Numerical Simulation of the Quasi-2D Turbulence on a Half Soap Bubble Heated at the Bottom

HE Xiaoqiu; XIONG Yongliang; XU Shun; PENG Zerui; CHEN Bo

doi:10.21656/1000-0887.430143

Volume 43 Issue 10

Oct. 2022

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HE Xiaoqiu, XIONG Yongliang, XU Shun, PENG Zerui, CHEN Bo. Numerical Simulation of the Quasi-2D Turbulence on a Half Soap Bubble Heated at the Bottom[J]. Applied Mathematics and Mechanics, 2022, 43(10): 1086-1104. doi: 10.21656/1000-0887.430143

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Numerical Simulation of the Quasi-2D Turbulence on a Half Soap Bubble Heated at the Bottom

doi: 10.21656/1000-0887.430143

Department of Mechanics School of Aerospace Engineering, Huazhong University of Science and Technology, Wuhan 430074, P.R.China

Received Date: 2022-04-22
Rev Recd Date: 2022-06-21

Available Online: 2022-09-20

Publish Date: 2022-10-31

Abstract

Abstract

The soap bubble heated at the bottom was introduced as a novel quasi-2D turbulence system. The curved geometry of the bubble brings challenges for the direct numerical simulations (DNS) of the turbulence on the bubble. In order to overcome the difficulties due to the curved geometry, a numerical method based on the stereographic projection was implemented for the DNS of the soap bubble. The numerical methods to compute the spectrum, the flux and the structure functions of the flows on the bubble were described in detail. Three different Rayleigh numbers Ra=3×10⁷，3×10⁹，3×10¹¹were used in the simulation based on the present numerical methods. Then, the related spectrum, flux and structure functions were calculated. The results indicate that, both the inversed energy cascade and forward enstrophy cascade can be observed in all the calculation cases. The Bo59 scaling law fits the small-scale fluctuations on the soap bubble. With the increase of the Rayleigh number, the turbulent energy decreases for the large-scale plumes, and the kinetic energy increases for the higher wave number structures.
- soap bubble,
- turbulence,
- structure function,
- direct numerical simulation

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References(26)

References

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