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Statistical analysis of a semilinear hyperbolic system advected by a white in time random velocity field

Gregory Eyink Jack Xin

Statistics Theory and Methods mathscidoc:1912.43903

Nonlinearity, 15, (3), 551, 2002.3
We study a system of semilinear hyperbolic equations passively advected by smooth white noise in time random velocity fields. Such a system arises in modelling non-premixed isothermal turbulent flames under single-step kinetics of fuel and oxidizer. We derive closed equations for one-point and multi-point probability distribution functions (PDFs) and closed-form analytical formulae for the one-point PDF function, as well as the two-point PDF function under homogeneity and isotropy. Exact solution formulae allow us to analyse the ensemble-averaged fuel/oxidizer concentrations and the motion of their level curves. We recover the empirical formulae of combustion in the thin reaction zone limit and show that these approximate formulae can either underestimate or overestimate average concentrations when the reaction zone is not tending to zero. We show that the averaged reaction rate slows down locally in
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@inproceedings{gregory2002statistical,
  title={Statistical analysis of a semilinear hyperbolic system advected by a white in time random velocity field},
  author={Gregory Eyink, and Jack Xin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210541035587467},
  booktitle={Nonlinearity},
  volume={15},
  number={3},
  pages={551},
  year={2002},
}
Gregory Eyink, and Jack Xin. Statistical analysis of a semilinear hyperbolic system advected by a white in time random velocity field. 2002. Vol. 15. In Nonlinearity. pp.551. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210541035587467.
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