Renormalization group theory for fluid and plasma turbulence

For the last several decades, renormalization group (RG, or RNG) methods have been applied to a wide variety of problems of turbulence in hydrodynamics and plasma physics. A comprehensive review of this work will be presented, covering RG methods in hydrodynamic turbulence and in turbulent systems with coupled fluctuating fields like magnetohydrodynamic (MHD) turbulence. This review will attempt to specifically consider several questions about RG: (1) Does RG provide an improvement over previous analytical theories like the direct interaction approximation, or is RG a useful simplification of those theories? (2) How are nonlocal, or ‘sweeping’ effects treated in RG formalisms, or are they ignored entirely? (3) Can RG theories treat both local and nonlocal interactions in turbulence?