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## Abstract

Vertical velocities in the ocean boundary layer were measured for two weeks at an open ocean, wintertime site using neutrally buoyant floats. Simultaneous measurements of the surface meteorology and surface waves showed a large variability in both wind and wave properties and only weak correlations between them. Buoyancy forcing was weak. The mean square vertical velocity in the boundary layer *σ*
^{2}
_{
w
}
*u*
^{2}
_{∗}
*σ*
^{2}
_{
w
}
*A*
*u*
^{2}
_{∗}
*ρ*
*u*
^{2}
_{∗}
*ρ* is the density of the water). The deviations from this relation can be attributed entirely to statistical variation and measurement error. The measured values of *σ*
^{2}
_{
w
}
*A*

## Abstract

Vertical velocities in the ocean boundary layer were measured for two weeks at an open ocean, wintertime site using neutrally buoyant floats. Simultaneous measurements of the surface meteorology and surface waves showed a large variability in both wind and wave properties and only weak correlations between them. Buoyancy forcing was weak. The mean square vertical velocity in the boundary layer *σ*
^{2}
_{
w
}
*u*
^{2}
_{∗}
*σ*
^{2}
_{
w
}
*A*
*u*
^{2}
_{∗}
*ρ*
*u*
^{2}
_{∗}
*ρ* is the density of the water). The deviations from this relation can be attributed entirely to statistical variation and measurement error. The measured values of *σ*
^{2}
_{
w
}
*A*

## Abstract

Three neutrally buoyant floats were air deployed ahead of Hurricane Dennis on 28 August 1999. These floats were designed to accurately follow three-dimensional water trajectories and measure pressure (i.e., their own depth) and temperature. The hurricane eye passed between two of the floats; both measured the properties of the ocean boundary layer beneath sustained 30 m s^{−1} winds. The floats repeatedly moved through a mixed layer 30–70 m deep at average vertical speeds of 0.03–0.06 m s^{−1}. The speed was roughly proportional to the friction velocity. Mixed layer temperature cooled about 2.8° and 0.75°C at the floats on the east and west sides of the northward-going storm, respectively. Much of the cooling occurred before the eye passage. The remaining terms in the horizontally averaged mixed layer heat budget, the vertical velocity–temperature covariance and the Lagrangian heating rate, were computed from the float data. Surface heat fluxes accounted for only a small part of the cooling. Most of the cooling was due to entrainment of colder water from below and, on the right-hand (east) side only, horizontal advection and mixing with colder water. The larger entrainment flux on this side of the hurricane was presumably due to the much larger inertial currents and shear. Although these floats can make detailed measurements of the heat transfer mechanisms in the ocean boundary layer under these severe conditions, accurate measurements of heat flux will require clusters of many floats to reduce the statistical error.

## Abstract

Three neutrally buoyant floats were air deployed ahead of Hurricane Dennis on 28 August 1999. These floats were designed to accurately follow three-dimensional water trajectories and measure pressure (i.e., their own depth) and temperature. The hurricane eye passed between two of the floats; both measured the properties of the ocean boundary layer beneath sustained 30 m s^{−1} winds. The floats repeatedly moved through a mixed layer 30–70 m deep at average vertical speeds of 0.03–0.06 m s^{−1}. The speed was roughly proportional to the friction velocity. Mixed layer temperature cooled about 2.8° and 0.75°C at the floats on the east and west sides of the northward-going storm, respectively. Much of the cooling occurred before the eye passage. The remaining terms in the horizontally averaged mixed layer heat budget, the vertical velocity–temperature covariance and the Lagrangian heating rate, were computed from the float data. Surface heat fluxes accounted for only a small part of the cooling. Most of the cooling was due to entrainment of colder water from below and, on the right-hand (east) side only, horizontal advection and mixing with colder water. The larger entrainment flux on this side of the hurricane was presumably due to the much larger inertial currents and shear. Although these floats can make detailed measurements of the heat transfer mechanisms in the ocean boundary layer under these severe conditions, accurate measurements of heat flux will require clusters of many floats to reduce the statistical error.

## Abstract

The evolution of near-inertial frequency currents is often thought to be controlled by the linear, inviscid equations of motion. This hypothesis is tested by simulating the near-inertial currents described in Part I using a two-dimensional, nearly inviscid, nonlinear layer model with realistic wind forcing and stratification. The β effect and mixing of momentum below the mixed layer during the storm are crucial to realistic modeling, whereas the nonlinear terms have only a minor effect. The model fails to simulate the observations in several ways. First, the mixed layer inertial currents decay more rapidly than predicted and propagate into the thermocline with a different pattern. Second, the shear at the base of the mixed layer decays much more rapidly than predicted. Third, mesoscale eddies modulate the evolution of the inertial currents much less than predicted. These differences are much larger than the errors in the observations and cannot be removed by reasonable variations of the forcing or stratification. The nearly linear and inviscid internal wave equations thus cannot accurately predict the observed evolution of the near-inertial currents; additional physical processes, perhaps nonlinear interactions with smaller-scale internal waves and/or fronts, are required in the equations.

