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  • Author or Editor: Gregory N. Ivey x
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Cynthia E. Bluteau, Nicole L. Jones, and Gregory N. Ivey

Abstract

A technique is presented to derive the dissipation of turbulent kinetic energy ϵ by using the maximum likelihood estimator (MLE) to fit a theoretical or known empirical model to turbulence shear spectral observations. The commonly used integration method relies on integrating the shear spectra in the viscous range, thus requiring the resolution of the highest wavenumbers of the turbulence shear spectrum. With current technology, the viscous range is not resolved at sufficiently large wavenumbers to estimate high ϵ; however, long inertial subranges can be resolved, making spectral fitting over both this subrange and the resolved portion of the viscous range an attractive method for deriving ϵ. The MLE takes into account the chi-distributed properties of the spectral observations, and so it does not rely on the log-transformed spectral observations. This fitting technique can thus take advantage of both the inertial and viscous subranges, a portion of both, or simply one of the subranges. This flexibility allows a broad range of ϵ to be resolved. The estimated ϵ is insensitive to the range of wavenumbers fitted with the model, provided the noise-dominated portion of the spectra and the low wavenumbers impacted by the mean flow are avoided. For W kg−1, the MLE fitting estimates agree with those obtained by integrating the spectral observations. However, with increasing ϵ the viscous subrange is not fully resolved and the integration method progressively starts to underestimate ϵ compared with the values obtained from fitting the spectral observations.

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Cynthia E. Bluteau, Nicole L. Jones, and Gregory N. Ivey

Abstract

For measurements from either profiling or moored instruments, several processing techniques exist to estimate the dissipation rate of turbulent kinetic energy ϵ, a core quantity used to determine oceanic mixing rates. Moored velocimeters can provide long-term measurements of ϵ, but they can be plagued by motion-induced contamination. To remove this contamination, two methodologies are presented that use independent measurements of the instrument’s acceleration and rotation in space. The first is derived from the relationship between the spectra (cospectra) and the variance (covariance) of a time series. The cospectral technique recovers the environmental (or true) velocity spectrum by summing the measured spectrum, the motion-induced spectrum, and the cospectrum between the motion-induced and measured velocities. The second technique recovers the environmental spectrum by correcting the measured spectrum with the squared coherency, essentially assuming that the measured signal shares variance with either the environmental signal or the motion signal. Both techniques are applied to moored velocimeters at 7.5 and 20.5 m above the seabed in 105 m of water. By estimating the orbital velocities from their respective spectra and comparing them against those obtained from nearby wave measurements, the study shows that the surface wave signature is recovered with the cospectral technique, while it is underpredicted with the squared coherency technique. The latter technique is particularly problematic when the instrument’s motion is in phase with the orbital (environmental) velocities, as it removes variance that should have been added to the measured spectrum. The estimated ϵ from the cospectral technique compares well with estimates from nearby microstructure velocity shear vertical profiles.

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Cynthia E. Bluteau, Rolf G. Lueck, Gregory N. Ivey, Nicole L. Jones, Jeffrey W. Book, and Ana E. Rice

Abstract

Ocean mixing has historically been estimated using Osborn’s model by measuring the rate of dissipation of turbulent kinetic energy ϵ and the background density stratification N while assuming a value of the flux Richardson number . A constant is typically assumed, despite mounting field, laboratory, and modeling evidence that varies. This challenge can be overcome by estimating the turbulent diffusivity of heat using the Osborn–Cox model. This model, however, requires measuring the rate of dissipation of thermal variance χ, which has historically been challenging, particularly in energetic flows because the high wavenumbers of the temperature gradient spectra are unresolved with current technology. To overcome this difficulty, a method is described that determines χ by spectral fitting to the inertial-convective (IC) subrange of the temperature gradient spectra. While this concept has been exploited for moored time series, particularly near the bottom boundary, it has yet to be adapted to vertical microstructure profilers such as gliders, and autonomous and ship-based vertical profilers from which there are the most measurements. By using the IC subrange, χ, and hence , can be estimated even in very energetic events—precisely the conditions requiring more field observations. During less energetic periods, the temperature gradient spectra can also be integrated to obtain χ. By combining these two techniques, microstrucure profiles at a field site known for its very energetic internal waves are analyzed. This study demonstrates that the spectral fitting approach resolves intense mixing events with . By equating the Osborn and Osborn–Cox models, indirect estimates for can also be obtained.

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