相关论文: Self-similar behavior of pre-turbulent fluctuation…

This paper is the first in a series of three papers that aim at understanding the scaling behaviour of hydrodynamic turbulence. We present in this paper a perturbative theory for the structure functions and the response functions of the…

We study the statistics of longitudinal and transverse structure functions, as well as velocity circulation in the inverse energy cascade of two-dimensional turbulence. By means of direct numerical simulations of the incompressible…

The majority of practical flows, particularly those flows in applications of importance to transport, distribution and climate, are turbulent and as a result experience complex three-dimensional motion with increased drag compared with the…

In this paper we present a novel, closed three-dimensional (3D) random vortex dynamics system, which is equivalent to the Navier--Stokes equations for incompressible viscous fluid flows. The new random vortex dynamics system consists of a…

Numerical simulations of turbulence provide non-intrusive access to all the resolved scales, although they often invoke idealizations that can compromise realism. In contrast, experimental measurements probe the true flow with lesser…

Modelling hydrodynamic lubrication is crucial in the design of engineering components as well as for a fundamental understanding of friction mechanisms. The cornerstone of thin-film flow modelling is the Reynolds equation -- a…

A unique form of turbulent-transport equations is derived based on first principles.The role of nonequilibrium statistical mechanics employed to describe the phenomenology is that it enables to single out the unique form consistent with…

How predictable are turbulent flows? Here we use theoretical estimates and shell model simulations to argue that Eulerian spontaneous stochasticity, a manifestation of the non-uniqueness of the solutions to the Euler equation that is…

Anomalous scaling problem in the stochastic Navier-Stokes equation is treated in the framework of the field theoretical approach, successfully applied earlier to the Kraichnan rapid advection model. Two cases of the space dimensions d=2 and…

The dynamics defined by the Navier-Stokes equations under the Marangoni boundary conditions in a two dimensional domain is considered. This model of fluid dynamics involve fundamental physical effects: convection, diffusion and capillary…

All complex fluid motions, such as transition and turbulence, obeying the Navier-Stokes equations are non-linear phenomena. Some aspects of the non-linear terms of these equations are not well understood and are, in fact, misunderstood. The…

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…

A coupled forward-backward stochastic differential system (FBSDS) is formulated in spaces of fields for the incompressible Navier-Stokes equation in the whole space. It is shown to have a unique local solution, and further if either the…

Hydrodynamics provides a universal description of the emergent collective dynamics of vastly different many-body systems, based solely on their symmetries and conservation laws. Here we harness this universality, encoded in the…

We observe a symmetry-breaking transition from a turbulent to a self-organized state in direct numerical simulation of the Navier-Stokes equation at very low Reynolds number. In this self-organized state the kinetic energy is contained only…

At sufficiently high Reynolds numbers, shear-flow turbulence close to a wall acquires universal properties. When length and velocity are rescaled by appropriate characteristic scales of the turbulent flow and thereby measured in \emph{inner…

The incompressible Navier-Stokes equations are considered. We find that there exist infinite non-trivial solutions of static Euler equations. Moreover there exist random solutions of static Euler equations. Provided Reynolds number is large…

In the present work, we investigate a numerical one-dimensional solver to the Navier-Stokes equation that retains all terms, including both pressure and dissipation. Solutions to simple examples that illustrate the actions of the nonlinear…

We study the Boltzmann equation with external forces, not necessarily deriving from a potential, in the incompressible Navier-Stokes perturbative regime. On the torus, we establish local-in-time, for any time, Cauchy theories that are…

The incompressible Navier-Stokes equations currently represent the primary model for describing stratified turbulent fluid flows at low Mach number. The validity of the incompressible assumption, however, has so far only been rigorously…