The Asymptotic State of Decaying Turbulence
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| Formato: | Preprint |
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2026
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| author | Rodhiya, Akash Sreenivasan, Katepalli R. |
| author_facet | Rodhiya, Akash Sreenivasan, Katepalli R. |
| contents | The long-time evolution of decaying homogeneous turbulence is a fundamental building block of the subject. We investigate the problem by using a comprehensive suite of Direct Numerical Simulations. The simulations cover initial Taylor microscale Reynolds numbers $Re_λ$ from $30 \text{ to } 145$, with multiple independent realizations obtained at each $Re_λ$ to ensure statistical robustness. The energy spectrum is initialized with the Birkhoff-Saffman (BS) form (with $E(k)\sim k^2$ for small $k$) in one case, and the Loitsianskii-Kolmogorov-Batchelor (LKB) form (with $E(k)\sim k^4$ for small $k$), in another. Simulations are performed for unprecedented durations, of the order of 200,000 initial eddy-turnover times in some instances. For both BS and LKB, the turbulent kinetic energy $En$ shows, after an initial transient, unambiguous power-law decay, $En\sim t^{-n}$, with nearly constant decay exponents $n$, whose values are consistent with past theoretical results (and thus not universal). We compute various length scales, second-order structure functions, and the spectral form at large wavenumbers; {we note that an initially set $-5/3$ slope disappears quickly, while a perceptible $-1$ power region appears.} In particular, we compare the present findings with predictions from the recent theory for decaying turbulence developed by Migdal \cite{migdal_this_issue}. The agreement for the BS case is excellent except for the large-wavenumber spectrum. A general discussion and assessment of results is provided in terms of the putative universality of energy decay. {A main conclusion is that the energy decay is significantly influenced by ``boundary effects", and that universality likely manifests only when those effects are removed. Alternatively, it may be more useful to discuss the universality of enstrophy decay.} |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12501 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Asymptotic State of Decaying Turbulence Rodhiya, Akash Sreenivasan, Katepalli R. Fluid Dynamics The long-time evolution of decaying homogeneous turbulence is a fundamental building block of the subject. We investigate the problem by using a comprehensive suite of Direct Numerical Simulations. The simulations cover initial Taylor microscale Reynolds numbers $Re_λ$ from $30 \text{ to } 145$, with multiple independent realizations obtained at each $Re_λ$ to ensure statistical robustness. The energy spectrum is initialized with the Birkhoff-Saffman (BS) form (with $E(k)\sim k^2$ for small $k$) in one case, and the Loitsianskii-Kolmogorov-Batchelor (LKB) form (with $E(k)\sim k^4$ for small $k$), in another. Simulations are performed for unprecedented durations, of the order of 200,000 initial eddy-turnover times in some instances. For both BS and LKB, the turbulent kinetic energy $En$ shows, after an initial transient, unambiguous power-law decay, $En\sim t^{-n}$, with nearly constant decay exponents $n$, whose values are consistent with past theoretical results (and thus not universal). We compute various length scales, second-order structure functions, and the spectral form at large wavenumbers; {we note that an initially set $-5/3$ slope disappears quickly, while a perceptible $-1$ power region appears.} In particular, we compare the present findings with predictions from the recent theory for decaying turbulence developed by Migdal \cite{migdal_this_issue}. The agreement for the BS case is excellent except for the large-wavenumber spectrum. A general discussion and assessment of results is provided in terms of the putative universality of energy decay. {A main conclusion is that the energy decay is significantly influenced by ``boundary effects", and that universality likely manifests only when those effects are removed. Alternatively, it may be more useful to discuss the universality of enstrophy decay.} |
| title | The Asymptotic State of Decaying Turbulence |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2602.12501 |