We analyze the possible effect of hydrodynamic spirality that develops in a rotating disk on the synergetic structurization of cosmic matter and on the development of negative turbulent viscosity in cosmic matter within the framework of the problem of the reconstruction of the evolution of the protoplanetary cloud that surrounded the early Sun. We show that comparatively slow damping of turbulence in the disk can be partially due to the lack of reflective symmetry of the anisotropic field of turbulent velocities about its equatorial plane. We formulate the general concept of the development of energy-intensive coherent mesoscale vortex structures in the thermodynamically open system of turbulent chaos associated with the realization of inverse cascade of kinetic energy in mirror–nonsymmetrical disk turbulence. Because of energy release, the inverse cascade produces a hierarchical system of mass concentrations with a fractal density distribution, which ultimately initiate the mechanisms of triggered cluster formation. We use the methods of nonequilibrium thermodynamics to prove the possibility of the development of negative viscosity in the three-dimensional case in terms of the twoscale hydrodynamic description of maximally developed disk turbulence. Negative viscosity in a rotating disk system appears to be a manifestation of cascade processes in spiral turbulence where inverse energy transfer from small to larger vortices occurs. Within the framework of asymmetric mechanics of turbulized continua, we physically substantiated the phenomenological formula for the turbulent stress tensor of Wasiutynski, which is widely used in the astrophysical literature to explain the differential rotation of various cosmic objects by “anisotropic viscosity.”

Mathematical modelling in actual problems of science and technics