| FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS) |
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On the Second Harmonic Generation through Bell–Plesset Effects in Cylindrical Geometry |
| GUO Hong-Yu1, YU Xiao-Jin2, WANG Li-Feng2,3, YE Wen-Hua2,3,4, WU Jun-Feng2**, LI Ying-Jun1** |
1State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Beijing 100083
2Institute of Applied Physics and Computational Mathematics, Beijing 100094
3HEDPS, Center for Applied Physics and Technology, Peking University, Beijing 100871
4Department of Physics, Zhejiang University, Hangzhou 310027
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| Cite this article: |
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GUO Hong-Yu, YU Xiao-Jin, WANG Li-Feng et al 2014 Chin. Phys. Lett. 31 044702 |
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Abstract Generation of the second harmonic initiated by Bell–Plesset effects in a cylindrical geometry is studied analytically. For an initial single-mode velocity perturbation, the second-order mode-coupling formula is obtained by expanding the perturbation displacement and velocity potential up to the second-order accuracy. It is found that the initially symmetric interface evolves into a significant bubble-spike asymmetric pattern. The second-order solutions clearly show that the amplitude of the spike grows faster than that of the bubble. The temporal evolutions of the amplitudes of the bubble and spike are dependent on the interface velocity V0. The larger interface velocity leads to the smaller amplitude of the perturbation at an arbitrary interface position in a cylindrically convergent geometry.
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Received: 26 July 2013
Published: 25 March 2014
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| PACS: |
47.20.Ib
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(Instability of boundary layers; separation)
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47.20.Ma
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(Interfacial instabilities (e.g., Rayleigh-Taylor))
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52.57.Fg
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(Implosion symmetry and hydrodynamic instability (Rayleigh-Taylor, Richtmyer-Meshkov, imprint, etc.))
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