| Rayleigh-Taylor不稳定性弱非线性阶段界面效应对谐波的影响 |
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| 作者姓名： | 刘万海 于长平 黄玉梅 梅杨 叶文华 |
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| 作者单位： | 1.绵阳师范学院计算物理研究中心，四川绵阳 621000 |
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| 基金项目： | 国家自然科学基金11472278国家自然科学基金11372330四川省自然基金18AZ0260四川省自然基金2018JY0454绵阳师范学院自然基金HX2017007绵阳师范学院自然基金MYSY2017JC06 |
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| 摘 要： | 为了更好地理解不同空间坐标系下流体界面对Rayleigh-Taylor（RT）不稳定性弱非线性阶段谐波的影响，文章采用3阶小扰动展开法，解析研究了球坐标空间经典RT不稳定性弱非线性阶段谐波的演化规律，并和柱坐标空间以及直角坐标空间相应结果进行了对比研究.当球坐标系和直角坐标系中RT不稳定性界面扰动波长相同，球坐标系中初始扰动半径为无穷大时（即球坐标下RT不稳定性初始扰动半径相对于扰动波长为无穷大时），球坐标下RT不稳定性前4次谐波的结果和直角坐标系下的相应结果相同.研究表明:由初始界面曲率引起的Bell-Plesset（BP）效应和空间效应（直角坐标空间、柱坐标空间和球坐标空间）对谐波发展有较大的影响.即在不同正交曲线坐标系下，不同曲率的流体界面效应对RT不稳定性谐波发展有较大的影响.对于柱坐标空间和球坐标空间，2阶对0次谐波的反馈加强了界面向内收缩.研究还表明:界面效应增加了2次谐波的负反馈，然而，对于基模和3次谐波却有不同的影响.
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| 关 键 词： | Rayleigh-Taylor不稳定性 谐波 小参数展开法 界面效应 弱非线性 |
| 收稿时间： | 2017-10-11 |
Interface Effects on Harmonics of the Weakly Nonlinear Stage in Rayleigh-Taylor Instability |
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| Affiliation: | 1.Research Center of Computational Physics, Mianyang Normal University, Mianyang 621000, China2.State Key Laboratory of High Temperature Gas Dynamics(LHD), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China3.Institute of Applied Physics and Computational Mathematics, Beijing 100088, China |
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| Abstract: | To better understand the fluid interface effects in different spatial coordinate systems on harmonics of the weakly nonlinear stage in Rayleigh-Taylor instability (RTI), employing the method of the parameter expansion up to the third order, this paper analytically investigated harmonics of the weakly nonlinear stage in classical Rayleigh-Taylor instability on spherical interface, and compared the spherical results with the cylindrical and the planar ones. The results show that the amplitudes of the first four harmonics will recover those in planar RTI as the initial radius of the interface tends to be infinity compared against the initial perturbation wavelength. When the initial radius is small, both the Bell-Plesset effect induced by curvature of the initial interface and the space effect including the planar, cylindrical and spherical geometries make a tremendous impact on the harmonic development. That is to say, the interface effect between two fluids in different coordinate systems plays an important role for the development of the first four harmonics in RTI. For the first four harmonics, the smaller the initial radius is, the faster they grow. This trend is more remarkable for spherical geometry than cylindrical one. Also, the second-order feedback to the zeroth harmonic for the cylindrical and spherical RTI strengthens the contract of the initial unperturbed interface. |
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