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- Author or Editor: James N. Moum x

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## Abstract

A low-power (<10 mW), physically small (15.6 cm long × 3.2 cm diameter), lightweight (600 g Cu; alternatively, 200 g Al), robust, and simply calibrated pitot-static tube to measure mean speed and turbulence dissipation ^{−1} bias, and root-mean-square error of residuals (observed minus fitted values) = 0.055 m s^{−1}. Direct estimates of ^{–9} m^{2} s^{–3}. In comparison to the airfoil (or shear) probe, the pitot-static tube provides the full spectrum of velocity, not just the dissipation range of the spectrum. In comparison to acoustic measurements of velocity, the pitot-static tube does not require acoustic scatters in the measurement volume. This makes the sensor a candidate for use in the deep ocean, for example, where acoustic scatterers are weak.

## Abstract

A low-power (<10 mW), physically small (15.6 cm long × 3.2 cm diameter), lightweight (600 g Cu; alternatively, 200 g Al), robust, and simply calibrated pitot-static tube to measure mean speed and turbulence dissipation ^{−1} bias, and root-mean-square error of residuals (observed minus fitted values) = 0.055 m s^{−1}. Direct estimates of ^{–9} m^{2} s^{–3}. In comparison to the airfoil (or shear) probe, the pitot-static tube provides the full spectrum of velocity, not just the dissipation range of the spectrum. In comparison to acoustic measurements of velocity, the pitot-static tube does not require acoustic scatters in the measurement volume. This makes the sensor a candidate for use in the deep ocean, for example, where acoustic scatterers are weak.

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## Abstract

A reexamination of turbulence dissipation measurements from the equatorial Pacific shows that the turbulence diffusivities are not a simple function of the gradient Richardson number. A widely used mixing scheme, the *K*-profile parameterization, overpredicts the turbulent vertical heat flux by roughly a factor of 4 in the stably stratified region between the surface mixed layer and the Equatorial Undercurrent (EUC). Additionally, the heat flux divergence is of the incorrect sign in the upper 80 m. An alternative class of parameterizations is examined that expresses the mixing coefficients in terms of the large-scale kinetic energy, shear, and Richardson number. These representations collapse the turbulence diffusivities above and below the Equatorial Undercurrent, and a tuned version is able to reproduce the vertical turbulence heat flux within the 50–180-m depth range. Kinetic energy is not Galilean invariant, so the collapse of the data with the new parameterization suggests that oceanic turbulence responds to boundary forcing at depths well below the surface mixed layer.

## Abstract

A reexamination of turbulence dissipation measurements from the equatorial Pacific shows that the turbulence diffusivities are not a simple function of the gradient Richardson number. A widely used mixing scheme, the *K*-profile parameterization, overpredicts the turbulent vertical heat flux by roughly a factor of 4 in the stably stratified region between the surface mixed layer and the Equatorial Undercurrent (EUC). Additionally, the heat flux divergence is of the incorrect sign in the upper 80 m. An alternative class of parameterizations is examined that expresses the mixing coefficients in terms of the large-scale kinetic energy, shear, and Richardson number. These representations collapse the turbulence diffusivities above and below the Equatorial Undercurrent, and a tuned version is able to reproduce the vertical turbulence heat flux within the 50–180-m depth range. Kinetic energy is not Galilean invariant, so the collapse of the data with the new parameterization suggests that oceanic turbulence responds to boundary forcing at depths well below the surface mixed layer.

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## Abstract

Direct determination of the irreversible turbulent flux of salinity in the ocean has not been possible because of the complexity of measuring salinity on the smallest scales over which it mixes. Presented is an analysis of turbulent salinity microstructure from measurements using a combined fast-conductivity/temperature probe on a slowly falling vertical microstructure profiler. Four hundred patches of ocean turbulence were selected for the analysis. Highly resolved spectra of salinity gradient Ψ_{
Sz
}
*k*
^{+1} dependence in the viscous–convective subrange, followed by a roll-off in the viscous–diffusive subrange, as suggested by Batchelor, and permit the dissipation rate of salinity variance *χ*
_{
S
} to be determined. Estimates of irreversible salinity flux from measurements of the dissipation scales (from *χ*
_{
S
}, following Osborn and Cox) are compared to those from the correlation method (〈*w*′*S*′〉), from TKE dissipation measurements (following Osborn), and to the turbulent heat flux. It is found that the ratio of haline to thermal turbulent diffusivities, *d*
_{
x
} = *K*
_{
S
}/*K*
_{
T
} = *χ*
_{
S
}/*χ*
_{
T
}(*dT*/*dS*)^{2} is 0.6 < *d*
_{
x
} < 1.1.

