Related papers: Eddy diffusivities in scalar transport
Diffusive motion is a fundamental transport mechanism in physical and biological systems, governing dynamics across a wide range of scales -- from molecular transport to animal foraging. In many complex systems, however, diffusion deviates…
An eigenvalue equation, for linear instability modes involving large scales in a convective hydromagnetic system, is derived in the framework of multiscale analysis. We consider a horizontal layer with electrically conducting boundaries,…
We study uncertainty in the dynamics of time-dependent flows by identifying barriers and enhancers to stochastic transport. This topological segmentation is closely related to the theory of Lagrangian coherent structures and is based on a…
This paper investigates L\'evy walks with random velocities, extending classical models beyond constant speed assumptions. We derive scaling limits, demonstrating that diffusion depends on interplay between heavy-tailed duration and…
We study anomalous dissipation in hydrodynamic turbulence in the context of passive scalars. Our main result produces an incompressible $C^\infty([0,T)\times \mathbb{T}^d)\cap L^1([0,T]; C^{1-}(\mathbb{T}^d))$ velocity field which…
We formulate a scaling theory for the long-time diffusive motion in a space occluded by a high density of moving obstacles in dimensions 1, 2 and 3. Our tracers diffuse anomalously over many decades in time, before reaching a diffusive…
Coarse resolution numerical ocean models must typically include a parameterisation for mesoscale turbulence. A common recipe for such parameterisations is to invoke down-gradient mixing, or diffusion, of some tracer quantity, such as…
Levy flights and subdiffusive processes and their properties are discussed. We derive the space- and time-fractional transport equations, and consider their solutions in external potentials. An extensive list of references is included.
Explicit examples of scalar enhanced diffusion due to resonances between different transport mechanisms are presented. Their signature is provided by the sharp and narrow peaks observed in the effective diffusivity coefficients and, in the…
We study far from equilibrium transport of a periodically driven inertial Brownian particle moving in a periodic potential. As detected recently for a SQUID ratchet dynamics (Spiechowicz J. & Luczka J. Phys. Rev. E 91, 062104 (2015)), the…
The advection-diffusion equation is studied via a global Lagrangian coordinate transformation. The metric tensor of the Lagrangian coordinates couples the dynamical system theory rigorously into the solution of this class of partial…
Frozen parametric disorder can lead to appearance of sets of localized convective currents in an otherwise stable (quiescent) fluid layer heated from below. These currents significantly influence the transport of an admixture (or any other…
A generalization of the Drude model is studied. On the one hand, the free motion of the particles is allowed to be sub- or superdiffusive; on the other hand, the distribution of the time delay between collisions is allowed to have a long…
Under low-Reynolds-number conditions, dynamics of convection and diffusion are usually considered separately because their dominant spatial and temporal scales are different, but cooperative effects of convection and diffusion can cause…
Standard eddy viscosity models, while robust, cannot represent backscatter and have severe difficulties with complex turbulence not at statistical equilibrium. This report gives a new derivation of eddy viscosity models from an equation for…
This study considers advective and diffusive transport of passive scalar fields by spatially-varying incompressible flows. Prior studies have shown that the eddy diffusivities governing the mean field transport in such systems can generally…
The dimensionality of turbulence in fluid layers determines their properties. We study electromagnetically driven flows in finite depth fluid layers and show that eddy viscosity, which appears as a result of three-dimensional motions, leads…
We study anomalous dissipation from a microscopic viewpoint. In the work by Drivas, Elgindi, Iyer and Jeong (2022), the property of anomalous dissipation provides the existence of non-unique weak solutions for a transport equation with a…
The issue of the parameterization of small scale (``subgrid'') turbulence is addressed in the context of passive scalar transport. We focus on the Kraichnan advection model which lends itself to the analytical investigation of the closure…
The original goal of Large Eddy Simulations of fully developed turbulent flows was to accurately describe large-scale flow features ${\bf u}(\Delta)$ at the scales $r\geq \Delta$ where $\Delta$ is a size of computational mesh. The effect of…