Pattern selection in a horizontally vibrated container

Abstract

We present results of an experimental and numerical investigation of the patterns realized by surface waves within an open rectangular container subjected to horizontal vibrations at frequencies of 40–100 Hz. The first instability exhibited by the primary harmonic wave field is subharmonic, and may be identified with the cross-wave instability often seen in wave tank experiments. We show that, contrary to common theoretical and experimental assumptions, and despite their name, these subharmonic waves are not oriented crosswise, but at an intermediate angle with respect to the axis of vibration. Hence, the pattern selection problem for horizontally forced Faraday waves is more complex than has previously been assumed. We establish the robustness of this obliquely oriented surface wave pattern by varying the forcing frequency and amplitude, the fluid viscosity, the fluid depth, and the boundary conditions. Previous work on cross-waves is reviewed and discussed in relation to the current results. Finally, numerical simulations using a reduced model with an appropriate forcing term are used to support the generality of the experimental observations.