Experimental evidence of internal wave attractor signatures hidden in large-amplitude multi-frequency wave fields

Abstract

Geometric focusing of monochromatic internal waves is a well-known linear mechanism that provides a pathway to smaller length scales and hence energy dissipation, especially when repeated reflection from inclined boundaries focuses these waves onto internal wave attractors (IWAs). While simple attractors have been well documented both theoretically and in idealized laboratory settings, the small aspect ratio and complex shape of the ocean has made it difficult to detect the narrow frequency bands where attractors may form. The greatest obstruction however is the restricted spatiotemporal resolution of measurements of the ocean's internal wave field. Moored instruments provide a detailed temporal but poor spatial resolution, except along line-segments spanning part of the water column only. The ability to measure a fully resolved two-dimensional section through a three-dimensional field, as in present-day laboratory experiments, is missing in the ocean. This prohibits the search for IWAs in ocean data, especially if this concerns a multi-frequency wave field. Mimicking an ocean observation set-up, our experimental study aims at detecting IWA signatures from laboratory observations along a vertical line-segment. We perform small and large amplitude forcing experiments at a fixed wavenumber with both monochromatic and broadband frequency components. We examine energy intensification at dissipative length scales at frequencies known to support attractors. Importantly, our laboratory experiments indicate that even in the presence of multiple forcing frequencies, or for large-amplitude monochromatic forcing (where beams become unstable to Triadic Resonant Instability), focusing reflections due to attractors are the predominant mechanism for transferring energy to dissipative scales.