Synergetic Mechanism of the Development of Coherent Structures in the Continual Theory of Developed Turbulence

Abstract

The aim of this paper is to further develop the continual theory of structurized turbulence in shear flows in a fluid modeled by a superposition of two mutually penetrating continua, where the first continuum refers to the averaged field of turbulent motion, and the second, to the turbulent spacetime chaos, which includes an ensemble of mesoscale coherent structures localized in space. It is believed that, in the case of an increase of the supercriticality level, mesoscale structures are generated by small-scale vortex formations, which, in the case of a two-level turbulence model, are described by additional internal parameters of chaos, e.g., generalized angular velocities characterizing vorticities of the pulsational hydrodynamic field. I discuss the possibility of synergetic formation of mesoscale coherent structures from turbulent chaos, which differs strongly from the complete chaos of thermodynamic equilibrium, due to phase synchronization of relatively large small-scale vortices (maximum oscillations within a certain spectral interval) in the presence of noise due to the “thermal” structure of the vortex continuum. I interpret such a mechanism of the formation and evolution of coherent structures in the thermodynamically open subsystem of turbulent chaos in terms of the theory of dynamical systems. The aim of this study is to develop a number of representative hydrodynamic models of natural space environments, including the evolution of the Solar System, turbulent transfer on planets and in their atmospheres, ecological problems, etc. It continues the stochastically thermodynamic approach to the synergetic description of structurized turbulence in astrogeophysical systems that I have been developing in a series of previous papers (Kolesnichenko, 2002, 2003, 2004).