By Alexei M. Fridman, Mikhail Ya. Marov, Ilya G. Kovalenko

ISBN-10: 1402043473

ISBN-13: 9781402043475

ISBN-10: 1402043481

ISBN-13: 9781402043482

This e-book bargains with collective and stochastic methods in astrophysical disks related to concept, observations, and the result of modelling. It examines the spiral-vortex constitution in galactic and accretion disks, and stochastic and ordered constructions in built turbulence. The booklet advances the examine during this very important department of astrophysics and should gain expert researchers, teachers, and graduate scholars.

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**Example text**

K. Sil’chenko, Sov. Astron. 35, 569, 1991. N. V. K. Sil’chenko, Astron. Zhurn. 69, 19, 1992. V. K. N. S. Trubnikov. Stabilization of tangential shear instability in shallow water with supersonic fluid flow. JETP, 37 (7), 378, 1983. G. F. Billings. J. , 71(2), 305, 1975. G. V. N. Snezhkin. Phys. , 109A, 228, 1985. M. ZhETP, 98, No. 4, 1121, 1990. V. M. N. Gor’kavyi, Physics of Planetary Rings, Springer, New-York etc, 1999. I. Mech. Zhid. i Gaza, 3, 145, 1984. D. “On the stability of tangential gaps in contracted fluid”.

One should note, however, that for the structure functions of n-order the εr)n/3 (where V ≡ u (x) − u (x + r)), following from the expression V n (¯ 4 Let us note that in the original work of Kolmogorov (1941) the two-third law follows from the condition ε¯(r) = const, where η < r < L0 occurs in the inertial interval. 5 Energy spectrum E(k), along with the function of energy dissipation spectrum 2νk 2 E(k) and the function of energy re-distribution over spectrum T (k), describe time variations of the spectral distribution of the turbulent energy.

Phenomenological macroscopic 3D model of the stationary non-equilibrium turbulence in the compessible fluid is developed with the account for collective non-linear processes. Internal parameters of the medium are introduced into the model, which characterizes the excitation of macroscopic degrees of freedom. It made possible to generalize Onsager formalism over turbulent pulsations relative to the average motion and describe thermodynamically the Kolmogorov cascade process. Various kinetic equations of the Fokker-Planck type in the configuration space for the functions of distribution of small-scale turbulence characteristics are deduced including the unsteady kinetic equation for the distribution of probability of dissipation of turbulent energy.

### Astrophysical Disks: Collective and Stochastic Phenomena (Astrophysics and Space Science Library) by Alexei M. Fridman, Mikhail Ya. Marov, Ilya G. Kovalenko

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