Diffusion of passive scalar in a finite-scale random flow

• Published in: Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2004-10, Vol.70 (4 Pt 2), p.046304-046304, Article 046304
• Main Authors: Schekochihin, Alexander A, Haynes, Peter H, Cowley, Steven C
• Format: Article
• Language: English
• ISSN: 1539-3755; 1550-2376
• DOI: 10.1103/PhysRevE.70.046304

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 k(-1 )(flow ) and the box size k(-1 )(box ) , the decay rate lambda proportional, variant ( k(box) / k(flow) )(2) is determined by the turbulent diffusion of the box-scale mode. Exponential decay at the rate lambda is preceded by a transient powerlike decay (the total scalar variance approximately t(-5/2) if the Corrsin invariant is zero, t(-3/2) otherwise) that lasts a time t approximately 1/lambda . Spectra are sharply peaked at k= k(box) . 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 ( k(box) k(flow) , where delta proportional lambda 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.