## Abstract

Direct determination of the irreversible turbulent flux of salinity in the ocean has not been possible because of the complexity of measuring salinity on the smallest scales over which it mixes. Presented is an analysis of turbulent salinity microstructure from measurements using a combined fast-conductivity/temperature probe on a slowly falling vertical microstructure profiler. Four hundred patches of ocean turbulence were selected for the analysis. Highly resolved spectra of salinity gradient Ψ_{
Sz
}
*k*
^{+1} dependence in the viscous–convective subrange, followed by a roll-off in the viscous–diffusive subrange, as suggested by Batchelor, and permit the dissipation rate of salinity variance *χ*
_{
S
} to be determined. Estimates of irreversible salinity flux from measurements of the dissipation scales (from *χ*
_{
S
}, following Osborn and Cox) are compared to those from the correlation method (〈*w*′*S*′〉), from TKE dissipation measurements (following Osborn), and to the turbulent heat flux. It is found that the ratio of haline to thermal turbulent diffusivities, *d*
_{
x
} = *K*
_{
S
}/*K*
_{
T
} = *χ*
_{
S
}/*χ*
_{
T
}(*dT*/*dS*)^{2} is 0.6 < *d*
_{
x
} < 1.1.

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## Abstract

Horizontal tow measurements of internal waves are rare and have been largely supplanted in recent decades by vertical profile measurements. Here, estimates of isotherm displacements and turbulence dissipation rate from a towed vehicle deployed near Hawaii are presented. The displacement data are interpreted in terms of horizontal wavenumber spectra of isopycnal slope. The spectra span scales from 5 km to 0.1 m, encompassing both internal waves and turbulence. The turbulence subrange is identified using a standard turbulence fit, and the rest of the motions are deemed to be internal waves. The remaining subrange has a slightly red slope (*ϕ* ∼ *k*
^{−1/2}
_{
x
}) and vertical coherences compatible with internal waves, in agreement with previous towed measurements. However, spectral amplitudes in the internal wave subrange exhibit surprisingly little variation despite a four-order-of-magnitude change in turbulence dissipation rate observed at the site. The shape and amplitude of the horizontal spectra are shown to be consistent with observations and models of vertical internal wave spectra that consist of two subranges: a “linear” subrange (*ϕ* ∼ *k*
^{0}
_{
z
}) and a red “saturated” subrange (*ϕ* ∼ *k*
^{−1}
_{
z
}). These two subranges are blurred in the transformation to horizontal spectra, yielding slopes close to those observed. The saturated subrange does not admit amplitude variations in the spectra yet is an important component of the measured horizontal spectra, explaining the poor correspondence with the dissipation rate.

## Abstract

Horizontal tow measurements of internal waves are rare and have been largely supplanted in recent decades by vertical profile measurements. Here, estimates of isotherm displacements and turbulence dissipation rate from a towed vehicle deployed near Hawaii are presented. The displacement data are interpreted in terms of horizontal wavenumber spectra of isopycnal slope. The spectra span scales from 5 km to 0.1 m, encompassing both internal waves and turbulence. The turbulence subrange is identified using a standard turbulence fit, and the rest of the motions are deemed to be internal waves. The remaining subrange has a slightly red slope (*ϕ* ∼ *k*
^{−1/2}
_{
x
}) and vertical coherences compatible with internal waves, in agreement with previous towed measurements. However, spectral amplitudes in the internal wave subrange exhibit surprisingly little variation despite a four-order-of-magnitude change in turbulence dissipation rate observed at the site. The shape and amplitude of the horizontal spectra are shown to be consistent with observations and models of vertical internal wave spectra that consist of two subranges: a “linear” subrange (*ϕ* ∼ *k*
^{0}
_{
z
}) and a red “saturated” subrange (*ϕ* ∼ *k*
^{−1}
_{
z
}). These two subranges are blurred in the transformation to horizontal spectra, yielding slopes close to those observed. The saturated subrange does not admit amplitude variations in the spectra yet is an important component of the measured horizontal spectra, explaining the poor correspondence with the dissipation rate.

