Lattice models of advection-diffusion

Chaos
Raymond T. Pierrehumbert

Abstract

We present a synthesis of theoretical results concerning the probability distribution of the concentration of a passive tracer subject to both diffusion and to advection by a spatially smooth time-dependent flow. The freely decaying case is contrasted with the equilibrium case. A computationally efficient model of advection-diffusion on a lattice is introduced, and used to test and probe the limits of the theoretical ideas. It is shown that the probability distribution for the freely decaying case has fat tails, which have slower than exponential decay. The additively forced case has a Gaussian core and exponential tails, in full conformance with prior theoretical expectations. An analysis of the magnitude and implications of temporal fluctuations of the conditional diffusion and dissipation is presented, showing the importance of these fluctuations in governing the shape of the tails. Some results concerning the probability distribution of dissipation, and concerning the spatial scaling properties of concentration fluctuation, are also presented. Though the lattice model is applied only to smooth flow in the present work, it is readily applicable to problems involving rough flow, and to chemically reacting tracers. (c) 2000 Am...Continue Reading

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Citations

May 9, 2013·Proceedings of the National Academy of Sciences of the United States of America·Georg A Gottwald, Ian Melbourne
Jun 5, 2003·Chaos·Jean-Luc Thiffeault, Stephen Childress
Jun 22, 2005·Journal of Theoretical Biology·György KárolyiIstván Scheuring
Jan 20, 2018·Physical Review. E·J M García de la CruzL Rossi
Dec 17, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alexander A SchekochihinSteven C Cowley
May 9, 2008·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·J David NeelinChristopher E Holloway
Aug 11, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Izabella Júlia Benczik
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Daniel A BirchWilliam R Young
Aug 8, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N Nirmal Thyagu, Neelima Gupte
Jul 7, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·K Ngan, J Vanneste
Mar 16, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Lennon O Náraigh, Jean-Luc Thiffeault
Jul 13, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jai Sukhatme
Aug 11, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Yue-Kin TsangEdward Ott
May 16, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·D Martinand, J C Vassilicos
Nov 13, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N Nirmal Thyagu, Neelima Gupte
Oct 15, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·E GouillartJ-L Thiffeault
Aug 11, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Weijiu Liu
Jan 7, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A Wonhas, J C Vassilicos
Mar 23, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·D R FeredayJ C Vassilicos

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