

STABILITY OF LONG WAVES ON AN INTERFACE OF HORIZONTAL FLOW OF TWOLAYER LIQUID
Arkhipov D.G.^{1,2}, Khabakhpashev G.A.^{1,2}, Tsvelodub O.Yu.^{1,2}
^{1} Novosibirsk State University, Novosibirsk, Russia ^{2} Institute of Thermophysics SB RAS, Novosibirsk, Russia
Citation:
Arkhipov, D.G., Khabakhpashev, G.A. and Tsvelodub, O.Yu., (2015) Stability of long waves on an interface of horizontal flow of twolayer liquid, Modern Science: Researches, Ideas, Results, Technologies, Iss. #1(16), PP. 236  240.

Keywords: instability; interface; long waves; twolayer flow; viscous fluid; Orr–Sommerfeld equation; Rayleigh equation 
Abstracts:
One of the simplest models of twolayer flows is Poiseuille flow in a plane channel, when the viscous fluids of different densities are assumed to be incompressible and immiscible. A study of linear gravitational waves stability on its interface is carried out. The obtained analytical solutions were compared with the numerical solution of Orr–Sommerfeld equations. It is shown analytically that there is instability in the absence of viscous dissipation. It clarified that this instability appears due to the generation of a critical layer like Miles instability. It is disclosed the interconnection of this instability with an interfacial mode studied in articles (Yih, 1967) and (Yiantsios and Higgins, 1988). A manifestation of one and the same disturbance mode in two limit cases is shown. 
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