Nearly Incompressible Modeling of the Solar Wind*

We develop a three-dimensional time dependent numerical model of compressible magnetohydrodynamic fluids describing super-Alfv\'enic, supersonic and strongly magnetized space and laboratory plasmas show a nonlinear relaxation towards a state of near incompressibility. The latter is characterized essentially by a subsonic turbulent Mach number. This transition is mediated dynamically by disparate spectral energy dissipation rates in compressible magnetosonic and shear Alfv\'enic modes. Nonlinear cascades lead to super-Alfv\'enic turbulent motions decaying to a sub- Alfv\'enic regime that couples weakly with (magneto)acoustic cascades. Consequently, the supersonic plasma motion is transformed into highly subsonic motion and density fluctuations experience a passive convection. This model provides a self-consistent explaination of the ubiquitous nature of incompressible magnetoplasma fluctuations in the solar wind and the interstellar medium.