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A variational principle based study of KPP minimal front speeds in random shears

Publication ,  Journal Article
Nolen, J; Xin, J
Published in: Nonlinearity
2005

The variational principle for Kolmogorov-Petrovsky-Piskunov (KPP) minimal front speeds provides an efficient tool for statistical speed analysis, as well as a fast and accurate method for speed computation. A variational principle based analysis is carried out on the ensemble of KPP speeds through spatially stationary random shear flows inside infinite channel domains. In the regime of small root mean square (rms) shear amplitude, the enhancement of the ensemble averaged KPP front speeds is proved to obey the quadratic law under certain shear moment conditions. Similarly, in the large rms amplitude regime, the enhancement follows the linear law. In particular, both laws hold for the Ornstein-Uhlenbeck (O-U) process in the case of two-dimensional channels. An asymptotic ensemble averaged speed formula is derived in the small rms regime and is explicit in the case of the O-U process of the shear. The variational principle based computation agrees with these analytical findings, and allows further study of the speed enhancement distributions as well as the dependence of the enhancement on the shear covariance. Direct simulations in the small rms regime suggest a quadratic speed enhancement law for non-KPP nonlinearities. © 2005 IOP Publishing Ltd and London Mathematical Society.

Duke Scholars

Published In

Nonlinearity

DOI

Publication Date

2005

Volume

18

Issue

4

Start / End Page

1655 / 1675

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
 

Citation

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Nolen, J., & Xin, J. (2005). A variational principle based study of KPP minimal front speeds in random shears. Nonlinearity, 18(4), 1655–1675. https://doi.org/10.1088/0951-7715/18/4/013
Nolen, J., and J. Xin. “A variational principle based study of KPP minimal front speeds in random shears.” Nonlinearity 18, no. 4 (2005): 1655–75. https://doi.org/10.1088/0951-7715/18/4/013.
Nolen, J., and J. Xin. “A variational principle based study of KPP minimal front speeds in random shears.” Nonlinearity, vol. 18, no. 4, 2005, pp. 1655–75. Scival, doi:10.1088/0951-7715/18/4/013.
Nolen J, Xin J. A variational principle based study of KPP minimal front speeds in random shears. Nonlinearity. 2005;18(4):1655–1675.

Published In

Nonlinearity

DOI

Publication Date

2005

Volume

18

Issue

4

Start / End Page

1655 / 1675

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics