Inverse cascades in incompressible fluid and magnetofluid turbulence

Absolute equilibrium statistical theory and numerical simulations are reviewed in the context of inverse cascades in two- and three-dimensional incompressible fluid and magnetofluid turbulence. Turbulent fluctuations of physically interesting quantities undergo inverse cascade to larger spatial scales, leading to self-organization under certain circumstances. In particular, most systems with more than one quadratic ideal invariant, or, having some kind of imposed anisotropy, exhibit inverse cascades. Anisotropic fluid turbulence in the presence of a uniform rotation and magnetofluid turbulence in the presence of a uniform magnetic field are considered. Both fluid and magnetofluid two-dimensional systems are presented as a special case of anisotropic turbulence constrained by the geometry. The presence of an external uniform magnetic field in such a geometry is also considered.