相关论文: Exact Second-Order Structure-Function Relationship…
We derive necessary conditions that traveling wave solutions of the Navier-Stokes equations must satisfy in the pipe, Couette, and channel flow geometries. Some conditions are exact and must hold for any traveling wave solution irrespective…
The connection between anomalous scaling of structure functions (intermittency) and numerical methods for turbulence simulations is discussed. It is argued that the computational work for direct numerical simulations (DNS) of fully…
Two-dimensional turbulence governed by the so-called $\alpha$ turbulence equations, which include the surface quasi-geostrophic equation ($\alpha=1$), the Navier--Stokes system ($\alpha=2$), and the governing equation for a shallow flow on…
We propose a new approach to the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence. We achieve this by constructing, for any given nonlinear model, a linear model of passive advection of an…
Rigorous estimates for the total - (kinetic) energy plus pressure - flux in R^3 are obtained from the three dimensional Navier-Stokes equations. The bounds are used to establish a condition - involving Taylor length scale and the size of…
The Euler and Navier-Stokes equations both belong to a closed system of three transport equations, describing the particle number density N, the macroscopic velocity v and the temperature T. These sytems are complete, leaving no room for…
This paper provides a rigorous mathematical analysis of the global regularity problem for the 3D incompressible Navier-Stokes (NS) equations, specifically addressing the conditions under which smooth initial data may lead to a loss of…
This paper reports several new classes of weakly unstable recurrent solutions of the 2+1-dimensional Euler equation on a square domain with periodic boundary conditions. These solutions have a number of remarkable properties which…
Exact budget equations are derived for the coherent and stochastic contributions to the second-order structure function tensor. They extend the anisotropic generalised Kolmogorov equations (AGKE) by considering the coherent and stochastic…
The problem of global-in-time regularity for the 3D Navier-Stokes equations, i.e., the question of whether a smooth flow can exhibit spontaneous formation of singularities, is a fundamental open problem in mathematical physics. Due to the…
Self-gravitating isothermal supersonic turbulence is analyzed in the asymptotic limit of large Reynolds numbers. Based on the inviscid invariance of total energy, an exact relation is derived for homogeneous, (not necessarily isotropic)…
The existence and dynamical role of particular unstable Navier-Stokes solutions (exact coherent structures) is revealed in laboratory studies of weak turbulence in a thin, electromagnetically-driven fluid layer. We find that the dynamics…
Turbulence is an ubiquitous phenomenon in natural and industrial flows. Since the celebrated work of Kolmogorov in 1941, understanding the statistical properties of fully developed turbulence has remained a major quest. In particular,…
We examine the conjecture of equivalence of nonequilibrium ensembles for turbulent flows in two-dimensions (2D) in a dual-cascade setup. We construct a formally time-reversible Navier-Stokes equations in 2D by imposing global constraints of…
Turbulence governed by the Navier-Stokes equations shows a tendency to evolve towards a state in which the nonlinearity is diminished. In fully developed turbulence this tendency can be measured by comparing the variance of the nonlinear…
We study the constraints imposed by conformal symmetry on the equations of fluid dynamics at second order in gradients of the hydrodynamic variables. At zeroth order conformal symmetry implies a constraint on the equation of state, E=2/3 P,…
New scalar structure functions with different sign-symmetry properties are defined. These structure functions possess different scaling exponents even when their order is the same. Their scaling properties are investigated for second and…
Conventional mathematical models for simulating incompressible fluid flow problems are based on the Navier-Stokes equations expressed in terms of pressure and velocity. In this context, pressure-velocity coupling is a key issue, and…
Second-order structure functions and power spectral densities are popular tools in the study of statistical properties across scales, particularly for the analysis of turbulent flows. Although intimately related, analyses primarily use one…
We study the statistical properties of stationary, isotropic and homogeneous turbulence in two-dimensional (2D) flows, focusing on the direct cascade, that is on wave-numbers large compared to the integral scale, where both energy and…