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Flow patterns and energy spectra in forced quasi-two-dimensional turbulence: effect of system size and damping rate

Published online by Cambridge University Press:  02 October 2024

Hang-Yu Zhu Open the ORCID record for Hang-Yu Zhu [Opens in a new window] ,
Jin-Han Xie Open the ORCID record for Jin-Han Xie [Opens in a new window]  and
Ke-Qing Xia Open the ORCID record for Ke-Qing Xia [Opens in a new window]
Hang-Yu Zhu
Affiliation:
Centre for Complex Flows and Soft Matter Research, Southern University of Science and Technology, Shenzhen 518055, PR China Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055 PR China Department of Mechanics, School of Aerospace Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China
Jin-Han Xie
Affiliation:
Department of Mechanics and Engineering Science at College of Engineering, and State Key Laboratory for Turbulence and Complex Systems, Peking University, Beijing 100871, PR China
Ke-Qing Xia*
Affiliation:
Centre for Complex Flows and Soft Matter Research, Southern University of Science and Technology, Shenzhen 518055, PR China Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055 PR China Department of Physics, Southern University of Science and Technology, Shenzhen 518055, PR China
*
†Email address for correspondence: [email protected]
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Abstract

An experimental investigation is conducted to study the flow patterns, spectral properties and energy fluxes in thin-layer turbulence with varying system sizes and damping rates. It is found that although a system-size vortex (an indicator of spectral condensation) occurs for small system sizes and does not for large ones, the spectra for different system sizes consistently exhibit a scaling close to $k^{-3}$ in inverse cascade (another indicator of spectral condensation). On the other hand, under a fixed system size larger than the friction-dominated length scale, the energy spectrum in the inverse cascade range changes from $k^{-3}$ to $k^{-5/3}$ as the damping rate increases, suggesting that the friction-dominated length scale may not be a suitable parameter for predicting spectral transition. At lower damping rates and large system sizes, turbulent structures grow larger via inverse cascade, manifesting as long streamers, and the small-scale vortices are suppressed. This suppression leads to a reduction of energy flux at intermediate scales and a change in the spectral shape. The dimensionless Taylor microscale is found to exhibit a monotonic dependence on the damping rate. With the reduction in the damping rate, the Taylor microscale increases to become comparable with the forcing scale, and the spectrum in inverse cascade transits to a steeper scaling, $k^{-3}$, indicating that the dimensionless Taylor microscale may be used as a diagnostic parameter for spectral transition.

JFM classification

Turbulent Flows: Turbulent Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 996 , 10 October 2024 , A39
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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