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

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) region. One possible reason for this overestimation is that vertical wavenumber spectra of internal wave energy are distorted from the canonical Garrett-Munk spectrum and have a spectral “hump” at low vertical wavenumbers. 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 on 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, in order 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. 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) region. One possible reason for this overestimation is that vertical wavenumber spectra of internal wave energy are distorted from the canonical Garrett-Munk spectrum and have a spectral “hump” at low vertical wavenumbers. 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 on 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, in order 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.