تقرير
Renormalization of shell model of turbulence
| العنوان: | Renormalization of shell model of turbulence |
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| المؤلفون: | Verma, Mahendra K., Alam, Shadab |
| سنة النشر: | 2023 |
| المجموعة: | Condensed Matter High Energy Physics - Theory Physics (Other) |
| مصطلحات موضوعية: | Physics - Fluid Dynamics, Condensed Matter - Statistical Mechanics, High Energy Physics - Theory |
| الوصف: | Renormalization enables a systematic scale-by-scale analysis of multiscale systems. In this paper, we employ \textit{renormalization group} (RG) to the shell model of turbulence and show that the RG equation is satisfied by $ |u_n|^2 =K_\mathrm{Ko} \epsilon^{2/3} k_n^{-2/3}$ and $ \nu_n = \nu_* \sqrt{K_\mathrm{Ko}} \epsilon^{1/3} k_n^{-4/3}$, where $k_n, u_n $ are the wavenumber and velocity of shell $ n $; $\nu_*, K_\mathrm{Ko}$ are RG and Kolmogorov's constants; and $ \epsilon $ is the energy dissipation rate. We find that $\nu_* \approx 0.5$ and $K_\mathrm{Ko} \approx 1.7$, consistent with earlier RG works on Navier-Stokes equation. We verify the theoretical predictions using numerical simulations. Comment: To appear in Phys. Rev. E |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1103/PhysRevE.107.064118 |
| URL الوصول: | http://arxiv.org/abs/2306.10027 |
| رقم الأكسشن: | edsarx.2306.10027 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1103/PhysRevE.107.064118 |
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