Experimental Investigation of Tidally-Forced Internal Wave Turbulence at High Reynolds Number

TL;DR

This study experimentally investigates how tidal forces generate internal wave turbulence at high Reynolds numbers, revealing energy cascades, triadic interactions, and the role of elastic scattering in ocean-like conditions.

Contribution

It provides the first detailed laboratory observation of internal wave turbulence and energy transfer mechanisms at high Reynolds numbers relevant to ocean conditions.

Findings

Observation of subharmonics driven by Triadic Resonant Instabilities

Confirmation of a backward cascade in frequency and forward cascade in wavenumber

Identification of elastic scattering as a significant nonlocal interaction

Abstract

Through basin-scale circulations, the ocean regulates global distributions of heat, nutrients, and greenhouse gases. To properly predict the future of the ocean under climate change, we need to develop a thorough understanding of the underlying mechanisms that drive global circulations. An estimated 2 TW of power is required to support interior mixing. Roughly half of this power is believed to come from tidal flow over topography, producing internal gravity waves (IGW's), which can radiate energy throughout the ocean interior. But it is difficult to track the subsequent journey from tidal injection to dissipation, as the energy cascade spans an enormous range of spatio-temporal scales and multiple different nonlinear transfer mechanisms. To investigate the full energy pathway from topographic forcing to irreversible mixing, we built a model ocean in a large-scale laboratory wavetank (9 m x 2.9 m x 0.75 m) allowing Reynolds numbers up to O(10$^5$). We replicate the tidal forcing by oscillating an idealized ocean ridge. We track energy transfer across the first cascade, driven by wave turbulence, using Background Oriented Schlieren (BOS) over the full tank. Through the BOS we observe the formation of various sets of subharmonics, driven by Triadic Resonant Instabilities (TRI). At later times, the subharmonics born from TRI engage in different interactions, which ultimately develop a continuum of waves at frequencies up to $N$. We validate the three-wave resonant conditions through a Fourier decomposition and confirm a backward cascade in frequency but a forward cascade in vertical wavenumber. Through our spatial analysis, we identify relevant three-wave interactions and show the significance of elastic scattering, a nonlocal interaction, in our fully evolved system. We note however that the majority of our triads are local, which have been historically overlooked.