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Influence of the Distortion of Vertical Wavenumber Spectra on Estimates of Turbulent Dissipation Using the Finescale Parameterization: Eikonal Calculations

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  • 1 a Department of Earth and Planetary Science, Graduate School of Science, The University of Tokyo, Tokyo, Japan
  • | 2 b Ocean and Earth Science, National Oceanography Centre, University of Southampton, Southampton, United Kingdom
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Abstract

The finescale parameterization, formulated on the basis of a weak nonlinear wave–wave interaction theory, is widely used to estimate the turbulent dissipation rate ε. However, this parameterization has previously been found to overestimate ε in the Antarctic Circumpolar Current (ACC). One possible reason for this overestimation is that vertical wavenumber spectra of internal wave energy are distorted from the canonical Garrett–Munk spectrum by a spectral hump at low wavenumbers (~0.01 cpm). Such distorted vertical wavenumber spectra were also observed in other mesoscale eddy-rich regions. In this study, using eikonal simulations, in which internal wave energy cascades are evaluated in the frequency–wavenumber space, we examine how the distortion of vertical wavenumber spectra impacts the accuracy of the finescale parameterization. It is shown that the finescale parameterization overestimates ε for distorted spectra with a low-vertical-wavenumber hump because it incorrectly takes into account the breaking of these low-vertical-wavenumber internal waves. This issue is exacerbated by estimating internal wave energy spectral levels from the low-wavenumber band rather than from the high-wavenumber band, which is often contaminated by noise in observations. Thus, to accurately estimate the distribution of ε in eddy-rich regions like the ACC, high-vertical-wavenumber spectral information free from noise contamination is indispensable.

Current affiliation: Applied Physics Laboratory, University of Washington, Seattle, Washington.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Anne Takahashi, annetaka@uw.edu

Abstract

The finescale parameterization, formulated on the basis of a weak nonlinear wave–wave interaction theory, is widely used to estimate the turbulent dissipation rate ε. However, this parameterization has previously been found to overestimate ε in the Antarctic Circumpolar Current (ACC). One possible reason for this overestimation is that vertical wavenumber spectra of internal wave energy are distorted from the canonical Garrett–Munk spectrum by a spectral hump at low wavenumbers (~0.01 cpm). Such distorted vertical wavenumber spectra were also observed in other mesoscale eddy-rich regions. In this study, using eikonal simulations, in which internal wave energy cascades are evaluated in the frequency–wavenumber space, we examine how the distortion of vertical wavenumber spectra impacts the accuracy of the finescale parameterization. It is shown that the finescale parameterization overestimates ε for distorted spectra with a low-vertical-wavenumber hump because it incorrectly takes into account the breaking of these low-vertical-wavenumber internal waves. This issue is exacerbated by estimating internal wave energy spectral levels from the low-wavenumber band rather than from the high-wavenumber band, which is often contaminated by noise in observations. Thus, to accurately estimate the distribution of ε in eddy-rich regions like the ACC, high-vertical-wavenumber spectral information free from noise contamination is indispensable.

Current affiliation: Applied Physics Laboratory, University of Washington, Seattle, Washington.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Anne Takahashi, annetaka@uw.edu
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