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Unsteady dissipation scaling in static- and active-grid turbulence

Published online by Cambridge University Press:  03 February 2023

Yulin Zheng Open the ORCID record for Yulin Zheng [Opens in a new window] ,
Kohtaro Nakamura ,
Koji Nagata Open the ORCID record for Koji Nagata [Opens in a new window]  and
Tomoaki Watanabe Open the ORCID record for Tomoaki Watanabe [Opens in a new window]
Yulin Zheng
Affiliation:
Department of Aerospace Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan
Kohtaro Nakamura
Affiliation:
Department of Aerospace Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan
Koji Nagata*
Affiliation:
Department of Aerospace Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan
Tomoaki Watanabe
Affiliation:
Education and Research Center for Flight Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan
*
†Email address for correspondence: nagata@nagoya-u.jp
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Abstract

A new time-dependent analysis of the global and local fluctuating velocity signals in grid turbulence is conducted to assess the scaling laws for non-equilibrium turbulence. Experimental datasets of static- and active-grid turbulence with different Rossby numbers $R_o({=}U/\varOmega M$: $U$ is the mean velocity, $\varOmega$ is the mean rotation rate and $M$ is the grid mesh size) are considered. Although the global (long-time-averaged) non-dimensional dissipation rate $C_\varepsilon$ is independent of the Reynolds number $Re_\lambda$ based on the global Taylor microscale, the local (short-time-averaged) non-dimensional dissipation rate $\left \langle C_\varepsilon (t_i) \right \rangle$ ($t_i$ is the local time) both in the static- and active-grid turbulence clearly show the non-equilibrium scaling $\left \langle C_\varepsilon (t_i)\right \rangle / \sqrt {Re_0} \propto \left \langle Re_\lambda (t_i) \right \rangle ^{-1}$ ($\left \langle Re_\lambda (t_i) \right \rangle$ and $Re_0$ are the Reynolds numbers based on the local Taylor microscale $\lambda (t_i)$ and the global integral length scale, respectively), which has only been confirmed for global statistics in the near field of grid turbulence. The local value of $\left \langle L(t_i) / \lambda (t_i) \right \rangle$ ($L(t_i)$ is the local integral length scale) shifts from the equilibrium to non-equilibrium scaling as $\left \langle Re_\lambda (t_i) \right \rangle$ increases, further confirming that the non-equilibrium scalings are recovered for local statistics both in the static- and active-grid turbulence. The local values of $\left \langle C_\varepsilon (t_i) \right \rangle$ and $\left \langle L(t_i) / \lambda (t_i) \right \rangle$ follow the theoretical predictions for global statistics (Bos & Rubinstein, Phys. Rev. Fluids, vol. 2, 2017, 022601).

JFM classification

Turbulent Flows: Turbulent Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 956 , 10 February 2023 , A20
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

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