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Curvature effect in shear flow: slowdown of turbulent flame speeds with Markstein number

Jiancheng Lyu University of California at Irvine Jack Xin University of California at Irvine Yifeng Yu University of California at Irvine

Analysis of PDEs mathscidoc:1802.03001

Comm. Math Physics, 2017
It is well-known in the combustion community that curvature effect in general slows down ame propagation speeds because it smooths out wrinkled ames. However, such a folklore has never been justi ed rigorously. In this paper, as the rst theoretical result in this direction, we prove that the turbulent ame speed (an e ective burning velocity) is decreasing with respect to the curvature di usivity (Markstein number) for shear flows in the well-known G-equation model. Our proof involves several novel and rather sophisticated inequalities arising from the nonlinear structure of the equation. On a related fundamental issue, we solve the selection problem of weak solutions or nd the "physical fluctuations" when the Markstein number goes to zero and solutions approach those of the inviscid G-equation model. The limiting solution is given by a closed form analytical formula.
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  • arxiv 1703.07050
@inproceedings{jiancheng2017curvature,
  title={Curvature effect in shear flow: slowdown of turbulent flame speeds with Markstein number},
  author={Jiancheng Lyu, Jack Xin, and Yifeng Yu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180214110013008894924},
  booktitle={Comm. Math Physics},
  year={2017},
}
Jiancheng Lyu, Jack Xin, and Yifeng Yu. Curvature effect in shear flow: slowdown of turbulent flame speeds with Markstein number. 2017. In Comm. Math Physics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180214110013008894924.
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