Ever since some pioneering work by Miles in the late 1950s, it has been known that waves in fluids can, in principle, be reflected from a sharp shear layer with a consequent increase in amplitude. There are, in other words, circumstances in which the reflection coefficient can actually be greater than 1.
When I first came across this `over-reflection', in 1975, all the previous examples suffered from one serious difficulty: the shear layer itself was unstable. It seemed to me that this clouded the whole issue of whether the phenomenon should be taken seriously, but I eventually constructed the first two examples of over-reflection in a stable system, and published them the following year, 1976.
My paper also attempted to clarify the way in which the waves extracted energy from the mean flow, and the precise sense in which the reflected wave might be said to carry `negative energy'.
J. Fluid Mech. Vol. 77, pp 433-472, 1976.
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