Self-Organization of Developed Turbulence and Formation Mechanisms of Coherent Structures

  • Mikhail Ya Marov
  • Aleksander V. Kolesnichenko
Part of the Astrophysics and Space Science Library book series (ASSL, volume 389)


Here the so-called H-theorem for the Kullback entropy is proved, from which it follows that any initial probability distribution for the internal coordinates of the subsystem of turbulent chaos under known assumptions asymptotically approaches a certain stationary state after a sufficiently long time. Here, we demonstrate that self-organization (i.e., the emergence of ordered dissipative structures with a lower symmetry than that of the initial state) is possible in principle in the thermodynamically open subsystem of turbulent chaos when the generation of coherent structures associated with the effect of multiplicative-noise-induced nonequilibrium phase transitions in the subsystem of chaos is possible in due course of temporal evolution of the quasi-equilibrium vortex subsystem. We show that if the multiplicative noise of chaos is intense enough, then the extrema of the probability density describing the stationary behavior of a stochastic vortex system differ significantly in both number and position from the stationary states corresponding to a deterministic system. Moreover, multiplicative noise can give rise to new stationary states, thereby changing the properties (in particular, the bifurcation diagrams) of the local stability of chaos themselves: the transition points can be displaced under the influence of intense noise in a turbulent fluid.

Based on the general concept of the generation of coherent vortex structures in the thermodynamically open subsystem of turbulent chaos (due to nonequilibrium phase transitions induced by the multiplicative noise of chaos), in this chapter we also consider one of the specific mechanisms for the formation and evolution of mesoscale vortex structures associated with the phase-frequency synchronization of the self-oscillations of those internal coordinates that refer to the coherent component of chaos. In addition, we study some of the scenarios for the dynamical influence of the incoherent component (fine-grained fluctuating field) of turbulent chaos on the formation and evolution of vortex structures. Such transitions are shown to interrelate with the self-organization of clusters with a lower symmetry than that of the initial state. In particular, we reach the important conclusion that whereas the growth in the sizes of solid particles during collisions in classical turbulence is hampered, they can coalesce and enlarge within such dissipative ordered structures. In other words, the emergence of vortex clusters facilitates the solution of a key problem of the evolution of accretion disks - the problem of solid particle enlargement through collisions even at relatively low velocities. This encounters obvious difficulties in attempting to reproduce similar processes in laboratory experiments.


Vortex Structure Multiplicative Noise Nonequilibrium Phase Transition Stationary Probability Density Mutual Synchronization 
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© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Mikhail Ya Marov
    • 1
  • Aleksander V. Kolesnichenko
    • 2
  1. 1.Department of Planetary Sciences and CosmochemistryV.I. Vernadsky Institute of Geochemistry and Analytical Chemistry Russian Academy of SciencesMoscowRussia
  2. 2.Department of Planetary Science and AeronomyKeldysh Institute of Applied Mathematics Russian Academy of SciencesMoscowRussia

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