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## Abstract

Isopycnal slope spectra were computed from thermistor data obtained using a microstructure platform towed through turbulence generated by internal tidal motions near the Hawaiian Ridge. The spectra were compared with turbulence dissipation rates *ε* that are estimated using shear probes. The turbulence subrange of isopycnal slope spectra extends to surprisingly large horizontal wavelengths (>100 m). A four-order-of-magnitude range in turbulence dissipation rates at this site reveals that isopycnal slope spectra ∝ *ε*
^{2/3}
*k*
^{1/3}
_{
x
}. The turbulence spectral subrange (*k _{x}
* > 0.4 cpm) responds to the dissipation rate as predicted by the Batchelor model spectrum, both in amplitude and towed vertical coherence. Scales between 100 and 1000 m are modeled by a linear combination of internal waves and turbulence while at larger scales internal waves dominate. The broad bandwidth of the turbulence subrange means that a fit of spectral amplitude to the Batchelor model yields reasonable estimates of

*ε*, even when applied at scales of tens of meters that in vertical profiles would be obscured by other fine structure.

## Abstract

Isopycnal slope spectra were computed from thermistor data obtained using a microstructure platform towed through turbulence generated by internal tidal motions near the Hawaiian Ridge. The spectra were compared with turbulence dissipation rates *ε* that are estimated using shear probes. The turbulence subrange of isopycnal slope spectra extends to surprisingly large horizontal wavelengths (>100 m). A four-order-of-magnitude range in turbulence dissipation rates at this site reveals that isopycnal slope spectra ∝ *ε*
^{2/3}
*k*
^{1/3}
_{
x
}. The turbulence spectral subrange (*k _{x}
* > 0.4 cpm) responds to the dissipation rate as predicted by the Batchelor model spectrum, both in amplitude and towed vertical coherence. Scales between 100 and 1000 m are modeled by a linear combination of internal waves and turbulence while at larger scales internal waves dominate. The broad bandwidth of the turbulence subrange means that a fit of spectral amplitude to the Batchelor model yields reasonable estimates of

*ε*, even when applied at scales of tens of meters that in vertical profiles would be obscured by other fine structure.

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## Abstract

A procedure for estimating thermal variance dissipation rate *χ _{T}
* by scaling the inertial-convective subrange of temperature gradient spectra from thermistor measurements on a Tropical Atmosphere Ocean (TAO) equatorial mooring, maintained by NOAA’s National Data Buoy Center, is demonstrated. The inertial-convective subrange of wavenumbers/frequencies is contaminated by the vertical motion induced by the pumping of the surface float by surface gravity waves through the local vertical temperature gradient. The uncontaminated signal can be retrieved by removing the part of the measured signal that is coherent with the signal induced by surface gravity waves, which must be measured independently. An estimate of

*χ*is then obtained by fitting corrected spectra to theoretical temperature gradient spectra over the inertial-convective subrange (0.05 <

_{T}*f*< 0.5 Hz); this estimate is referred to as

*χ*

_{T}^{IC}. Here

*χ*

_{T}^{IC}was calculated over 120-min intervals and compared with estimates of

*χ*determined by scaling temperature gradient spectra at high wavenumbers (viscous-convective and viscous-diffusive subranges). Large differences up to a factor of 20 and of unknown origin occur infrequently, especially when both background currents and vertical temperature gradients are weak, but the results herein indicate that 75% of the data pairs are within a factor of 3 of each other. Tests on 15-, 30-, 60-, 120-min intervals demonstrate that differences between the two methods are nearly random, unbiased, and less than estimates of natural variability determined from unrelated experiments at the same location. Because the inertial-convective subrange occupies a lower-frequency range than is typically used for turbulence measurements, the potential for more routine measurements of

_{T}^{o}*χ*exists. The evaluation of degraded signals (resampled from original measurements) indicates that a particularly important component of such a measurement is the independent resolution of the surface wave–induced signal.

