Author(s)

E Dolven & H Yeh

Abstract

When a body of water is subjected to vertical oscillations, a standing wave field forms on the surface. These waves are called Faraday waves after Michael Faraday [l] who first documented them in 1831. We propose this as a model for the rough surface waves, known as seaquakes, observed in conjunction with earthquakes at sea. These waves have a frequency, W , half that of the forcing and a wave number given by the deep water dispersion relation k* = w2/9. In bounded domains this results in unbounded growth of the primary free surface Faraday mode. In this paper, we introduce radiation as a mechanism for stabilizing the resonant amplitude, and develop a BIEM code to study the problem. The code accurately reproduces analytic solutions based on linear theory. We use this to develop a scaling relationship between the forcing area and amplitude that preserves initial wave development. We find that the open boundaries allow for bursts of energy to escape as the wave drifts out of phase with the bottom paddle oscillation. The result is a slow modulation of the wave envelope amplitude accompanied by a phase shift. As the wave drifts further into anti-phase, it experiences a burst of resonant pumping, and the cycle continues. We demonstrate the development of nonlinear triad interactions that further redistribute the energy into higher modes.

Keywords