arXiv subjects

A. S. Ilyin

Publications and source records attributed to A. S. Ilyin.

4 recordsLinked to original sources

arXiv2007

Lagrangian structure functions in fully-developed hydrodynamical turbulence

The Lagrangian velocity structure functions in the inertial range of fully developed fluid turbulence are derived basing on the Navier-Stokes equations. For time $τ$ much smaller than the correlation time, the structure functions are shown to obey the scaling relations $K_n(τ)\propto τ^{ζ_n}$. The scaling exponents $ζ_n$ are calculated analytically. The obtained values are in amazing agreement with the unique experimental results of the Bodenschatz group \cite{Bod2}. New notion -- the Lagrangian position structure functions $R_n(τ)$ is introduced. All the $R_n$ of the order $n>3$ are shown to have a universal scaling.

physics.flu-dyn↗

arXiv2006

Generation of small-scale structures in the developed turbulence

The Navier-Stokes equation for incompressible liquid is considered in the limit of infinitely large Reynolds number. It is assumed that the flow instability leads to generation of steady-state large-scale pulsations. The excitation and evolution of the small-scale turbulence is investigated. It is shown that the developed small-scale pulsations are intermittent. The maximal amplitude of the vorticity fluctuations is reached along the vortex filaments. Basing on the obtained solution, the pair correlation function in the limit $r\to 0$ is calculated. It is shown that the function obeys the Kolmogorov law $r^{2/3}$.

physics.flu-dyn↗

arXiv2004

The growth of supermassive black holes in the centers of galaxies: absorption of stars and activity of galactic nuclei

The evolution of a supermassive black hole in the center of galaxy is considered. We analyze the kinetic equation describing relaxation processes associated with stellar encounters. The initial distribution function of stars is assumed to be isothermal, and it changes in accordance with consumption of stars by the black hole. We calculate the consumption rate and obtain the law of growth of supermassive black hole, i.e. the dependence of the black hole mass on time and on the velocity dispersion of stars. The obtained values of mean black hole mass and mean rate of stars consumption by a black hole are in reasonable agreement with observational data.

astro-ph↗

arXiv2003

Dark matter in galaxies and growth of giant black holes

The connection between dark matter and giant black holes in the galactic nuclei is investigated. The joint evolution of dark and luminous matter in averaged self-consistent gravitational potential is considered. It is shown that the distribution of dark matter remains spherically symmetric even in presence of essential asymmetry of luminous matter in the galaxy. The kinetic equation describing evolution of dark matter particles distribution function which takes into account their dynamics in gravitational potential and scattering on stars is derived. It is shown that significant flux of dark matter on a seed black hole in the center of galaxy should appear. The growth law of seed black hole due to absorption of dark matter is derived. It appears that during the lifetime of galaxy the seed black hole should grow significantly, up to observed value. Brief analysis of observational data shows that the presented theory is in reasonable agreement with observations.

astro-ph↗