Related papers: Anomalous dissipation and regularization in isotro…
The problem of anomalous diffusion in momentum (velocity) space is considered based on the master equation and the appropriate probability transition function (PTF). The approach recently developed by the author for coordinate space, is…
The energy dissipation in the inviscid limit is a central problem in turbulence theory. Kolmogorov's K41 theory predicts a positive dissipation rate independent of viscosity -- a phenomenon known as anomalous dissipation. Bru\'e and De…
We study a model of fully developed turbulence of a compressible fluid, based on the stochastic Navier-Stokes equation, by means of the field theoretic renormalization group. In this approach, scaling properties are related to the fixed…
We investigate the Navier-Stokes turbulence driven by a stochastic random Gaussian force. Using a field-theoretic approach, we uncover an anomaly that brings hidden structure to the theory. The anomaly is generated by a non-self-adjoint…
Anomalous dissipation is a dissipation mechanism of kinetic energy which is established by a sufficiently spatially rough velocity field. It implies that the rescaled mean kinetic energy dissipation rate becomes constant with respect to…
Diffusion with stochastic transport is investigated here when the random driving process is a very general Gaussian process, including Fractional Brownian motion. The purpose is the comparison with a deterministic PDE, which in certain…
The modelling of fluid particle accelerations in homogeneous, isotropic turbulence in terms of second-order stochastic models for the Lagrangian velocity is considered. The basis for the Reynolds model (A. M. Reynolds, \textit{Phys. Rev.…
We study the Lagrangian trajectories of statistically isotropic, homogeneous, and stationary divergence free spatiotemporal random vector fields. We design this advecting Eulerian velocity field such that it gets asymptotically rough and…
We propose a novel approach to induce anomalous dissipation through advection driven by turbulent fluid flows. Specifically, we establish the existence of a velocity field $v$ satisfying randomly forced Navier-Stokes equations, leading to…
We show anomalous dissipation of scalars advected by weak solutions to the incompressible Euler equations with $C^{(\sfrac{1}{3})^-}$ regularity, for an arbitrary initial datum in $\dot H^1 (\T^3)$. This is the first rigorous derivation of…
We investigate the dynamics of a single tracer exploring a course of fixed obstacles in the vicinity of the percolation transition for particles confined to the infinite cluster. The mean-square displacement displays anomalous transport,…
In this paper, we show that suitable transport noises produce anomalous dissipation of both enstrophy of solutions to 2D Navier-Stokes equations and of energy of solutions to diffusion equations in all dimensions. The key ingredients are…
Spontaneous stochasticity is a modern paradigm for turbulent transport at infinite Reynolds numbers. It suggests that tracer particles advected by rough turbulent flows and subject to additional thermal noise, remain non-deterministic in…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
Turbulent viscosity is frequently used in accretion disk theory to replace the microphysical viscosity in order to accomodate the observational need for in- stabilities in disks that lead to enhanced transport. However, simply replacing the…
We investigate the statistical properties, based on numerical simulations and analytical calculations, of a recently proposed stochastic model for the velocity field of an incompressible, homogeneous, isotropic and fully developed turbulent…
The statistical features of homogeneous, isotropic, two-dimensional stochastic turbulence are discussed. We derive some rigorous bounds for the mean value of the bulk energy dissipation rate $\mathbb{E} [\varepsilon ]$ and enstrophy…
Transport in collisionless plasmas is usually called anomalous, being due to the interaction between the particles and the self-generated turbulence by their collective interactions. Because of its relevance for astrophysical and space…
We investigate dissipative anomalies in a turbulent fluid governed by the compressible Navier-Stokes equation. We follow an exact approach pioneered by Onsager, which we explain as a non-perturbative application of the principle of…
The stochastic motion in a nonhomogeneous medium with traps is studied and diffusion properties of that system are discussed. The particle is subjected to a stochastic stimulation obeying a general L\'evy stable statistics and experiences…