相关论文: Enhanced dissipation, hypoellipticity for passive …
Consider a passive scalar which is advected by an incompressible flow $u$ and has small molecular diffusivity $\kappa$. Previous results show that if $u$ is exponentially mixing and $C^1$, then the dissipation time is $O(|\log \kappa|^2)$.…
We consider an advection of a passive scalar by a flow which is a superposition of random waves. We find that such a flow can lead to an exponential growth of the passive scalar fluctuations. We calculate the growth rate at the fourth order…
The standard dissipation inequality for passivity is extended from storage functions to general Lagrange subspaces. This is shown to have some interesting consequences. A classical factorization result for passive systems is extended to…
Using a classical technique introduced by Achi E. Brandt for elliptic equations, we study a general class of nonlocal equations obtained as a superposition of classical and fractional operators in different variables. We obtain that the…
We consider a passive scalar field under the action of pumping, diffusion and advection by a smooth flow with a Lagrangian chaos. We present theoretical arguments showing that scalar statistics is not conformal invariant and formulate new…
We derive sharp decay estimates and prove holomorphic extensions for the solutions of a class of semilinear nonlocal elliptic equations with linear part given by a sum of Fourier multipliers with finitely smooth symbols at the origin.…
In this paper, we consider the two-dimensional surface quasi-geostrophic equation with fractional horizontal dissipation and fractional vertical thermal diffusion. Global existence of classical solutions is established when the dissipation…
We present a new rigorous method for estimating statistical quantities in fluid dynamics such as the (average) energy dissipation rate directly from the equations of motion. The method is tested on shear flow, channel flow,…
In this article we consider the stability and damping problem for the 2D Boussinesq equations with partial dissipation near a two parameter family of stationary solutions which includes Couette flow and hydrostatic balance. In the first…
We study a passive scalar equation on the two-dimensional torus, where the advecting velocity field is given by a cellular flow with a randomly moving center. We prove that the passive scalar undergoes mixing at a deterministic exponential…
Many equations that model fluid behaviour are derived from systems that encompass multiple physical forces. When the equations are written in non dimensional form appropriate to the physics of the situation, the resulting partial…
We use direct numerical simulations to compute structure functions, scaling exponents, probability density functions and turbulent transport coefficients of passive scalars in turbulent rotating helical and non-helical flows. We show that…
We present a general method, based on a multiple-scale approach, for deriving the perturbative solutions of the scaling equations governing the expansion of superfluid ultracold quantum gases released from elongated harmonic traps. We…
The motion of a scalar field that interacts with a hot plasma, like the inflaton during reheating, is damped, which is a dissipative process. At high temperatures the damping can be described by a local term in the effective equation of…
Forced advection of passive scalar by a smooth $d$-dimensional incompressible velocity in the presence of a linear damping is studied. Acting separately advection and dumping do not lead to an essential intermittency of the steady scalar…
We investigate the properties of an abstract family of advection diffusion equations in the context of the fractional Laplacian. Two independent diffusion parameters enter the system, one via the constitutive law for the drift velocity and…
We describe recent attempts to extract the shear viscosity of the dilute Fermi gas at unitarity from experiments involving scaling flows. A scaling flow is a solution of the hydrodynamic equations that preserves the shape of the density…
Motivated in part by the work of Vanneste and Byatt-Smith, we study mixing and enhanced dissipation for the advection-diffusion equation with velocity field $\mathbf{u}(x,y,t)=(\sin(y-ct),0)$, a shear flow whose profile translates rigidly…
An exact relation is derived between scalar dissipation due to molecular diffusivity and the randomness of stochastic Lagrangian trajectories for flows without bounding walls. This "Lagrangian fluctuation-dissipation relation" equates the…
In this paper, we develop an energy dissipative numerical scheme for gradient flows of planar curves, such as the curvature flow and the elastic flow. Our study presents a general framework for solving such equations. To discretize time, we…