## Turbulence and Self-Organization: Modeling Astrophysical ObjectsThe book deals with the development of continual models of turbulent natural media. Such models serve as a ground for the statement and numerical evaluation of the key problems of the structure and evolution of the numerous astrophysical and geophysical objects. The processes of ordering (self-organization) in an originally chaotic turbulent medium are addressed and treated in detail with the use of irreversible thermodynamics and stochastic dynamics approaches which underlie the respective models. Different examples of ordering set up in the natural environment and outer space are brought and thoroughly discussed, the main focus being given to the protoplanetary discs formation and evolution. |

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### Contents

1 | |

Chapter 2 Foundations of Mathematical Modeling of Reacting Gas Mixtures | 145 |

Chapter 3 Closed System of Hydrodynamic Equations to Describe Turbulent Motions of Multicomponent Media | 189 |

Chapter 4 Differential Models for the Closure of Turbulently Averaged Hydrodynamic Equations for a Chemically Active Continuous Medium
| 255 |

Chapter 5 StochasticThermodynamic Modeling of Developed Structured Turbulence | 295 |

Chapter 6 SelfOrganization of Developed Turbulence and Formation Mechanisms of Coherent Structures | 373 |

Chapter 7 Foundations of Mechanics of Heterogeneous Media for Accretion Disks | 424 |

### Other editions - View all

Turbulence and Self-Organization: Modeling Astrophysical Objects Mikhail Ya Marov,Aleksander V. Kolesnichenko No preview available - 2013 |

Turbulence and Self-Organization: Modeling Astrophysical Objects Mikhail Ya Marov,Aleksander V. Kolesnichenko No preview available - 2011 |

Turbulence and Self-Organization: Modeling Astrophysical Objects Mikhail Ya Marov,Aleksander V. Kolesnichenko No preview available - 2013 |

### Common terms and phrases

accretion disks angular angular momentum approximation atmosphere averaged motion balance equation cascade chaotic characteristic chemical reactions cloud coefﬁcients components continuum correlation corresponding deﬁned deﬁning relations deﬁnition derived developed turbulence differential differentially rotating diffusion coefﬁcients dust particles dynamical ensemble entropy equilibrium evolution ﬁrst ﬂuctuations ﬂuid ﬂux formation function gas—dust gradient heat ﬂux hydrodynamic hydrodynamic equations inﬂuence interaction kinetic energy Kolesnichenko Kolmogorov Lyapunov exponents macroscopic magnetic ﬁeld Marov mass mechanism medium mixture molecular momentum multicomponent nonequilibrium nonlinear oscillators parameters phase transitions planetary planetesimals planets plasma probability density problem processes protoplanetary protoplanetary disk pulsations quantity reﬂection regions Reynolds number Reynolds stress rotating scale self-organization signiﬁcant Solar space speciﬁc stable stationary stochastic stress tensor subdisk subsystem of turbulent surface temperature theory thermal thermodynamic transfer equation turb turbulent chaos turbulent energy turbulent ﬂow turbulent motion turbulent viscosity turbulized ﬂuid vector velocity viscosity vortex vortex structures vortices