Numerical Investigation of Mechanisms Underlying Oceanic Internal Gravity Wave Power-Law Spectra

Abstract

We consider the power-law spectra of internal gravity waves in a rotating and stratified ocean. Field measurements have shown considerable variability of spectral slopes compared to the high-wavenumber high-frequency portion of the Garrett-Munk (GM) spectrum. Theoretical explanations have been developed through wave turbulence theory (WTT), where different power-law solutions of the kinetic equation can be found depending on the mechanisms underlying the nonlinear interactions. Mathematically, these are reflected by the convergence properties of the so-called collision integral (CL) at low and high frequency limits. In this work, we study the mechanisms in the formation of the power-law spectra of internal gravity waves, utilizing numerical data from the high-resolution modeling of internal waves (HRMIW) in a region north-west of Hawaii. The model captures the power-law spectra in broad ranges of space and time scales, with scalings ω−2.05±0.2 in frequency and m−2.58±0.4 in vertical wavenumber. The latter clearly deviates from the GM76 spectrum but is closer to a family of induced-diffusion-dominated solutions predicted by WTT. Our analysis of nonlinear interactions is performed directly on these model outputs, which is fundamentally different from previous work assuming a GM76 spectrum. By applying a bi-coherence analysis and evaluations of modal energy transfer, we show that the CL is dominated by non-local interactions between modes in the power-law range and low-frequency inertial motions. We further identify induced diffusion and the near-resonances at its spectral vicinity as dominating the formation of power-law spectrum.

Downscale energy fluxes in scale-invariant oceanic internal wave turbulence

“…This is consistent with recent results from direct numerical simulations where the dominating interactions were located in the ID regime but also throughout all of the interval (Pan et al. 2020). Despite the latter effect was investigated in Pan et al (2020) as a broadening of ID due to large nonlinearity, we find that it may be consistent with the collinear resonances depicted in figure 2( b ).…”

“…In this section, we have shown how the formation of the stationary solution of the wave kinetic equation can be interpreted via two independent balances, between near-collinear triads and between the ID triads of the extreme scale-separated regions. This is consistent with recent results from direct numerical simulations where the dominating interactions were located in the ID regime but also throughout all of the interval k 1 ∈ [0, 1.4k] (Pan et al 2020). Despite the latter effect was investigated in Pan et al (2020) as a broadening of ID due to large nonlinearity, we find that it may be consistent with the collinear resonances depicted in figure 2(b).…”

“…2020). Despite the latter effect was investigated in Pan et al (2020) as a broadening of ID due to large nonlinearity, we find that it may be consistent with the collinear resonances depicted in figure 2( b ).…”

Frequency dependence of near-surface oceanic kinetic energy from drifter observations and global high-resolution models

“…Global IGW models, especially HYCOM and MITgcm LLC4320, have been widely used by the community, to plan for field campaigns (e.g., J. Wang et al, 2018), understand interactions between motions at different length and time scales (e.g., Pan et al, 2020), and provide boundary forcing for higher-resolution regional models (Nelson et al, 2020). HYCOM and MITgcm LLC4320 have been used to quantify the relative contributions of low-and high-frequency motions to SSH and KE as a function of geographical location (e.g., Richman et al, 2012;Savage et al, 2017aSavage et al, , 2017bQiu et al, 2018;Torres et al, 2018).…”

Scale Separated Approaches to the Interaction of Oceanic Internal Waves, part I: Theory

“…There is a renewed theoretical interest to investigating the internal waves in the ocean due to recent developments in our ability to perform high resolution numerical modeling, with internal wave permitting Global Ocean Simulations, e.g. Arbic et al (2018); Pan et al (2020).…”