2005/01/03 by Gregory Falkovich, A. Fouxon, Alexander Fouxon · 25 citations
Economics, Econometrics and Finance · Engineering · Mathematics · Physics and Astronomy · #Classical mechanics #Complex Systems and Time Series Analysis #Compressibility #Domain (mathematical analysis) #Fluid Dynamics and Turbulent Flows #Geometry #Mathematical analysis #Mathematics #Mechanics #Physics #Quantum mechanics #Scalar (mathematics) #Scale (ratio) #Scale invariance #Scaling #Statistical Mechanics and Entropy #Statistical physics #Turbulence #cond-mat.stat-mech #hep-th #nlin.CD #physics.flu-dyn
paper · pdf · doi:10.1103/physrevlett.94.214502
published in Physical Review Letters 94(21), 214502 (American Physical Society)
arxiv created 2005/01/03 · openalex publication_date 2005/06/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We analyze the multipoint correlation functions of a tracer in an incompressible flow at scales far exceeding the scale L at which fluctuations are generated (quasiequilibrium domain) and compare them with the correlation functions at scales smaller than L (turbulence domain). We demonstrate that scale invariance can be broken in the equilibrium domain and trace this breakdown to the statistical integrals of motion (zero modes) as has been done before for turbulence. Employing the Kraichnan model of short-correlated velocity we identify the new type of zero modes, which break scale invariance and determine an anomalously slow decay of correlations at large scales.