_{T}## Abstract

A procedure for estimating thermal variance dissipation rate *χ _{T}
* by scaling the inertial-convective subrange of temperature gradient spectra from thermistor measurements on a Tropical Atmosphere Ocean (TAO) equatorial mooring, maintained by NOAA’s National Data Buoy Center, is demonstrated. The inertial-convective subrange of wavenumbers/frequencies is contaminated by the vertical motion induced by the pumping of the surface float by surface gravity waves through the local vertical temperature gradient. The uncontaminated signal can be retrieved by removing the part of the measured signal that is coherent with the signal induced by surface gravity waves, which must be measured independently. An estimate of

*χ*is then obtained by fitting corrected spectra to theoretical temperature gradient spectra over the inertial-convective subrange (0.05 <

_{T}*f*< 0.5 Hz); this estimate is referred to as

*χ*

_{T}^{IC}. Here

*χ*

_{T}^{IC}was calculated over 120-min intervals and compared with estimates of

*χ*determined by scaling temperature gradient spectra at high wavenumbers (viscous-convective and viscous-diffusive subranges). Large differences up to a factor of 20 and of unknown origin occur infrequently, especially when both background currents and vertical temperature gradients are weak, but the results herein indicate that 75% of the data pairs are within a factor of 3 of each other. Tests on 15-, 30-, 60-, 120-min intervals demonstrate that differences between the two methods are nearly random, unbiased, and less than estimates of natural variability determined from unrelated experiments at the same location. Because the inertial-convective subrange occupies a lower-frequency range than is typically used for turbulence measurements, the potential for more routine measurements of

_{T}^{o}*χ*exists. The evaluation of degraded signals (resampled from original measurements) indicates that a particularly important component of such a measurement is the independent resolution of the surface wave–induced signal.

_{T}^{ }

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## Abstract

At the smallest length scales, conductivity measurements include a contribution from salinity fluctuations in the inertial–convective and viscous–diffusive ranges of the turbulent scalar variance spectrum. Interpreting these measurements is complicated because conductivity is a compound quantity of both temperature and salinity. Accurate estimates of the dissipation rate of salinity variance *χ*
_{
S
} and temperature variance *χ*
_{
T
} from conductivity gradient spectra _{
C
z
}(*k*)_{
S
z
T
z
}(*k*)_{
S
z
T
z
}|_{
S
z
}Ψ_{
T
z
}

Highly resolved conductivity measurements were made using a four-point conductivity probe mounted on the loosely tethered vertical profiler *Chameleon* during cruises in 1991 and 1992. Thirty-eight turbulent patches were selected for homogeneity in shear, temperature gradient, and salinity gradient fluctuations and for clear relationship between temperature and salinity. Estimates of *χ*
_{
T
} and *χ*
_{
S
} from the conductivity probe are found to agree with independent estimators from a conventional thermistor probe.

## Abstract

At the smallest length scales, conductivity measurements include a contribution from salinity fluctuations in the inertial–convective and viscous–diffusive ranges of the turbulent scalar variance spectrum. Interpreting these measurements is complicated because conductivity is a compound quantity of both temperature and salinity. Accurate estimates of the dissipation rate of salinity variance *χ*
_{
S
} and temperature variance *χ*
_{
T
} from conductivity gradient spectra _{
C
z
}(*k*)_{
S
z
T
z
}(*k*)_{
S
z
T
z
}|_{
S
z
}Ψ_{
T
z
}

Highly resolved conductivity measurements were made using a four-point conductivity probe mounted on the loosely tethered vertical profiler *Chameleon* during cruises in 1991 and 1992. Thirty-eight turbulent patches were selected for homogeneity in shear, temperature gradient, and salinity gradient fluctuations and for clear relationship between temperature and salinity. Estimates of *χ*
_{
T
} and *χ*
_{
S
} from the conductivity probe are found to agree with independent estimators from a conventional thermistor probe.

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## Abstract

A scheme for significantly reducing data sampled on turbulence devices (*χ*pods) deployed on remote oceanographic moorings is proposed. Each *χ*pod is equipped with a pitot-static tube, two fast-response thermistors, a three-axis linear accelerometer, and a compass. In preprocessing, voltage means, variances, and amplitude of the *χ* from which other turbulence quantities, such as heat flux, are derived. On 10-min averages, this scheme reduces the data by a factor of roughly 24 000 with a small (5%) low bias compared to complete estimates using inertial-convective subrange scaling of calibrated temperature gradient spectra.

