The presence of macroscopic flows in hot plasmas is of great importance in nuclear fusion experiments. For pedagogical purposes, the spontaneous appearance of the flow is studied using the Hasegawa–Mima equation (HME) driven by external noise. The noise is assumed to model a bath of microscopic-scale turbulence. If the noise has a parity-nonconserving element, it is shown that an advective term associated with a uniform flow is inherently generated in the HME. A renormalization-group approach up to the lowest order is taken in the analysis of the asymptotic state. Parity-conserving noise is shown to lead to the renormalizations of field and viscosity and the critical dimensions are obtained.
Theory of fully developed turbulence in buoyancy-driven fluids and pressure-gradient-driven plasmas