Abstract
It is known that a vertical film flow is always unstable [T. B. Benjamin, J. Fluid Mech. 554, 505 (1957); C. S. Yih, Phys. Fluids 6, 321 (1963)] with respect to long surface wave disturbances. It has been shown [S. P. Lin et al., Phys. Fluids 8, 3247 (1996)] that the unstable two-dimensional waves in a vertical film can be suppressed by use of appropriate amplitudes and frequencies of the plate oscillation. It is shown here that the Squire theorem for the present problem does not exist. By use of the Chebyshev series solution with Floquet theory we show that three-dimensional unstable waves can also be suppressed, although they are not necessarily less dangerous than two-dimensional disturbances.
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