Related papers: A Simple Passive Scalar Advection-Diffusion Model
Scale independence is a ubiquitous feature of complex systems which implies a highly skewed distribution of resources with no characteristic scale. Research has long focused on why systems as varied as protein networks, evolution and stock…
Stationary probability distributions of one-dimensional random walks on lattices with aperiodic disorder are investigated. The pattern of the distribution is closely related to the diffusional behavior, which depends on the wandering…
We discuss on an example a general mechanism of apparition of anomalous scaling in scale invariant systems via zero modes of a scale invariant operator. We discuss the relevance of such mechanism in turbulence, and point out a peculiarity…
We study the dynamic scaling hypothesis in invariant surface growth. We show that the existence of power-law scaling of the correlation functions (scale invariance) does not determine a unique dynamic scaling form of the correlation…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
Implicit time-stepping for advection is applied locally in space and time where Courant numbers are large, but standard explicit time-stepping is used for the remaining solution which is typically the majority. This adaptively implicit…
Recent theoretical progress using multiscale asymptotic analysis has revealed various possible regimes of stratified turbulence. Notably, buoyancy transport can either be dominated by advection or diffusion, depending on the effective…
The effects of passive scalar anisotropy on subgrid-scale (SGS) physics and modeling for Large-Eddy Simulations are studied experimentally. Measurements are performed across a moderate Reynolds number wake flow generated by a heated…
We test the ability of a general low-dimensional model for turbulence to predict geometry-dependent dynamics of large-scale coherent structures, such as convection rolls. The model consists of stochastic ordinary differential equations,…
One challenge in developing a statistical field theory of turbulence is the analysis of the functional equations that govern the complete statistics of the flow field. Simplified models of turbulence may help to develop such a statistical…
Using high-fidelity numerical simulations based on a lattice Boltzmann framework, the advection-enhanced transport of a passive scalar from a prolate spheroid in simple shear flow has been thoroughly investigated across various parameters,…
Active and passive scalars transported by an incompressible two-dimensional conductive fluid are investigated. It is shown that a passive scalar displays a direct cascade towards the small scales while the active magnetic potential builds…
We provide a concise PDE-based proof of anomalous diffusion in the Kraichan model -- a stochastic, white-in-time model of passive scalar turbulence. That is, we show an exponential rate of $L^2$ decay in expectation of a passive scalar…
The phenomenology of the scaling behavior of higher order structure functions of velocity differences across a scale $R$ in turbulence should be built around the irreducible representations of the rotation symmetry group. Every irreducible…
This article concerns a systemic manifestation of small scale interfacial heterogeneities in large scale quantities of interest to a variety of diverse applications spanning the earth, biological and ecological sciences. Beginning with…
The decay of a passive scalar in a three-dimensional chaotic flow is studied using high-resolution numerical simulations. The (volume-preserving) flow considered is a three-dimensional extension of the randomised alternating sine flow…
A new approach to the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence has been proposed and tested through numerical simulations. This is achieved by constructing, for any given nonlinear…
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…
Stochastic models for spatio-temporal transport face a critical trade-off between physical realism and interpretability. The advection model with a single constant velocity is interpretable but physically limited by its perfect correlation…
We show that the limiting variance of a sequence of estimators for a structured covariance matrix has a general form that appears as the variance of a scaled projection of a random matrix that is of radial type and a similar result is…