On the absence of dissipative instability of negative energy waves in hydrodynamic shear flows

摘要

Stability criterion for the surface gravity capillary waves in a flowingtwo-layered fluid system with viscous dissipation is investigated. It is seenthat the dissipative instability of negative energy waves is absent,- contraryto what earlier authors have concluded. Their error is identified to arise froman erroneous choice of the dissipation law, in which the wave profile velocityis wrongly equated to the particle velocity. Our corrected dissipation law isalso shown to restore Galilean invariance to the stability condition of thesystem.