Methods and Applications of Analysis

Variational Principle Based Computation of KPP Average Front Speeds in Random Shear Flows

James Nolen and Jack Xin

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Abstract

Variational principle of Kolmogorov-Petrovsky-Piskunov (KPP) minimal front speeds provides a fast and accurate way for speed calculations. A variational principle based computation is carried out on a large ensemble of KPP random speeds through spatial, mean zero, stationary, Gaussian random shear flows inside two dimensional channel domains. In the regime of small root mean square (rms) shear amplitude, the enhancement of the ensemble averaged KPP front speed obeys the quadratic law. In the large rms amplitude regime, the enhancement follows the linear law. An asymptotic ensemble averaged speed formula is derived and agrees well with the numerics. Related theoretical results are presented with a brief outline of the ideas in the proofs. The ensemble averaged speed is found to increase sublinearly with enlarging channel widths, while the speed variance decreases. Direct simulations in the small rms regime suggest quadratic speed enhancement law for non-KPP nonlinearities.

Article information

Source
Methods Appl. Anal., Volume 11, Number 3 (2004), 389-398.

Dates
First available in Project Euclid: 11 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.maa/1147353061

Mathematical Reviews number (MathSciNet)
MR2214682

Zentralblatt MATH identifier
1128.76050

Citation

Nolen, James; Xin, Jack. Variational Principle Based Computation of KPP Average Front Speeds in Random Shear Flows. Methods Appl. Anal. 11 (2004), no. 3, 389--398. https://projecteuclid.org/euclid.maa/1147353061


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