1996/05/23 by Gregory L. Eyink, Gregory Eyink, Jack Xin +2
Biochemistry, Genetics and Molecular Biology · Earth and Planetary Sciences · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Geomagnetism and Paleomagnetism Studies #Geophysics and Gravity Measurements #chao-dyn #nlin.CD
paper · pdf · doi:10.48550/arxiv.chao-dyn/9605012
4 pages, olatex, submitted to Phys. Rev. Letter
arxiv created 1996/05/23 · openalex publication_date 1996/05/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish by exact, nonperturbative methods a universality for the correlation functions in Kraichnan's ``rapid-change'' model of a passively advected scalar field. We show that the solutions for separated points in the convective range of scales are unique and independent of the particular mechanism of the scalar dissipation. Any non-universal dependences therefore must arise from the large length-scale features. The main step in the proof is to show that solutions of the model equations are unique even in the idealized case of zero diffusivity, under a very modest regularity requirement (square-integrability). Within this regularity class the only zero-modes of the global many-body operators are shown to be trivial ones (i.e. constants). In a bounded domain of size L, with physical boundary conditions, the ``ground-state energy'' is strictly positive and scales as L-γ with an exponent γ>0.