Wave kinetics of inhomogeneous incompressible 2-D MHD turbulence

Traditional wave-kinetic approaches to MHD turbulence have been limited to the weak-turbulence regime and rely on scale separation between the turbulent Alfvenic fluctuations and background inhomogeneities. Such approaches are inapplicable to describing strongly nonlinear coherent structures, which are commonly found in MHD turbulence. Here, we present an alternative, Wigner-Moyal approach that is free from this limitation. MHD turbulence is treated within the Wigner-Moyal approach approach as plasma of effective quantumlike particles (Alfven waves) that have non-negligible wavelengths and interact via mean fields. We analytically explore phase-space dynamics and structure formation (modulational instabilities) in such "plasmas" using incompressible 2-D MHD equations for the Elsasser vorticities as the base model.