arXiv subjects
Publications and source records attributed to Sergey G. Chefranov.
It is shown that the threshold of the observed Vavilov-Cherenkov radiation is more accurately described by the new quantum theory, based on the theory of Abraham (1909), compared with the quantum theory of Ginzburg (1940), based on the theory of Minkowski (1908).
The well-known paradox of linear stability for the some bounded shear flows is not solved up to now and is bypassed on the basis of the non-linear mechanisms consideration. We prove that it is arising only due to an idealized assumption of an exact space periodicity for the small hydrodynamic perturbations. When finite non-zero viscosity is taken into account only quasi-periodic boundary conditions must be used. The conditions of linear instability to the Hagen-Poiseuille flow and to the plane Couette flow are obtained.
In the linear theory of hydrodynamic stability up to now there exist examples of flows for which there is full quantitative distinction, as for cylindrical Hagen-Poiseuille (HP) flow in a pipe with round section, between theory conclusions and experimental data on the threshold Reynolds number Reth. In the present work, we show that to get a conclusion of linear instability of the HP flow for finite Reynolds numbers Re, it is necessary to abandon the use of traditional 'normal' form of disturbances which assumes an opportunity of separation of variables describing disturbances variability depending on radial and longitudinal (along the pipe axis) coordinates. In the result of the absence of such variables separation, in the suggested linear theory, it is proposed to use Bubnov-Galerkin's approximation method modification that gives an opportunity to account longitudinal variability periods distinctions for different radial modes defined a priori in the result of standard Galerkin-Cantorovich's method to the equation of evolution of extremely small axially symmetric velocity field tangential component disturbances. We found that when considering even two linearly interacting radial modes for the HP flow, linear instability is possible only when there exists mentioned above conditionally periodic longitudinal along the pipe axis disturbance variability when Re_th(p) very sensitively depends on the ratio p of two longitudinal periods each of which describes longitudinal variability for its own radial mode only. Obtained for the HP flow linear instability realization minimal value Re_th=448 (when p=1.527) quantitatively agrees with the Tolmin-Shlihting waves in the boundary layer emergence, where also Re_th=420. We get quantitative agreeing of the phase velocity values of the considered disturbances with experimental data on the fronts of the turbulent 'puffs' spreading in the pipe.
An alternative to the well-known complete form of the Mie-Grüneisen equation of state (EOS) for water is suggested. A closed analytical description of the self-consistent EOS for an arbitrary medium based only on the first law of thermodynamics and on a new form of virial theorem is obtained. This form of the virial theorem (allowing a variable power-law exponent of the particles interaction potential) is a result of the generalization of the known method of similarity (Feynman et al., 1949). In the new EOS, the description of the internal potential energy as a solution of a nonlinear Riemann-Hopf type equation is proposed.
New analytical solution of the piston and shock evolution for the wire electrical explosion in water is obtained. This is provided on the base of the compressible Euler equations without usually a prior introduction of any self-similarity hypothesis. It is shown that diverging cylindrical shock is transformed into acoustic wave in a finite time, even without taking into account of dissipation. The correspondence with experimental data on underwater electrical explosion of thin wire is represented.
The commonly applied self-similar solution of the problem of the converging shock wave (shock) evolution with constant compression of the medium behind the shock front results in an unlimited increase of the medium velocity in the vicinity of the implosion. In this paper, the convergence of cylindrical shocks in water is analyzed using the mass conservation law, when the water compression behind the shock front is a variable. The model predicts a finite range of radii, which depends on the adiabatic index of water and where the increase in pressure exceeds the sum of the change of the kinetic and internal energy densities behind the shock front. In this range of radii only the finite increase of the shock and water flow velocities is realized.
