二维不可压流体Kelvin-Helmholtz不稳定性的弱非线性研究  

Study on the Kelvin-Helmholtz instability in two-dimensional incompressible fluid

作　　者：王立锋[1,2] 叶文华[2,3] 范征锋[2] 李英骏[1] 

机构地区：[1]中国矿业大学(北京),北京100083 [2]北京应用物理与计算数学研究所,北京100088 [3]浙江大学物理系,杭州310028

出　　处：《物理学报》2009年第7期4787-4792,共6页Acta Physica Sinica

基　　金：国家重点基础研究发展计划(973)项目(批准号:2007CB815100);高等学校博士学科点专项科研基金(批准号:20070290008);国家自然科学基金(批准号:10775020和10874242)资助的课题~~

摘　　要：通过将扰动速度势展至三阶,提出了Kelvin-Helmholtz(KH)不稳定性的弱非线性理论.在模耦合过程中观察到一个重要的共振现象,共振使得模耦合过程变得相当复杂,单模扰动很快进入非线性区,产生大量高次谐波,共振加强了非线性作用.分析了单模扰动中二次和三次谐波产生效应,以及对基模指数增长的非线性校正.模拟结果支持了解析理论.利用该理论,分析了KH不稳定的非线性阈值问题.A weakly nonlinear model is proposed for the Kelvin-Helmholtz instability by expanding the perturbation velocity potential to third order. It is found that there is an important resonance in the process of mode coupling. This resonance makes the coupling processes very complex and interesting. Single-mode perturbation enters nonlinear stage quickly and produces lots of harmonics. The resonance reinforces the action of nonlinear process. The second and third harmonic generation efficiency of a single-mode disturbance is computed, as well as the nonlinear correction to the exponential growth of the fundamental modulation. Our simulations support the weakly nonlinear results from our analytic model. The nonlinear threshold phenomenon is also analyzed.

关 键 词：KELVIN-HELMHOLTZ不稳定性 弱非线性理论 非线性阈值 

分 类 号：O351.3[理学—流体力学]