相关论文: On the effect of the Coriolis force on the enstrop…
We consider the 2D incompressible Navier-Stokes equation in a rectangle with the usual no-slip boundary condition prescribed on the upper and lower boundaries. We prove that for any positive time, for any finite energy initial data, there…
Two-dimensional turbulence with linear (Ekman) friction exhibits spectral properties that deviate from the classical Kraichnan prediction for the direct enstrophy cascade. In particular, for sufficiently small viscosity and large friction,…
We present two phenomenological models for 2D turbulence in which the energy spectrum obeys a nonlinear fourth-order and a second-order differential equations respectively. Both equations respect the scaling properties of the original…
We establish pointwise decay estimates for the velocity field of a steady two-dimensional Stokes flow around a rotating body via a new approach rather than analysis adopted in the previous literature. The novelty is to analyze the singular…
Bounding curves in the energy,enstrophy-plane are derived for the 3D Navier-Stokes equations under an assumption on coherence of the vorticity direction. The analysis in the critical case where the direction is H\"older continuous with…
In this paper, we establish the asymptotic linear stability of a class of Coriolis-driven columnar vortices for the 3-D axisymmetric Euler equations. This result represents a critical step toward proving the nonlinear asymptotic stability…
We report evidence for an enstrophy cascade in large-scale point-vortex simulations of decaying two-dimensional quantum turbulence. Devising a method to generate quantum vortex configurations with kinetic energy narrowly localized near a…
We prove the nonlinear stability of the planar viscous shock up to a time-dependent shift for the three-dimensional (3D) compressible Navier-Stokes equations under the generic perturbations, in particular, without zero mass conditions.…
The scale-invariant inverse energy cascade is a hallmark of 2D turbulence, with its theoretical energy spectrum observed in both direct numerical simulations (DNS) and laboratory experiments. Under this scale-invariance assumption, the…
For wavenumbers k such that k * alpha > 1, corresponding to spatial scales smaller than alpha, there are three candidate power laws for the energy spectrum of the Navier-Stokes-alpha model, corresponding to three possible dynamical eddy…
The purpose of this note is to analyze the long term stability of the Navier-Stokes equations supplemented with the Coriolis force and the stress-free boundary condition. It is shown that, if the flow domain is axisymmetric, spurious…
We derive the scale-by-scale uncertainty energy budget equation and demonstrate theoretically and computationally the presence of a self-similar equilibrium cascade of decorrelation in an inertial range of scales during the time range of…
We find strong evidence for intermittency in forced two dimensional (2D) turbulence in a flowing soap film experiment. In the forward enstrophy cascade the structure function scaling exponents are nearly indistinguishable from 3D studies.…
In this paper, we present an overview of concepts and data concerning inverse cascades of excitation towards scales larger than the forcing scale in a variety of contexts, from two-dimensional fluids and wave turbulence, to geophysical…
We develop a model of the forces on a spherical particle suspended in flow through a curved duct under the assumption that the particle Reynolds number is small. This extends an asymptotic model of inertial lift force previously developed…
Turbulent behavior of the two-parameter family of generalized surface quasigeostrophic equations is examined both rigorously and numerically. We adapt a cascade mechanism argument to derive an energy spectrum that scales as…
We consider the incompressible Navier-Stokes equations in a two-dimensional exterior domain, with no-slip boundary conditions. We assume that the initial velocity is a finite-energy and L^q-summable perturbation of the Oseen vortex with…
Fully-developed incompressible Navier-Stokes turbulence in three dimensions is a dissipative dynamical system that exhibits strong departure from absolute equilibrium. Nevertheless, several kinds of representation by Tsallis equilibria have…
We study the direct enstrophy cascade in a two-dimensional flow generated in an electromagnetically driven thin layer of fluid. Due to the presence of bottom friction, the energy spectrum deviates from the classical Kraichnan prediction…
Stratified flows forced by internal waves similar to those obtained in the Coriolis platform (LEGI, Grenoble, France) \cite{Savaro2020} are studied by pseudospectral triply-periodic simulations. The experimental forcing mechanism consisting…