Stability of a viscous fluid in an oscillating gravitational field

The stability of the interface of a viscous incompressible fluid superimposed on a massless fluid is studied for the case of an oscillating gravitational field. For the viscous case, the dispersion relation is shown to represent an infinite determinant of the Hill type, which is investigated analytically. The method presented allows one to find the whole dispersion curve of the instability and its asymptotics in an explicit form. The stabilizing effect of the externally imposed oscillations leads to the appearance of stability windows on the growth rate spectrum. Illustrations are given for the influence of all the parameters of the problem on this effect.