Harmonic instability of the free surface of a low-viscous liquid in a vertically oscillating vessel (Q2761282)

The authors study vertical harmonic oscillations of a vessel with viscous incompressible fluid with free surface. At the initial instant, a perturbation occurs in the fluid in the form of a standing wave with infinitely small amplitude and with a frequency close to the vessel oscillation frequency. Using the idea of boundary layer and Krylov-Bogolyubov averaging method, the authors establish conditions under which the initial perturbation grows with time. This phenomenon is known as harmonic instability.