放大的低频表面波的波动
Undulations from amplified low frequency surface waves
摘要：
研究了纵向非均匀定常流中重力波的散射问题。当流动变得超临界时，逆流传播的浅波被阻挡并转换成深波。我们表明，反射波被放大的方式，在零频率的限制，自由表面发展的波动，即，波节位于特定位置的大振幅零频率波。这种放大涉及负能量波，并意味着未受扰动的平坦表面对任意小振幅的入射扰动是不稳定的。讨论了这种不稳定性与黑洞辐射（霍金效应）之间的关系。
英文摘要：
We study the scattering of gravity waves in longitudinal inhomogeneous stationary flows. When the flow becomes supercritical, counterflow propagating shallow waves are blocked and converted into deep waves. We show that the reflected waves are amplified in such a way that, in the zero-frequency limit, the free surface develops an undulation, i.e., a zero-frequency wave of large amplitude with nodes located at specific places. This amplification involves negative energy waves, and implies that the unperturbed flat surface is unstable against incoming perturbations of arbitrary small amplitude. The relation between this instability and black hole radiation (the Hawking effect) is discussed.
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