Harmonic instability of the free surface of a low-viscosity liquid in a vertically oscillating vessel

The linear problem of the parametric excitation of three-dimensional standi ng waves on the free surface of a Liquid of low viscosity in a vessel of ar bitrary shape, undergoing vertical oscillations, is investigated. The so-ca lled harmonic instability, for which the natural frequency of the excited w aves is close to the oscillation frequency of the vessel, is considered. Us ing the idea of a boundary layer and the Krylov-Bogolyubov averaging method , approximate formulae are derived for the quantities which define the cond itions for harmonic instability-for the threshold oscillation amplitude of the vessel and the limits of the resonance zones. It is shown experimentall y that it is possible for harmonic instability to occur on the surface of w ater in a rectangular vessel. The calculated values of the threshold amplit ude and the limits of the resonance zones agree well with those measured ex perimentally. (C) 2000 Elsevier Science Ltd. All rights reserved.