Non-Gaussian invariant measures for the Majda model of decaying turbulent transport

DOI10.1002/cpa.3001zbMath1036.76025OpenAlexW2135031046MaRDI QIDQ4790275

Eric Vanden-Eijnden

Publication date: 28 January 2003

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/cpa.3001

zbMATH Keywords

probability distributionvelocity fieldpassive scalar advectionintermittencyturbulent transportMajda modelfinite correlation timeinfinite correlation time

Mathematics Subject Classification ID

Statistical turbulence modeling (76F55) Applications of stochastic analysis (to PDEs, etc.) (60H30) Turbulent transport, mixing (76F25)

Related Items (14)

Dynamics of probability density functions for decaying passive scalars in periodic velocity fields ⋮ Non-Gaussian limit of a tracer motion in an incompressible flow ⋮ Ergodicity and invariant measures for a diffusing passive scalar advected by a random channel shear flow and the connection between the Kraichnan-Majda model and Taylor-Aris dispersion ⋮ Elementary models for turbulent diffusion with complex physical features: eddy diffusivity, spectrum and intermittency ⋮ On the symmetry properties of a random passive scalar with and without boundaries, and their connection between hot and cold states ⋮ An explicit family of probability measures for passive scalar diffusion in a random flow ⋮ An internal splash: Levitation of falling spheres in stratified fluids ⋮ Evolution of the probability measure for the Majda model: new invariant measures and breathing PDFs ⋮ Intermittency in passive scalar decay ⋮ Conditional statistics for a passive scalar with a mean gradient and intermittency ⋮ Analysis of a stratified Kraichnan flow ⋮ Enhanced diffusivity and skewness of a diffusing tracer in the presence of an oscillating wall ⋮ Linear and nonlinear statistical response theories with prototype applications to sensitivity analysis and statistical control of complex turbulent dynamical systems ⋮ Persisting asymmetry in the probability distribution function for a random advection-diffusion equation in impermeable channels

Cites Work

• Slow modes in passive advection
• Small ball estimates for Gaussian processes under Sobolev type norms
• The problem of moments and the Majda model for scalar intermittency
• Phase transition in the passive scalar advection
• Rigorous estimates of the tails of the probability distribution function for the random linear shear model.
• Explicit inertial range renormalization theory in a model for turbulent diffusion
• The random uniform shear layer: An explicit example of turbulent diffusion with broad tail probability distributions
• An explicit example with non-Gaussian probability distribution for nontrivial scalar mean and fluctuation
• Generalized flows, intrinsic stochasticity, and turbulent transport
• Small-Scale Structure of a Scalar Field Convected by Turbulence
• Scalar intermittency and the ground state of periodic Schrödinger equations

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