Effect of the Wind Fluctuation on the Stability of a Liquid Layer Flowing down an Inclined Plane

Abstract

The stability problem of a liquid layer flowing down an inclined plane wall is studied theoretically, taking into account the time dependent wind stress on its free surface. The Floquet theory is applied to a differential system with periodic coefficients of this problem. This system is solved by the long wave approximation. The critical Reynolds number for this flow depends on the square of the amplitude of the wind fluctuation. The frequency of the wind fluctuation has the greatest influence on the instability of the liquid layer when the thickness of the liquid layer is of the same order as the thickness of the Stokes layer due to the oscillating motion. In case of low frequency the flow is destabilized by the wind fluctuation, but in a range of high frequencies the flow can be stabilized slightly.