Forward and inverse energy cascade and fluctuation relation in fluid turbulence adhere to Kolmogorov's refined similarity hypothesis
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| Format: | Preprint |
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2023
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| _version_ | 1866911853487063040 |
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| author | Yao, H. Yeung, P. K. Zaki, T. A. Meneveau, C. |
| author_facet | Yao, H. Yeung, P. K. Zaki, T. A. Meneveau, C. |
| contents | We study fluctuations of the local energy cascade rate $Φ_\ell$ in turbulent flows at scales ($\ell$) in the inertial range. According to the Kolmogorov refined similarity hypothesis (KRSH), relevant statistical properties of $Φ_\ell$ should depend on $ε_\ell$, the viscous dissipation rate locally averaged over a sphere of size $\ell$, rather than on the global average dissipation. However, the validity of KRSH applied to $Φ_\ell$ has not yet been tested from data. Conditional averages such as $\langle Φ_\ell|ε_{\ell}\rangle$ as well as of higher-order moments are measured from Direct Numerical Simulations data, and results clearly adhere to the predictions from KRSH. Remarkably, the same is true when considering forward ($Φ_\ell>0$) and inverse ($Φ_\ell<0$) cascade events separately. Measured ratios of forward and inverse cascade probability densities further show that a fluctuation relation adhering to the KRSH can be observed, raising the hope that important features of turbulence may be described using concepts from non-equilibrium thermodynamics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_06546 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Forward and inverse energy cascade and fluctuation relation in fluid turbulence adhere to Kolmogorov's refined similarity hypothesis Yao, H. Yeung, P. K. Zaki, T. A. Meneveau, C. Fluid Dynamics We study fluctuations of the local energy cascade rate $Φ_\ell$ in turbulent flows at scales ($\ell$) in the inertial range. According to the Kolmogorov refined similarity hypothesis (KRSH), relevant statistical properties of $Φ_\ell$ should depend on $ε_\ell$, the viscous dissipation rate locally averaged over a sphere of size $\ell$, rather than on the global average dissipation. However, the validity of KRSH applied to $Φ_\ell$ has not yet been tested from data. Conditional averages such as $\langle Φ_\ell|ε_{\ell}\rangle$ as well as of higher-order moments are measured from Direct Numerical Simulations data, and results clearly adhere to the predictions from KRSH. Remarkably, the same is true when considering forward ($Φ_\ell>0$) and inverse ($Φ_\ell<0$) cascade events separately. Measured ratios of forward and inverse cascade probability densities further show that a fluctuation relation adhering to the KRSH can be observed, raising the hope that important features of turbulence may be described using concepts from non-equilibrium thermodynamics. |
| title | Forward and inverse energy cascade and fluctuation relation in fluid turbulence adhere to Kolmogorov's refined similarity hypothesis |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2307.06546 |