In differentially rotating discs with no self-gravity, density waves cannotpropagate around the corotation, where the wave pattern rotation speed equalsthe fluid rotation rate. Waves incident upon the corotation barrier may besuper-reflected (commonly referred to as corotation amplifier), but thereflection can be strongly affected by wave absorptions at the corotationresonance/singularity. The sign of the absorption is related to the Rossby wavezone very near the corotation radius. We derive the explicit expressions forthe complex reflection and transmission coefficients, taking into account waveabsorption at the corotation resonance. We show that for generic discs, thisabsorption plays a much more important role than wave transmission across thecorotation barrier. Depending on the sign of the gradient of the specificvorticity of the disc the corotation resonance can either enhance or diminishthe super-reflectivity, and this can be understood in terms of the location ofthe Rossby wave zone relative to the corotation radius. Our results provide theexplicit conditions (in terms of disc thickness, rotation profile and specificvorticity gradient) for which super-reflection can be achieved. Globaloverstable disc modes may be possible for discs with super-reflection at thecorotation barrier.
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