Experiments on ripple instabilities. Part 1. Resonant triads

Abstract

Water waves for which both gravitation and surface tension are important (ripples) exhibit a variety of instabilities. Here, experimental results are presented for ripple wavetrains on deep water with frequencies greater than 19.6 Hz where a continuum of resonant triad interactions are dynamically admissible. The experimental wave-trains are indeed unstable, and the instability becomes more pronounced as non-linearity is increased. The unstable wavefield is characterized by significant spatial disorder while temporal measurements at fixed spatial locations remain quite ordered. In fact, for most experiments temporal measurements suggest that a selection process exists in which a single triad dominates evolution. The dominant triad typically does not involve a subharmonic frequency of the generated wave and persists over a wide range of amplitudes for the initial wave. Viscosity does not appear to be important in the selection process; however, it may be responsible for the lack of subsequent triad production by the excited waves of the initial triad. The presence of a selection process contradicts previous conjecture, based on the form of the interaction coefficients, that a broad-banded spectrum of waves should occur. The general absence of subharmonic growth also contradicts previously reported experiments. Results are also presented for wavetrains at the parametric boundary of 19.6 Hz and a degenerate case of resonant triads at 9.8 Hz (Wilton's ripples). In addition to resonant triads, the experiments show evidence of (generally) weaker narrow-band interactions.