Is Landau Damping Possible in a Shear Fluid Flow?

Asymptotic analysis for small long-wave perturbations of a given stationary shear flow of an ideal fluid with free boundary as is performed. It is shown that small disturbances of the flow are attracted to periodic solution in the case where the governing equations are hyperbolic on the main shear flow solution. A class of shear flows for which Landau damping is realizable, is described. Analytical results obtained are validated by numerical calculations.