Nonlinear hydrodynamic interface instabilities driven by time-dependent accelerations

We present a model for nonlinear hydrodynamic instabilities of interfaces and the formation of bubbles driven by time-dependent accelerations g(t). To obtain analytic solutions, we map the equation for the bubble amplitude η(t) onto the Schroedinger equation and solve it as an initial value (η0,η0) problem in time instead of an eigenvalue problem in space. Very good agreement is obtained with full hydrodynamic simulations. We then apply the WKB approximation to derive scaling with s=∫√(g(t))dt. Bubbles scale while spikes do not. Zitterbewegung, meaning rapid oscillations of g(t) around an average value, has little effect on η(t).