Varieties of Fully Resolved Spectra of Vertical Shear

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  • 1 Applied Physics Laboratory and School of Oceanography, College of Ocean and Fishery Sciences, University of Washington, Seattle, Washington
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Abstract

The Multi-Scale profiler (MSP) resolves shear between vertical wavenumbers of 0.01 cpm and the viscous cutoff of small-scale turbulence. Observations from five sites reveal varied spectral shapes and amplitudes. Spectral amplitudes measured at low latitude do not increase toward the equator, contrary to Munk, and their shapes differ from the Garrett and Munk model by having weak maxima between 0.02 and 0.05 cpm. Moreover, at wavenumbers larger than 0.1 cpm these spectra roll off more steeply, k3−1, than do spectra at midlatitude. Of two average spectra from midlatitude, one is close to the Garrett and Munk model at low wavenumbers, and at 0.1 cpm it begins to roll off as k3−1. The second midlatitude spectrum has amplitudes well above Garrett and Munk at low wavenumbers, begins a k3−1 rolloff near 0.04 cpm, and has a well-developed turbulent range near 1 cpm. The decrease in the start of the rolloff is not linearly proportional to the increase in spectral amplitude at low wavenumber, unlike the spectra observed by Duda and Cox and models proposed by Munk and also Garrett. In spite of the diversity of shapes and amplitudes at low wavenumbers, all shear spectra have nearly the same amplitude at 0.14 cpm, which is in the rolloff range. The rolloff range cannot be a buoyancy subrange of three-dimensional turbulence because the largest overturns occur only at the high-wavenumber end of the range. Rather, the rolloff must be the signature of the high-wavenumber decay of the internal wave field. Near 0.5kE = (N3/ε)1/2 spectra change from the internal wave rolloff to the turbulent dissipation range, which is adequately represented by Nasmyth's “universal” spectrum. Midlatitude spectra with amplitudes close to the Garrett and Munk model have very weak turbulent spectra, but those with substantially larger low-wavenumber amplitudes have well-developed turbulent spectra with distinct inertial subranges. Owing to their steeper rolloffs, the low-latitude records also have weak dissipation spectra even though their spectra rise above Garrett and Munk at wavenumbers slightly less than the rolloff.

Abstract

The Multi-Scale profiler (MSP) resolves shear between vertical wavenumbers of 0.01 cpm and the viscous cutoff of small-scale turbulence. Observations from five sites reveal varied spectral shapes and amplitudes. Spectral amplitudes measured at low latitude do not increase toward the equator, contrary to Munk, and their shapes differ from the Garrett and Munk model by having weak maxima between 0.02 and 0.05 cpm. Moreover, at wavenumbers larger than 0.1 cpm these spectra roll off more steeply, k3−1, than do spectra at midlatitude. Of two average spectra from midlatitude, one is close to the Garrett and Munk model at low wavenumbers, and at 0.1 cpm it begins to roll off as k3−1. The second midlatitude spectrum has amplitudes well above Garrett and Munk at low wavenumbers, begins a k3−1 rolloff near 0.04 cpm, and has a well-developed turbulent range near 1 cpm. The decrease in the start of the rolloff is not linearly proportional to the increase in spectral amplitude at low wavenumber, unlike the spectra observed by Duda and Cox and models proposed by Munk and also Garrett. In spite of the diversity of shapes and amplitudes at low wavenumbers, all shear spectra have nearly the same amplitude at 0.14 cpm, which is in the rolloff range. The rolloff range cannot be a buoyancy subrange of three-dimensional turbulence because the largest overturns occur only at the high-wavenumber end of the range. Rather, the rolloff must be the signature of the high-wavenumber decay of the internal wave field. Near 0.5kE = (N3/ε)1/2 spectra change from the internal wave rolloff to the turbulent dissipation range, which is adequately represented by Nasmyth's “universal” spectrum. Midlatitude spectra with amplitudes close to the Garrett and Munk model have very weak turbulent spectra, but those with substantially larger low-wavenumber amplitudes have well-developed turbulent spectra with distinct inertial subranges. Owing to their steeper rolloffs, the low-latitude records also have weak dissipation spectra even though their spectra rise above Garrett and Munk at wavenumbers slightly less than the rolloff.

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