相关论文: A comment on the theory of turbulence without pres…

General scenario of turbulence theory is proposed and applied to streaky wall-bounded turbulence. This scenario introduces a new field of transverse waves. Significance of the theory rests on a mathematical theorem associated with the…

We consider initial-boundary-value problems for a class of nonlinear third order equations having non-autonomous forcing terms and get new asymptotic stability results by means of the Liapunov second method. The class includes equations…

This is a survey of some invariances that arise in dynamical systems theory in the presence of zero Lyapunov exponents.

The turbulent energy flux through scales, $\bar{\epsilon}$, remains constant and non vanishing in the limit of zero viscosity, which results in the fundamental anomaly of time irreversibility. It was considered straightforward to deduce…

The physical nature of compressible turbulence is of fundamental importance in a variety of astrophysical settings. We present the first direct evidence that mean kinetic energy cascades conservatively beyond a transitional "conversion"…

A landmark of out-of-equilibrium physics is Kolmogorov's phenomenological theory of turbulence. However, the past 20 years have provided evidence of a new, universal type of turbulence cascade, which does not abide to Kolmogorov physics. To…

The first-order relativistic fluid theories of dissipation proposed by Eckart and Landau-Lifshitz have been proved to be unstable. They admit solutions which start in proximity of equilibrium and depart exponentially from it. We show that…

In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the…

We consider the hydrodynamic regime of theories with quantum anomalies for global currents. We show that a hitherto discarded term in the conserve current is not only allowed by symmetries, but is in fact required by triangle anomalies and…

It has been recently demonstrated, [3], that according to the principle of release of constraints, absence of shear stresses in the Euler equations must be compensated by additional degrees of freedom, and that led to a Reynolds-type…

We analyze a class of linear shell models subject to stochastic forcing in finitely many degrees of freedom. The unforced systems considered formally conserve energy. Despite being formally conservative, we show that these dynamical systems…

A defining feature of 3D hydrodynamic turbulence is that the rate of energy dissipation is bounded away from zero as viscosity is decreased (Reynolds number increased). This phenomenon - anomalous dissipation - is sometimes called the…

For any \theta<1/10 we construct periodic weak solutions of the incompressible Euler equations which dissipate the total kinetic energy and are H\"older-continuous with exponent \theta. A famous conjecture of Onsager states the existence of…

For the p-system with large BV initial data, an assumption introduced in [3] by Bakhvalov guarantees the global existence of entropy weak solutions with uniformly bounded total variation. The present paper provides a partial converse to…

An open question of whether phenomenological fluid equations to be used for direct numerical simulation of turbulence are warranted on `first principles' is addressed, and the problem is posed using Klimontovich microscopic density to…

This article begins with an overview, then gives the precise definition of isotropic turbulence, and follows that with the basic conservation equations, in both real space and wavenumber space. These provide the foundations of all…

A novel model of wave turbulence is presented which allows to explain in the same frame various nonlinear wave phenomena: intermittency, form and direction of the energy cascades, formation of a zero-frequency band with non-zero energy,…

Polyakov recently showed how to use conformal field theory to describe two-dimensional turbulence. Here we construct an infinite hierarchy of solutions, both for the constant enstrophy flux cascade, and the constant energy flux cascade. We…

Differential models for hydrodynamic, passive-scalar and wave turbulence given by nonlinear first- and second-order evolution equations for the energy spectrum in the $k$-space were analysed. Both types of models predict formation an…

We investigate the exact results of the Navier-Stokes equations using the methods developed by Polyakov. It is shown that when the velocity field and the density are not independent, the Burgers equation is obtained leading to exact N-point…