Self-Similar Decay in the Kraichnan Model of a Passive Scalar

1999/10/15 by Gregory L. Eyink, G. Eyink, Jack Xin +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics #chao-dyn #cond-mat.stat-mech #math-ph #math.MP #nlin.CD

paper · pdf · doi:10.48550/arxiv.chao-dyn/9910022

Now 68 pages. A proof of nonrealizability of scaling solutions with a>(d+γ)/γis added. Other minor changes and improvements. Accepted to appear in J. Stat. Phys

openalex publication_date 1999/10/15 · arxiv created 2000/03/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the two-point correlation function of a freely decaying scalar in Kraichnan's model of advection by a Gaussian random velocity field, stationary and white-noise in time but fractional Brownian in space with roughness exponent 0

Citations

• Lectures on Phase Transitions and the Renormalization Group
• Turbulent decay of a passive scalar in the Batchelor limit: Exact results from a quantum-mechanical approach

Cited by

• Emergence of long-range non-equilibrium correlations in free liquid diffusion

Related

• On the Kraichnan Model of Passive Scalar Advection Near the Batchelor limit
• Anomalous Regularization in Kraichnan's Passive Scalar Model
• On anomalous diffusion in the Kraichnan model and correlated-in-time variants
• Numerical Proof of Self-Similarity in Burgers' Turbulence
• Universality of the Inertial-Convective Range in Kraichnan's Model of a Passive Scalar