论文标题
流动驱动的界面波：一项无渐进的渐近研究
Flow driven interfacial waves: an inviscid asymptotic study
论文作者
论文摘要
通过风吹过的风，我们使用渐近方法来研究由这些流的联合作用驱动的短波长界面波的演变。我们解决了雷利方程的剪切流量稳定性，并为扰动的流函数或特征功能构建一个均匀有效的近似值。然后，我们在逆波数的功率系列中扩展了特征值的实际部分，相位速度，并表明虚构部分成倍小。我们为里程的增长率（1957）和波纹（例如Young＆Wolfe 2013）的不稳定性提供了表达方式，这些不可接受对于任意剪切流有效。在风和电流都具有指数曲线的情况下，与特征值问题的精确解决方案进行比较，可以证明结果的准确性。
Motivated by wind blowing over water, we use asymptotic methods to study the evolution of short wavelength interfacial waves driven by the combined action of these flows. We solve the Rayleigh equation for the stability of the shear flow, and construct a uniformly valid approximation for the perturbed streamfunction, or eigenfunction. We then expand the real part of the eigenvalue, the phase speed, in a power series of the inverse wavenumber and show that the imaginary part is exponentially small. We give expressions for the growth rates of the Miles (1957) and rippling (e.g., Young & Wolfe 2013) instabilities that are valid for an arbitrary shear flow. The accuracy of the results is demonstrated by a comparison with the exact solution of the eigenvalue problem in the case when both the wind and the current have an exponential profile.
