| PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES |
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Cylindrical effects in weakly nonlinear Rayleigh–Taylor instability |
| Liu Wan-Hai (刘万海)a b, Ma Wen-Fang (马文芳)a, Wang Xu-Lin (王绪林)a |
a Research Center of Computational Physics, Mianyang Normal University, Mianyang 621000, China;
b HEDPS and CAPT, Peking University, Beijing 100871, China |
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Abstract The classical Rayleigh-Taylor instability (RTI) at the interface between two variable density fluids in the cylindrical geometry is explicitly investigated by the formal perturbation method up to the second order. Two styles of RTI, convergent (i.e., gravity pointing inward) and divergent (i.e., gravity pointing outwards) configurations, compared with RTI in Cartesian geometry, are taken into account. Our explicit results show that the interface function in the cylindrical geometry consists of two parts: oscillatory part similar to the result of the Cartesian geometry, and non-oscillatory one contributing nothing to the result of the Cartesian geometry. The velocity resulting only from the non-oscillatory term is followed with interest in this paper. It is found that both the convergent and the divergent configurations have the same zeroth-order velocity, whose magnitude increases with the Atwood number, while decreases with the initial radius of the interface or mode number. The occurrence of non-oscillation terms is an essential character of the RTI in the cylindrical geometry different from Cartesian one.
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Received: 01 April 2014
Revised: 13 May 2014
Accepted manuscript online:
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PACS:
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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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47.20.Ma
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(Interfacial instabilities (e.g., Rayleigh-Taylor))
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52.35.Py
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(Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.))
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52.65.Vv
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(Perturbative methods)
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| Fund: Project supported by the National Basic Research Program of China (Grant No. 10835003), the National Natural Science Foundation of China (Grant No. 11274026), the Scientific Research Foundation of Mianyang Normal University, China (Grant Nos. QD2014A009 and 2014A02), and the National High-Tech ICF Committee. |
Corresponding Authors:
Wang Xu-Lin
E-mail: wxln177@163.com
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Cite this article:
Liu Wan-Hai (刘万海), Ma Wen-Fang (马文芳), Wang Xu-Lin (王绪林) Cylindrical effects in weakly nonlinear Rayleigh–Taylor instability 2015 Chin. Phys. B 24 015202
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