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Curvature Effect in Shear Flow: Slowdown of Turbulent Flame Speeds with Markstein Number

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Abstract

It is well-known in the combustion community that curvature effect in general slows down flame propagation speeds because it smooths out wrinkled flames. However, such a folklore has never been justified rigorously. In this paper, as the first theoretical result in this direction, we prove that the turbulent flame speed (an effective burning velocity) is decreasing with respect to the curvature diffusivity (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 find 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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Authors and Affiliations

  1. Department of Mathematics, University of California at Irvine, Irvine, CA, 92697, USA

    Jiancheng Lyu, Jack Xin & Yifeng Yu

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  1. Jiancheng Lyu
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  2. Jack Xin
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  3. Yifeng Yu
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Corresponding author

Correspondence to Yifeng Yu.

Additional information

Communicated by L. Caffarelli

The work was partly supported by NSF Grants DMS-1211179 (JX), DMS-0901460 (YY), and CAREER Award DMS-1151919 (YY).

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Lyu, J., Xin, J. & Yu, Y. Curvature Effect in Shear Flow: Slowdown of Turbulent Flame Speeds with Markstein Number. Commun. Math. Phys. 359, 515–533 (2018). https://doi.org/10.1007/s00220-017-3060-1

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  • DOI: https://doi.org/10.1007/s00220-017-3060-1

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