Analytical modeling of the evolution of cylindrical and spherical shock waves (shocks) during an implosion in water is presented for an intermediate range of convergence radii. Up to now this range is determined only in experiments observations as a range of implosion radii which are already far from the piston influence, but yet not described by well-known self-similar solutions. The model is based on an analysis of the change in pressure and kinetic energy density, as well as on the corresponding fluxes of internal and kinetic energy densities behind the shock front. It shows that the spatial evolution of the shock velocity strongly depends on the initial compression, the adiabatic index of water, and the geometry of convergence. The model also explains the transition to a rapid like self-similar increase in the shock velocity at only a certain radius of the shock that is observed in experiments. The dependence of the threshold radius, where the shock implosion follows the power law (quasi self-similarity), on the initial compression is determined. It is stated that in the entire range of the shock radii the internal and kinetic energy density fluxes are equal, which is in agreement with known experimental data.
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.
The condition of linear instability for a converging cylindrical shock wave in an arbitrary inviscid medium is obtained. The shape of resulting shock wave front is not changed significantly, but the restriction of energy cumulation can be caused by exponential grows of the medium rotation behind the front. The correspondence with experimental and simulation data is considered.
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.
It is shown that the hydrodynamics equations for a thin spherical liquid layer are satisfied by the stream function of a pair of antipodal vortices-APV, in contrast to the stream function of a single point vortex on a sphere with a background of a uniform opposite sign vorticity. A simple zero solution of the equation of the absolute vorticity conservation is used for bypassing well-known nonlinear problem of a point vortices interaction with regular vorticity field and an exact solution for APVs dynamics problem on a rotating sphere is obtained. Due to this a new stable stationary solution for the dynamics of APV is obtained, which can model the dynamics of the global vortex structures such as atmospheric centers of action.
The condition of linear instability for a converging cylindrical strong shock wave (SW) in an arbitrary viscous medium is obtained in the limit of a large stationary SW radius, when it is possible to consider the same Rankine-Hugoniot jump relations as for the plane SW. This condition of instability is substantially different from the condition of instability for the plane SW because a cylindrical SW does not have chiral symmetry in the direction of the SW velocity (from left to right or vice versa) as in the case of a plane SW. The exponential growth rate of perturbations for the converging cylindrical SW is positive only for nonzero viscosity in the limit of high, but finite, Reynolds numbers as well as for the instability of a plane SW.
A new condition for the linear dissipative instability of the strong plane shock wave in an arbitrary medium is obtained. The instability of the shock is realized due to the flow instability behind its front, which is similar to the known dissipative instability in the boundary layer for the Tollmien-Schlichting waves. It is found that within the limit of low viscosity the one-dimensional longitudinal disturbances grow much faster than the two-dimensional corrugation ones. It points to a better correspondence to experiment of the new condition for the absolute instability of the shock in comparison with theory, which does not take viscosity into account.
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.).
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.
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.
An exact correspondence is established between mathematical description of the single "elementary vortex" (EV)velocity on the sphere (Zermelo,1902;Bogomolov,1977) and the Dirac magnetic monopole (DMM) vector potential (Dirac, 1931). Similar analogy with DMM was noted only for the vortices in quantum fluid He-3A (Blaha,1976;Volovik,Mineev,1976). Singular EV on a sphere is usually considered using compensating vortex field, uniformly distributed over the sphere. It is necessary to meet the Gauss-Kelvin theorem with zero integral vorticity over the sphere. However since Bogomolov (1977)(see also Dritshel,Boatto,2015)uniform vorticity impact on dynamics is neglected when only the velocity field of singular EV is taken into account. It is not true because the hydrodynamic equations do not allow existence of a solution in the form of an isolated EV but allow solutions in the form of the antipodal EV pairs. It is also suggested the possibility of DMM existence only in the form of the point magnetic dipoles, consisting of two DMM with different signs of the magnetic charge.
A new exact solution of the hydrodynamic equations is obtained in the form of the Burgers vortex generalization (BVG)accounting for the medium rotation as a whole and linear uniform friction. The nonlinear dissipative-centrifugal instability(DCI)condition, associated with some superthreshold rotation angular velocity and nonzero friction, for solid-body rotating core of BVG is obtained. The new effect of cyclone-anticyclone vortex asymmetry, arising during DCI of BVG vortex core, is shown to be similar to that observed for the atmospheres of high speed rotating planets and laboratory experiments.