Related papers: Statistical Estimates for 2D stochastic Navier-Sto…
Mathematical estimates for the Navier-Stokes equations are traditionally expressed in terms of the Grashof number, which is a dimensionless measure of the magnitude of the forcing and hence a control parameter of the system. However,…
The Navier-Stokes (NS) equations as a turbulence model have been widely applied in lots of fields. The NS equations contain such a fundamental assumption that all small physical/artificial disturbances could be neglected. Is this assumption…
We discuss two possible scenario for the direct cascade in two dimensional turbulent systems in presence of friction which differ by the presence or not of enstrophy dissipation in the inviscid limit.They are distinguished by the existence…
The dual cascade of energy and enstrophy in 2D turbulence cannot easily be understood in terms of an analog to the Richardson-Kolmogorov scenario describing the energy cascade in 3D turbulence. The coherent up- and downscale fluxes points…
The addition of suitable volume forces to the Navier-Stokes equation allows to simulate flows in the presence of a homogeneous shear. Because of the explicit form of the driving the flows are accessible to rigorous mathematical treatment…
Classical shell models of turbulence do not display dual cascade - inverse of energy and direct of enstrophy - because they fail to reproduce the right thermal spectra. We propose here a multi-branch shell model, including a geometry…
Hydrodynamic helicity signatures the parity symmetry breaking, chirality, of the flow. Statistical hydrodynamics thus respect chirality, as symmetry breaking and restoration are key to their fundamentals, such as the spectral transfer…
Turbulence -- ubiquitous in nature and engineering alike [1-5] -- is traditionally viewed as an intrinsically inertial phenomenon, emerging only when the Reynolds number (Re), which quantifies the ratio of inertial to dissipative forces…
Geometrical random multiplicative cascade processes are often used to model positive-valued multifractal fields such as the energy dissipation in fully developed turbulence. We propose a dynamical generalization describing the energy…
We derive upper bounds for the number of degrees of freedom of two-dimensional Navier--Stokes turbulence freely decaying from a smooth initial vorticity field $\omega(x,y,0)=\omega_0$. This number, denoted by $N$, is defined as the minimum…
We use the recently developed Macroscopic Forcing Method [Mani and Park, Physical Review Fluids, 6:054607, 2021] to compute the scale-dependent eddy diffusivity characterizing ensemble-averaged scalar and momentum transport in…
Using a recent alternative form of the Kolmogorov-Monin exact relation for fully developed hydrodynamics (HD) turbulence, the incompressible energy cascade rate $\varepsilon$ is computed. Under this current theoretical framework, for…
First, we consider Kolmogorov flow (a shear flow with a sinusoidal velocity profile) for 2D Navier-Stokes equation on a torus. Such flows, also called bar states, have been numerically observed as one type of metastable states in the study…
We study the statistical properties of orientation and rotation dynamics of elliptical tracer particles in two-dimensional, homogeneous and isotropic turbulence by direct numerical simulations. We consider both the cases in which the…
We extend the formalism of the statistical theory developed for the 2D Euler equation to the case of shallow water system. Relaxation equations towards the maximum entropy state are proposed, which provide a parametrization of sub-grid…
We consider the zero viscosity limit of long time averages of solutions of damped and driven Navier-Stokes equations in ${\mathbb R}^2$. We prove that the rate of dissipation of enstrophy vanishes. Stationary statistical solutions of the…
A particular interest on two-dimensional turbulence is the inverse energy cascade from small to large sales, which leads to an energy condensation accompanied by the formation of large-scale vortical structures. Indeed, such a phenomenon is…
We consider on the torus the scaling limit of stochastic 2D (inviscid) fluid dynamical equations with transport noise to deterministic viscous equations. Quantitative estimates on the convergence rates are provided by combining analytic and…
A simplified thermodynamic approach of the incompressible 2D Euler equation is considered based on the conservation of energy, circulation and microscopic enstrophy. Statistical equilibrium states are obtained by maximizing the…
Numerical and analytical studies of decaying, two-dimensional (2D) Navier-Stokes (NS) turbulence at high Reynolds numbers are reported. The effort is to determine computable distinctions between two different formulations of maximum entropy…