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| Autori principali: | , , |
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| Natura: | Preprint |
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2024
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| Accesso online: | https://arxiv.org/abs/2412.18502 |
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| _version_ | 1866909454874705920 |
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| author | Jing, Wenjia Xin, Jack Yu, Yifeng |
| author_facet | Jing, Wenjia Xin, Jack Yu, Yifeng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18502 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Does Yakhot's growth law for turbulent burning velocity hold? Jing, Wenjia Xin, Jack Yu, Yifeng Analysis of PDEs Fluid Dynamics 35B27, 35B40, 35F21 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. |
| title | Does Yakhot's growth law for turbulent burning velocity hold? |
| topic | Analysis of PDEs Fluid Dynamics 35B27, 35B40, 35F21 |
| url | https://arxiv.org/abs/2412.18502 |