2004/04/30 by A. A. Schekochihin, Peter Haynes, P. H. Haynes +1 · 3 citations
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Fluid Dynamics and Turbulent Flows #Meteorological Phenomena and Simulations #Quantum chaos and dynamical systems #astro-ph #nlin.CD #physics.ao-ph #physics.flu-dyn
paper · pdf · doi:10.1103/physreve.70.046304
published as Phys.Rev.E70:046304,2004 · revtex4, 8 pages, 4 figures; final published version
openalex publication_date 2004/10/13 · arxiv created 2004/12/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a solvable model of the decay of scalar variance in a single-scale random velocity field. We show that if there is a separation between the flow scale kflow^\ensuremath-1 and the box size kbox^\ensuremath-1, the decay rate \ensuremathλ\ensuremath∝(kbox∕kflow)2 is determined by the turbulent diffusion of the box-scale mode. Exponential decay at the rate \ensuremathλ is preceded by a transient powerlike decay (the total scalar variance \ensuremath∼t^\ensuremath-5∕2 if the Corrsin invariant is zero, t^\ensuremath-3∕2 otherwise) that lasts a time t\ensuremath∼1∕\ensuremathλ. Spectra are sharply peaked at k=kbox. The box-scale peak acts as a slowly decaying source to a secondary peak at the flow scale. The variance spectrum at scales intermediate between the two peaks (kbox⪡k⪡kflow) is \ensuremath∼k+ak2+…\phantom\rule0.3em0ex(a>0). The mixing of the flow-scale modes by the random flow produces, for the case of large P'eclet number, a k^\ensuremath-1+\ensuremathδ spectrum at k⪢kflow, where \ensuremathδ\ensuremath∝\ensuremathλ is a small correction. Our solution thus elucidates the spectral make up of the ``strange mode,'' combining small-scale structure and a decay law set by the largest scales.