Self-similar formation of the Kolmogorov spectrum in the Leith model of turbulence

The last stage of evolution toward the stationary Kolmogorov spectrum of hydrodynamic turbulence is studied using the Leith model [1] . This evolution is shown to manifest itself as a reflection wave in the wavenumber space propagating from the largest toward the smallest wavenumbers, and is described by a self-similar solution of a new (third) kind. This stage follows the previously studied stage of an initial explosive propagation of the spectral front from the smallest to the largest wavenumbers reaching arbitrarily large wavenumbers in a finite time, and which was described by a self-similar solution of the second kind [2, 3, 4]. Nonstationary solutions corresponding to“warm cascades” characterised by a thermalised spectrum at large wavenumbers are also obtained

Invariant Sets and Explicit Solutions to a Third-Order Model for the Shearless Stratified Turbulent Flow

We study dynamics of the shearless stratified turbulent flows. Using the method of differential constraints we find a class of explicit solutions to the problem under consideration and establish that the differential constraint obtained coincides with the well-known Zeman--Lumley model for stratified flows.Comment: arxiv version is already officia

Steady states in Leith's model of turbulence

We present a comprehensive study and full classification of the stationary solutions in Leith's model of turbulence with a generalised viscosity. Three typical types of boundary value problems are considered: Problems 1 and 2 with a finite positive value of the spectrum at the left (right) and zero at the right (left) boundaries of a wave number range, and Problem 3 with finite positive values of the spectrum at both boundaries. Settings of these problems and analysis of existence of their solutions are based on a phase–space analysis of orbits of the underlying dynamical system. One of the two fixed points of the underlying dynamical system is found to correspond to a 'sharp front' where the energy flux and the spectrum vanish at the same wave number. The other fixed point corresponds to the only exact power-law solution—the so-called dissipative scaling solution. The roles of the Kolmogorov, dissipative and thermodynamic scaling, as well as of sharp front solutions, are discussed

Registration of the First Thermonuclear X-ray Burst from AX J1754.2-2754

During the analysis of the INTEGRAL observatory archival data we found a powerful X-ray burst, registered by JEM-X and IBIS/ISGRI telescopes on April 16, 2005 from a weak and poorly known source AX J1754.2-2754. Analysis of the burst profiles and spectrum shows, that it was a type I burst, which result from thermonuclear explosion on the surface of nutron star. It means that we can consider AX J1754.2-2754 as an X-ray burster. Certain features of burst profile at its initial stage witness of a radiation presure driven strong expansion and a corresponding cooling of the nutron star photosphere. Assuming, that the luminosity of the source at this phase was close to the Eddington limit, we estimated the distance to the burst source d=6.6+/-0.3 kpc (for hidrogen atmosphere of the neutron star) and d=9.2+/-0.4 kpc (for helium atmosphere).Comment: 12 pages, 6 figure

A Chorin-Type Formula for Solutions to a Closure Model for the von Kármán-Howarth Equation

Abstract The article is devoted to studying the Millionshtchikov closure model (a particular case of a model introduced by Oberlack [14]) for isotropic turbulence dynamics which appears in the context of the theory of the von Kármán-Howarth equation. We write the model in an abstract form that enables us to apply the theory of contractive semigroups and then to present a solution to the initial-boundary value problem by Chorin-type formula