Mathematical models with exact renormalization for turbulent transport. II: Fractal interfaces, non-Gaussian statistics and the sweeping effect
type: Item
instance of: scholarly article
title: Mathematical models with exact renormalization for turbulent transport. II: Fractal interfaces, non-Gaussian statistics and the sweeping effect
zbMATH Open document ID: 0754.76046
DOI: 10.1007/BF02099212
author: Marco Avellaneda
author: Andrew J. Majda
published in: Communications in Mathematical Physics
publication date: 1992-09-27T00:00:00Z
review text: [For part I see: Commun. Math. Phys. 131, No. 2, 381-429 (1990; Zbl 0703.76042).] This paper continues the study of a model for turbulent transport with an exact renormalization theory which has recently been proposed and developed by the authors. Three important topics are analyzed with complete mathematical rigor for this model: (1) Renormalized higher order statistics of a passively advected scalar such as the pair distance distribution and the fractal dimension of interfaces, (2) the effect of non-Gaussian turbulent velocity statistics on renormalization theory, (3) the ``sweeping'' effect of additional large scale mean velocities. A special emphasis is placed on renormalization theory in the vicinity of the value of the analogue of the Kolmogorov-spectrum in the model.
Mathematics Subject Classification ID: 76F20
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 61999
zbMATH Keywords: renormalized higher order statistics
zbMATH Keywords: fractal dimension
zbMATH Keywords: Kolmogorov- spectrum
MaRDI profile type: Publication
cites work: Mathematical models with exact renormalization for turbulent transport
cites work: Approximate and exact renormalization theories for a model for turbulent transport
cites work: An integral representation and bounds on the effective diffusivity in passive advection by laminar and turbulent flows
cites work: Q3974081
cites work: Q5560061
cites work: A Limit Theorem for Solutions of Differential Equations with Random Right-Hand Side
cites work: Navier-Stokes equations and area of interfaces
cites work: Q5512461
cites work: Some Limit Theorems for Stationary Processes
cites work: A limit theorem for turbulent diffusion
cites work: Ergodic Properties of Recurrent Diffusion Processes and Stabilization of the Solution to the Cauchy Problem for Parabolic Equations
cites work: Anomalous diffusion due to long-range velocity fluctuations in the absence of a mean flow
cites work: The method of averaging and walks in inhomogeneous environments
cites work: Q4003710
cites work: Q5585820
cites work: Some specific features of atmospheric tubulence
cites work: Homogenization of a diffusion process in a divergence-free random field
cites work: Gaussian sample functions and the Hausdorff dimension of level crossings
cites work: A central limit theorem for \(m\)-dependent random variables
cites work: Analytical theory of turbulent diffusion
cites work: Eddy diffusivity, eddy noise and subgrid-scale modelling
cites work: Renormalization group analysis of turbulence. I: Basic theory
cites work: Diffusion and geometric effects in passive advection by random arrays of vortices
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description: scientific article; zbMATH DE number 61999