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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 northwest of Hawaii (figure 1). The model captures the power-law spectra in broad ranges of space and time scales, with exponents -2.05±0.2 in frequency and -2.58±0.4 in vertical wavenumber (figures 2, 3). 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 (figure 4) and evaluations of modal energy transfer (figure 5), 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.
figure 1: Left: The Northeast Pacific region showing a colored box at the location of the simulation domain; Right: A close-up of the simulation domain including the local bathymetry (color), and the regions H1 (solid-line box) and H2 (dash-line box) used in analysis.
figure 2: A typical frequency spectrum of kinetic energy.
figure 2: A typical frequency spectrum of kinetic energy.
figure 3: A typical vertical wavenumber spectrum of kinetic energy.
figure 3: A typical vertical wavenumber spectrum of kinetic energy.
figure 4: Contour map of temporal bi-coherence
figure 4: Contour map of temporal bi-coherence
figure 5: Direct evaluations of collision integral to show the IR divergence and UV convergence.
figure 5: Direct evaluations of collision integral to show the IR divergence and UV convergence.
Publication:
Publication:
Pan, Y., Arbic, B.K., Nelson, A.D., Menemenlis, D., Peltier, W.R., Xu, W. and Li, Y. 2020, Numerical investigation of mechanisms underlying oceanic internal gravity wave power-law spectra, Journal of Physical Oceanography, 50.
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