Cylindrical effects in weakly nonlinear Rayleigh Taylor instability

• Published in: Chinese physics B 2015, Vol.24 (1), p.388-393
• Main Author: 刘万海 马文芳 王绪林
• Format: Article
• Language: English
• Subjects: Cartesian; Density; Fluid dynamics; Fluid flow; Fluids; Gravitation; Perturbation methods; Rayleigh-Taylor instability; 不稳定性; 几何形状; 圆柱; 弱非线性; 振荡条件; 接口功能; 泰勒; 瑞利
• ISSN: 1674-1056; 2058-3834; 1741-4199
• DOI: 10.1088/1674-1056/24/1/015202

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.