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Zhang S, Liu H, Kang W, Xiao Z, Tao J, Zhang P, Zhang W, He XT. Coupling effects and thin-shell corrections for surface instabilities of cylindrical fluid shells. Phys Rev E 2020; 101:023108. [PMID: 32168666 DOI: 10.1103/physreve.101.023108] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2019] [Accepted: 02/10/2020] [Indexed: 11/07/2022]
Abstract
We show that when linear azimuthal perturbations on the surfaces of a fluid shell are regrouped according to α^{m}, they can be divided into Bell model terms, coupling terms, and the newly identified thin-shell correction terms, where α is the ratio of R_{out} to R_{in}, and m is the mode number of a given unstable mode on the surfaces. It is also revealed that α^{m} is a convenient index variable of coupling effects, with which we show that the evolution of instability is composed of three stages, i.e., strongly coupled stage, transition stage, and uncoupled stage. Roughly, when α^{m}<6, the fluid shell is in the strongly coupled stage, where both coupling effects and the newly identified thin-shell corrections play important roles. Strong feed through is expected to be observed. The uncoupled stage is reached at α^{m}∼36, where Bell's model of independent surface holds. In between is the transition stage, where mode competitions on the two surfaces are expected to be observed. These results afford an intuitive picture which is easy to use in guiding the design of experiments. They may also help to quickly grasp major features of instability experiments of this kind.
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Affiliation(s)
- Shuai Zhang
- HEDPS, Center for Applied Physics and Technology, and College of Engineering, Peking University, Beijing 100871, China
| | - Hao Liu
- Department of Applied Physics, School of Physics and Electronics, Hunan University, Changsha 410082, China
| | - Wei Kang
- HEDPS, Center for Applied Physics and Technology, and College of Engineering, Peking University, Beijing 100871, China
| | - Zuoli Xiao
- HEDPS, Center for Applied Physics and Technology, and College of Engineering, Peking University, Beijing 100871, China.,Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China
| | - Jianjun Tao
- HEDPS, Center for Applied Physics and Technology, and College of Engineering, Peking University, Beijing 100871, China.,Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China
| | - Ping Zhang
- HEDPS, Center for Applied Physics and Technology, and College of Engineering, Peking University, Beijing 100871, China.,Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
| | - Weiyan Zhang
- HEDPS, Center for Applied Physics and Technology, and College of Engineering, Peking University, Beijing 100871, China.,China Academy of Engineering Physics, Mianyang 621900, China
| | - X T He
- HEDPS, Center for Applied Physics and Technology, and College of Engineering, Peking University, Beijing 100871, China.,Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
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