The dynamics of internal wave resonance in periodically forced narrow basins

Abstract

Laboratory experiments were conducted to determine the steady state internal wave response of a periodically forced, density-stratified, basin characterized by both horizontal and vertical length scales and a known seiche period. The system was two-layer stratified and was subjected to periodic forcing over a wide frequency range. The forcing amplitude and ratio of the forcing frequency (f) to horizontal mode one (H1) internal seiche frequency (1) governed the system response. For f > 1, higher-mode internal seiches were observed; for f < 1, a nonresonant forced H1 internal seiche was observed; and for f1, a resonant H1 internal seiche was observed. For this resonant regime, progressive nonlinear internal waves (NLIWs) formed upon the H1 seiche. When the NLIWs amplitudes were large, Kelvin-Helmholtz instabilities grew within the wave troughs, leading to significant diapycnal mixing within the basin interior. Resonant amplification was most pronounced for small forcing amplitudes because weakly forced waves have the most potential for growth prior to energy flux to NLIWs and ultimate turbulent dissipation and mixing. This observation suggests that each mode has a maximum energy density that, when exceeded, leads to a nonlinear energy cascade. The resonant wave response was modeled as a driven underdamped harmonic oscillator, where the damping coefficient was interpreted as the sum of the effects of mixing and dissipation. © 2012. American Geophysical Union. All Rights Reserved.