arXiv subjects

Artem S. Chefranov

Publications and source records attributed to Artem S. Chefranov.

6 recordsLinked to original sources

arXiv2022

Universal turbulence scaling law -8/3 at fusion implosion

The new interpretation of the known results of simulation of the turbulent regime at the time before stagnation stage of the fusion implosion is stated. For this aim the universal turbulence energy spectrum obtained by the authors with a scaling law -8/3, which corresponds to the exact solution of one-dimensional Euler equations for the dynamics of a compressible medium, is used. It is stated that the scaling law -8/3 has more relevance in comparison with the Kolmogorov spectrum of -5/3 in the inertial sub-range of scales for the compressible turbulence at this stage of fusion implosion. A possible mechanism for the occurrence of the anisotropic spectrum -8/3 in turbulence associated with hydrodynamic instability of the rotation of the medium behind the shock wave front is considered.

physics.flu-dyn↗

arXiv2022

Cosmic rays density fluctuations with turbulence universal spectrum -8/3

An exact turbulence universal scaling law-8/3 for the density fluctuations of cosmic ray (CR) is obtained on the basis of a new analytical compressible turbulence theory and known two-fluid model of the CR dynamics. It is shown that the origin of this scaling law may be due to the breaking of the nonlinear simple waves in CR medium near the scale of their Larmor radii as for the space plasma of solar wind and magnetosheath.

astro-ph.HE↗

arXiv2021

Exact solution to the main turbulence problem for a compressible medium and the universal -8/3 turbulence spectrum of breaking waves

An explicit analitical description of the compressible turbulence, based on the exact solution of the one-dimensional Euler equations in the unbounded case is obtained. The Onsager dissipative anomaly is resolved. The exact universal -8/3 energy spectrum corresponding to the finite time collapse of Euler's solution is stated. That spectrum is relevant to strong acoustic turbulence and observation in the space turbulence.

physics.flu-dyn↗

arXiv2019

Exact Time-Dependent Solution to the Three-Dimensional Euler- Helmholtz and Riemann-Hopf Equations for Vortex Flow of a Compressible Medium and the Sixth Millennium Prize Problem

For the first time the exact vortex solution of the Cauchy problem in unbounded space is obtained for the three-dimensional Euler-Helmholtz (EH) equation in the case of a nonzero-divergence velocity field for an ideal compressible medium. The solution obtained describes the inertial vortex motion and coincides with the exact solution to the three-dimensional Riemann-Hopf (RH) equation which simulates turbulence without pressure [Chefranov, 1991]. A necessary and sufficient condition of the onset of a singularity in the evolution of the enstrophy in finite time t=t0 is obtained for this solution when its continuation is possible in times t>=t0 in the Sobolev space H^0(R^3) but cannot be made in H^1(R^3). A closed description of the evolution of the enstrophy and the all other moments of the velocity and vortex fields is given, i.e., the main problem of theory of turbulence is solved exactly. The possibility of continuation of the obtained smooth solution to the EH an RH equations in the Sobolev space H^q(R^3) is also demonstrated for any q>=1 and t>=t0 due to introduction of a fairly large homogeneous friction or by introducing an arbitrary small effective volume viscosity. A new analytic solution of the Cauchy problem for the three-dimensional Navier-Stokes (NS) equation is obtained. This solution coincides with the above-mentioned smooth solution to the EH and RH equations, which take into account the viscosity effect of a compressible medium and also the sufficient condition of positive definiteness of the growth rate of the entropy in the form of a linear relation between the pressure and the divergence of the velocity field. This gives the positive solution to the generalization of the Millennium Prize Problem on the compressible Navier-Stokes equation where only the modification of viscous force is used (by introduction of homogeneous friction and etc.).

physics.gen-ph↗

arXiv2019

New exact solution of the Navier-Stokes equations for turbulence in a compressible medium

A new exact solution of the Navier-Stokes equation is derived for the compressible flows which are far from equilibrium in the limit of extremely low shear viscosity and relatively large volume viscosity. The closed description of the evolution of statistical moments of velocity is obtained, thereby bypassing the closure problem in the theory of turbulence.

physics.flu-dyn↗

arXiv2018

New solution of the compressible Navier-Stokes equation

We use the general exact solution of the Cauchy problem for the compressible Euler vortex equation in unbounded space which was obtained earlier (S.G.Chefranov, Sov. Phys. Dokl., 36, 286, 1991). This solution loses its smoothness in finite time and coincides with the exact solution of the Hopf equation, describing the inertial motion of the ideal fluid without pressure. On this base we obtain here the new smooth at all times solution to the compressible Navier-Stokes (NS) equation with the pressure field shows linear proportionality to the divergence of the velocity field, as it is known for an out-of-equilibrium systems with large second viscosity and small first viscosity. For example, directly from this solution of the NS equation for the case of two-dimensional (2D) compressible flow the exact representation of energy spectrum well known for 2D incompressible case (R.H.Kraichnan, Phys.Fluids,vol.10,1417,1967) is obtained.

physics.flu-dyn↗