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- Author or Editor: Cynthia E. Bluteau x

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## 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 ^{−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.

## 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 ^{−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.

## 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.

## 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.

## 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 *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 *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

## 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 *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 *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

## Abstract

Using 18 days of field observations, we investigate the diurnal (D1) frequency wave dynamics on the Tasmanian eastern continental shelf. At this latitude, the D1 frequency is subinertial and separable from the highly energetic near-inertial motion. We use a linear coastal-trapped wave (CTW) solution with the observed background current, stratification, and shelf bathymetry to determine the modal structure of the first three resonant CTWs. We associate the observed D1 velocity with a superimposed mode-zero and mode-one CTW, with mode one dominating mode zero. Both the observed and mode-one D1 velocity was intensified near the thermocline, with stronger velocities occurring when the thermocline stratification was stronger and/or the thermocline was deeper (up to the shelfbreak depth). The CTW modal structure and amplitude varied with the background stratification and alongshore current, with no spring–neap relationship evident for the observed 18 days. Within the surface and bottom Ekman layers on the shelf, the observed velocity phase changed in the cross-shelf and/or vertical directions, inconsistent with an alongshore propagating CTW. In the near-surface and near-bottom regions, the linear CTW solution also did not match the observed velocity, particularly within the bottom Ekman layer. Boundary layer processes were likely causing this observed inconsistency with linear CTW theory. As linear CTW solutions have an idealized representation of boundary dynamics, they should be cautiously applied on the shelf.

## Abstract

Using 18 days of field observations, we investigate the diurnal (D1) frequency wave dynamics on the Tasmanian eastern continental shelf. At this latitude, the D1 frequency is subinertial and separable from the highly energetic near-inertial motion. We use a linear coastal-trapped wave (CTW) solution with the observed background current, stratification, and shelf bathymetry to determine the modal structure of the first three resonant CTWs. We associate the observed D1 velocity with a superimposed mode-zero and mode-one CTW, with mode one dominating mode zero. Both the observed and mode-one D1 velocity was intensified near the thermocline, with stronger velocities occurring when the thermocline stratification was stronger and/or the thermocline was deeper (up to the shelfbreak depth). The CTW modal structure and amplitude varied with the background stratification and alongshore current, with no spring–neap relationship evident for the observed 18 days. Within the surface and bottom Ekman layers on the shelf, the observed velocity phase changed in the cross-shelf and/or vertical directions, inconsistent with an alongshore propagating CTW. In the near-surface and near-bottom regions, the linear CTW solution also did not match the observed velocity, particularly within the bottom Ekman layer. Boundary layer processes were likely causing this observed inconsistency with linear CTW theory. As linear CTW solutions have an idealized representation of boundary dynamics, they should be cautiously applied on the shelf.

## Abstract

Near-inertial waves (NIWs) are often an energetic component of the internal wave field on windy continental shelves. The effect of baroclinic geostrophic currents, which introduce both relative vorticity and baroclinicity, on NIWs is not well understood. Relative vorticity affects the resonant frequency *f*
_{eff}, while both relative vorticity and baroclinicity modify the minimum wave frequency of freely propagating waves *ω*
_{min}. On a windy and narrow shelf, we observed wind-forced oscillations that generated NIWs where *f*
_{eff} was less than the Coriolis frequency *f*. If everywhere *f*
_{eff} > *f* then NIWs were generated where *ω*
_{min} < *f* and *f*
_{eff} was smallest. The background current not only affected the location of generation, but also the NIWs’ propagation direction. The estimated NIW energy fluxes show that NIWs propagated predominantly toward the equator because *ω*
_{min} > *f* on the continental slope for the entire sample period. In addition to being laterally trapped on the shelf, we observed vertically trapped and intensified NIWs that had a frequency *ω* within the anomalously low-frequency band (i.e., *ω*
_{min} < *ω* < *f*
_{eff}), which only exists if the baroclinicity is nonzero. We observed two periods when *ω*
_{min} < *f* on the shelf, but the relative vorticity was positive (i.e., *f*
_{eff} > *f*) for one of these periods. The process of NIW propagation remained consistent with the local *ω*
_{min}, and not *f*
_{eff}, emphasizing the importance of baroclinicity on the NIW dynamics. We conclude that windy shelves with baroclinic background currents are likely to have energetic NIWs, but the current and seabed will adjust the spatial distribution and energetics of these NIWs.

## Abstract

Near-inertial waves (NIWs) are often an energetic component of the internal wave field on windy continental shelves. The effect of baroclinic geostrophic currents, which introduce both relative vorticity and baroclinicity, on NIWs is not well understood. Relative vorticity affects the resonant frequency *f*
_{eff}, while both relative vorticity and baroclinicity modify the minimum wave frequency of freely propagating waves *ω*
_{min}. On a windy and narrow shelf, we observed wind-forced oscillations that generated NIWs where *f*
_{eff} was less than the Coriolis frequency *f*. If everywhere *f*
_{eff} > *f* then NIWs were generated where *ω*
_{min} < *f* and *f*
_{eff} was smallest. The background current not only affected the location of generation, but also the NIWs’ propagation direction. The estimated NIW energy fluxes show that NIWs propagated predominantly toward the equator because *ω*
_{min} > *f* on the continental slope for the entire sample period. In addition to being laterally trapped on the shelf, we observed vertically trapped and intensified NIWs that had a frequency *ω* within the anomalously low-frequency band (i.e., *ω*
_{min} < *ω* < *f*
_{eff}), which only exists if the baroclinicity is nonzero. We observed two periods when *ω*
_{min} < *f* on the shelf, but the relative vorticity was positive (i.e., *f*
_{eff} > *f*) for one of these periods. The process of NIW propagation remained consistent with the local *ω*
_{min}, and not *f*
_{eff}, emphasizing the importance of baroclinicity on the NIW dynamics. We conclude that windy shelves with baroclinic background currents are likely to have energetic NIWs, but the current and seabed will adjust the spatial distribution and energetics of these NIWs.