Abstract
An exact long-wavelength asymptotic solution is constructed for the problem of interphase stability in the Couette flow of a two-layer system of Newtonian liquids with different viscosities and with shallow depths. It is shown that the dispersion relation for the complex velocity of a wave of disturbances can be represented as an expansion in fractional powers of the wave number which are multiples of 1/3. New stability criteria, different from those obtained previously, are found.
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