Generation of surface waves by shear-flow instability
Generation of surface waves by shear-flow instability
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DOI：
10.1017/jfm.2013.617
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发表时间：
2013-12
影响因子：
3.7
通讯作者：
W. Young;C. Wolfe
中科院分区：
文献类型：
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作者：
W. Young;C. Wolfe
摘要考虑了具有重力和毛细作用的无粘空气在水面上平行剪切流的线性稳定性。空气中的速度剖面从海面向上单调递增，呈凸形；而水中的速度剖面从海面向上单调递减，呈凹形。一个典型的例子，“双指数”轮廓，是解析解决和详细研究。我们证明，在某些情况下，有两种类型的不稳定模式可以共存。第一种是“英里模式”，由表面重力波和空气中的临界水平之间的共振相互作用产生。第二种不稳定模式是水面重力波与水中某个临界水平面的相互作用，导致波纹的增长。参与第二次共振的重力-毛细波具有负的本征相速度，但经过多普勒频移，使其实际相速度为正，并与临界水平上基态电流的速度相匹配。在这两种情况下，指数增长波的雷诺应力将动量从临界水平附近转移到表面波波峰和波谷之间的区域。
Abstract We consider the linear stability of an inviscid parallel shear flow of air over water with gravity and capillarity. The velocity profile in the air is monotonically increasing upwards from the sea surface and is convex, while the velocity in the water is monotonically decreasing from the surface and is concave. An archetypical example, the ‘double-exponential’ profile, is solved analytically and studied in detail. We show that there are two types of unstable mode which can, in some cases, co-exist. The first type is the ‘Miles mode’ resulting from a resonant interaction between a surface gravity wave and a critical level in the air. The second unstable mode is an interaction between surface gravity waves and a critical level in the water, resulting in the growth of ripples. The gravity–capillary waves participating in this second resonance have negative intrinsic phase speed, but are Doppler shifted so that their actual phase speed is positive, and matches the speed of the base-state current at the critical level. In both cases, the Reynolds stresses of an exponentially growing wave transfer momentum from the vicinity of the critical level to the zone between the crests and troughs of a surface wave.