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

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.