found to be unobservably small compared to the classical value. Implications for further experiments are discussed.

Electrostatic ion cyclotron waves: Plasma heating, frequency shifts and linewidths

A detailed numerical study has been made of the turbulent damping of the convective cells and of lower hybrid waves for a plasma near thermal equilibrium. It is found that some of the theories of strong turbulence, taking into account the diffusing orbits of particles, are inadequate for describing the observations; observations are, however, in good agreement with the linear dispersion relation with a turbulent diffusion coefficient.

Turbulent damping of the convective cells and the lower hybrid waves

It is well known that the properties of stable quiescent plasma may be calculated by a method known as the ‘superposition of dressed particles’. In this paper an analogous superposition principle is constructed for turbulent plasmas. This shows that the turbulent fluctuations may suppress the growth of the instabilities that give rise to them. The fluctuation spectrum, diffusion coefficient and dielectric constant of turbulent plasma are calculated for the guiding centre model. The relationship of this theory to that of Dupree and Weinstock is discussed.

I. Cook

Papers

Electric field fluctuations in turbulent plasmas