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arXiv · 2412.18502

Does Yakhot's growth law for turbulent burning velocity hold?

Wenjia Jing·Jack Xin·Yifeng Yu
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Abstract

Using formal renormalization theory, Yakhot derived in ([32], 1988) an $O\left(\frac{A}{\sqrt{\log A}}\right)$ growth law of the turbulent flame speed with respect to large flow intensity $A$ based on the inviscid G-equation. Although this growth law is widely cited in combustion literature, there has been no rigorous mathematical discussion to date about its validity. As a first step towards unveiling the mystery, we prove that there is no intermediate growth law between $O\left(\frac{A}{\log A}\right)$ and $O(A)$ for two dimensional incompressible Lipschitz continuous periodic flows with bounded swirl sizes. In particular, we do not assume the non-degeneracy of critical points. Additionally, other examples of flows with lower regularity, Lagrangian chaos, and related phenomena are also discussed.

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Wenjia Jing, Jack Xin, Yifeng Yu. 2025-01-13. Does Yakhot's growth law for turbulent burning velocity hold?. https://arxiv.org/abs/2412.18502

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