## Abstract

A scheme for significantly reducing data sampled on turbulence devices (*χ*pods) deployed on remote oceanographic moorings is proposed. Each *χ*pod is equipped with a pitot-static tube, two fast-response thermistors, a three-axis linear accelerometer, and a compass. In preprocessing, voltage means, variances, and amplitude of the *χ* from which other turbulence quantities, such as heat flux, are derived. On 10-min averages, this scheme reduces the data by a factor of roughly 24 000 with a small (5%) low bias compared to complete estimates using inertial-convective subrange scaling of calibrated temperature gradient spectra.

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## Abstract

Turbulent bottom Ekman layers are among the most important energy conversion sites in the ocean. Their energetics are notoriously complex, in particular near sloping topography, where the feedback between cross-slope Ekman transports, buoyancy forcing, and mixing affects the energy budget in ways that are not well understood. Here, the authors attempt to clarify the energy pathways and different routes to mixing, using a combined theoretical and modeling approach. The analysis is based on a newly developed energy flux diagram for turbulent Ekman layers near sloping topography that allows for an exact definition of the different energy reservoirs and energy pathways. Using a second-moment turbulence model, it is shown that mixing efficiencies increase for increasing slope angle and interior stratification, but do not exceed the threshold of 5% except for very steep slopes, where the canonical value of 20% may be reached. Available potential energy generated by cross-slope advection may equal up to 70% of the energy lost to dissipation for upwelling-favorable flow, and up to 40% for downwelling-favorable flow.

## Abstract

Turbulent bottom Ekman layers are among the most important energy conversion sites in the ocean. Their energetics are notoriously complex, in particular near sloping topography, where the feedback between cross-slope Ekman transports, buoyancy forcing, and mixing affects the energy budget in ways that are not well understood. Here, the authors attempt to clarify the energy pathways and different routes to mixing, using a combined theoretical and modeling approach. The analysis is based on a newly developed energy flux diagram for turbulent Ekman layers near sloping topography that allows for an exact definition of the different energy reservoirs and energy pathways. Using a second-moment turbulence model, it is shown that mixing efficiencies increase for increasing slope angle and interior stratification, but do not exceed the threshold of 5% except for very steep slopes, where the canonical value of 20% may be reached. Available potential energy generated by cross-slope advection may equal up to 70% of the energy lost to dissipation for upwelling-favorable flow, and up to 40% for downwelling-favorable flow.

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## Abstract

The role of turbulent mixing in regulating the ocean’s response to the Madden–Julian oscillation (MJO) is assessed from measurements of surface forcing, acoustic, and microstructure profiles during October–early December 2011 at 0°, 80.5°E in the Indian Ocean. During the active phase of the MJO, the surface mixed layer was cooled from above by air–sea fluxes and from below by turbulent mixing, in roughly equal proportions. During the suppressed and disturbed phases, the mixed layer temperature increased, primarily because of the vertical divergence between net surface warming and turbulent cooling. Despite heavy precipitation during the active phase, subsurface mixing was sufficient to increase the mixed layer salinity by entraining salty Arabian Sea Water from the pycnocline. The turbulent salt flux across the mixed layer base was, on average, 2 times as large as the surface salt flux. Wind stress accelerated the Yoshida–Wyrtki jet, while the turbulent stress was primarily responsible for decelerating the jet through the active phase, during which the mean turbulent stress was roughly 65% of the mean surface wind stress. These turbulent processes may account for systematic errors in numerical models of MJO evolution.

## Abstract

The role of turbulent mixing in regulating the ocean’s response to the Madden–Julian oscillation (MJO) is assessed from measurements of surface forcing, acoustic, and microstructure profiles during October–early December 2011 at 0°, 80.5°E in the Indian Ocean. During the active phase of the MJO, the surface mixed layer was cooled from above by air–sea fluxes and from below by turbulent mixing, in roughly equal proportions. During the suppressed and disturbed phases, the mixed layer temperature increased, primarily because of the vertical divergence between net surface warming and turbulent cooling. Despite heavy precipitation during the active phase, subsurface mixing was sufficient to increase the mixed layer salinity by entraining salty Arabian Sea Water from the pycnocline. The turbulent salt flux across the mixed layer base was, on average, 2 times as large as the surface salt flux. Wind stress accelerated the Yoshida–Wyrtki jet, while the turbulent stress was primarily responsible for decelerating the jet through the active phase, during which the mean turbulent stress was roughly 65% of the mean surface wind stress. These turbulent processes may account for systematic errors in numerical models of MJO evolution.