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We inquire the scaling properties of the 2d Navier-Stokes equation sustained by a forcing field with Gaussian statistics, white-noise in time and with power-law correlation in momentum space of degree $2-2 \eps$. This is at variance with…
Turbulence is a fundamental flow phenomenon, typically anisotropic at large scales and approximately isotropic at small scales. The classical Kolmogorov scaling laws (2/3, -5/3 and 4/5) have been well-established for turbulence without…
In this article we consider a damped version of the incompressible Navier-Stokes equations in the whole three-dimensional space with a divergence-free and time-independent external force. Within the framework of a well-prepared force and…
The subject of this work is the instability mechanism of simple shear flows, like Hagen-Poiseuille pipe flow, which is a long-standing problem in fluid mechanics [1,2]. A possible analogy with phenomenological theory of ideal plasticity in…
Nonlinear phenomena and turbulence are central to our understanding and modeling the dynamics of fluids and plasmas, and yet they still resist analytical resolutions in many instances. However, progress has been made recently, displaying a…
Advanced measurement techniques and high performance computing have made large data sets available for a wide range of turbulent flows that arise in engineering applications. Drawing on this abundance of data, dynamical models can be…
Using the observation that slip in simple fluids at low and moderate shear rates is a thermally activated process driven by the shear stress in the fluid close to the solid boundary, we develop a molecular-kinetic model for simple fluid…
Spontaneous emergence of periodic oscillations due to self-organization is ubiquitous in turbulent flows. The emergence of such oscillatory instabilities in turbulent fluid mechanical systems is often studied in different system-specific…
Multi-fractal scaling in the transition to the dissipative regime for fully-developed compressible turbulence is considered. The multi-fractal power law scaling behavior breaks down for very small length scales thanks to viscous effects.…
It is shown that in the presence of anisotropic kinetic dissipation existence of scale invariant power law spectrum of plasma turbulence is possible. Obtained scale invariant spectrum is not associated with the constant flux of any physical…
The feedback forces exerted by particles suspended in a turbulent flow is shown to lead to a new scaling law for velocity fluctuations associated to a power-spectra $\propto k^{-2}$. The mechanism at play relies on a direct transfer of…
State of the art numerical models of the Geodynamo are still performed in a parameter regime extremely remote from the values relevant to the physics of the Earth's core. In order to establish a connection between dynamo modeling and the…
Following the idea that dissipation in turbulence at high Reynolds number is by events singular in space-time and described by solutions of the inviscid Euler equations, we draw the conclusion that in such flows scaling laws should depend…
It is well known that the fluid-particle acceleration is intimately related to the dissipation rate of turbulence, in line with the Kolmogorov assumptions. On the other hand, various experimental and numerical works have reported as well…
Unbalanced probability circulation, which yields cyclic motions in phase space, is the defining characteristics of a stationary diffusion process without detailed balance. In over-damped soft matter systems, such behavior is a hallmark of…
We analyze a class of linear shell models subject to stochastic forcing in finitely many degrees of freedom. The unforced systems considered formally conserve energy. Despite being formally conservative, we show that these dynamical systems…
Passive scalar mixing (metals, molecules, etc.) in the turbulent interstellar medium (ISM) is critical for abundance patterns of stars and clusters, galaxy and star formation, and cooling from the circumgalactic medium. However, the…
We establish the large-time behavior for the coupled kinetic-fluid equations. More precisely, we consider the Vlasov equation coupled to the compressible isentropic Navier-Stokes equations through a drag forcing term. For this system, the…
The statistical properties of turbulence are considered to be universal at sufficiently small length scales, i. e., independent of boundary conditions and large-scale forces acting on the fluid. Analyzing data from numerical simulations of…
A method for finding reduced-order approximations of turbulent flow models is presented. The method preserves bounds on the production of turbulent energy in the sense of the $\curly{L}_2$ norm of perturbations from a notional laminar…