## Abstract

The evolution of near-inertial frequency currents is often thought to be controlled by the linear, inviscid equations of motion. This hypothesis is tested by simulating the near-inertial currents described in Part I using a two-dimensional, nearly inviscid, nonlinear layer model with realistic wind forcing and stratification. The β effect and mixing of momentum below the mixed layer during the storm are crucial to realistic modeling, whereas the nonlinear terms have only a minor effect. The model fails to simulate the observations in several ways. First, the mixed layer inertial currents decay more rapidly than predicted and propagate into the thermocline with a different pattern. Second, the shear at the base of the mixed layer decays much more rapidly than predicted. Third, mesoscale eddies modulate the evolution of the inertial currents much less than predicted. These differences are much larger than the errors in the observations and cannot be removed by reasonable variations of the forcing or stratification. The nearly linear and inviscid internal wave equations thus cannot accurately predict the observed evolution of the near-inertial currents; additional physical processes, perhaps nonlinear interactions with smaller-scale internal waves and/or fronts, are required in the equations.

## Abstract

The interaction of strong near-inertial frequency currents generated by a storm with preexisting subinertial frequency currents is investigated. For 10 days after the storm, the near-inertial currents remain in the mixed layer and the subinertial currents are steady, so their interaction is particularly simple. Linearized models predict that the frequency of the near-inertial currents should be shifted by ½ζ where ζ is the subinertial vorticity. This theory, combined with values of ζ estimated either from velocity measurements or from the vorticity equation, produces frequency shifts in the inertial currents at least five times larger than the confidence limits on the observations. Possible explanations include the concentration of ζ in narrow frontal zones and nonlinear wave-wave interactions.

## Abstract

The interaction of strong near-inertial frequency currents generated by a storm with preexisting subinertial frequency currents is investigated. For 10 days after the storm, the near-inertial currents remain in the mixed layer and the subinertial currents are steady, so their interaction is particularly simple. Linearized models predict that the frequency of the near-inertial currents should be shifted by ½ζ where ζ is the subinertial vorticity. This theory, combined with values of ζ estimated either from velocity measurements or from the vorticity equation, produces frequency shifts in the inertial currents at least five times larger than the confidence limits on the observations. Possible explanations include the concentration of ζ in narrow frontal zones and nonlinear wave-wave interactions.

## Abstract

Rain in tropical cyclones is studied using eight time series of underwater ambient sound at 40–50 kHz with wind speeds up to 45 m s^{−1} beneath three tropical cyclones. At tropical cyclone wind speeds, rain- and wind-generated sound levels are comparable, and therefore rain cannot be detected by sound level alone. A rain detection algorithm that is based on the variations of 5–30-kHz sound levels with periods longer than 20 s and shorter than 30 min is proposed. Faster fluctuations (<20 s) are primarily due to wave breaking, and slower ones (>30 min) are due to overall wind variations. Higher-frequency sound (>30 kHz) is strongly attenuated by bubble clouds. This approach is supported by observations that, for wind speeds < 40 m s^{−1}, the variation in sound level is much larger than that expected from observed wind variations and is roughly comparable to that expected from rain variations. The hydrophone results are consistent with rain estimates by the Tropical Rainfall Measuring Mission (TRMM) satellite and with Stepped-Frequency Microwave Radiometer (SFMR) and radar estimates by surveillance flights. The observations indicate that the rain-generated sound fluctuations have broadband acoustic spectra centered around 10 kHz. Acoustically detected rain events usually last for a few minutes. The data used in this study are insufficient to produce useful estimation of rain rate from ambient sound because of limited quantity and accuracy of the validation data. The frequency dependence of sound variations suggests that quantitative rainfall algorithms from ambient sound may be developed using multiple sound frequencies.

### Significance Statement

Rain is an indispensable process in forecasting the intensity and path of tropical cyclones. However, its role in the air–sea interaction is still poorly understood, and its parameterization in numerical models is still in development. In this work, we analyzed sound measurements made by hydrophones on board Lagrangian floats beneath tropical cyclones. We find that wind, rain, and breaking waves each have distinctive signatures in underwater ambient sound. We suggest that the air–sea dynamic processes in tropical cyclones can be explored by listening to ambient sound using hydrophones beneath the sea surface.

## Abstract

Rain in tropical cyclones is studied using eight time series of underwater ambient sound at 40–50 kHz with wind speeds up to 45 m s^{−1} beneath three tropical cyclones. At tropical cyclone wind speeds, rain- and wind-generated sound levels are comparable, and therefore rain cannot be detected by sound level alone. A rain detection algorithm that is based on the variations of 5–30-kHz sound levels with periods longer than 20 s and shorter than 30 min is proposed. Faster fluctuations (<20 s) are primarily due to wave breaking, and slower ones (>30 min) are due to overall wind variations. Higher-frequency sound (>30 kHz) is strongly attenuated by bubble clouds. This approach is supported by observations that, for wind speeds < 40 m s^{−1}, the variation in sound level is much larger than that expected from observed wind variations and is roughly comparable to that expected from rain variations. The hydrophone results are consistent with rain estimates by the Tropical Rainfall Measuring Mission (TRMM) satellite and with Stepped-Frequency Microwave Radiometer (SFMR) and radar estimates by surveillance flights. The observations indicate that the rain-generated sound fluctuations have broadband acoustic spectra centered around 10 kHz. Acoustically detected rain events usually last for a few minutes. The data used in this study are insufficient to produce useful estimation of rain rate from ambient sound because of limited quantity and accuracy of the validation data. The frequency dependence of sound variations suggests that quantitative rainfall algorithms from ambient sound may be developed using multiple sound frequencies.

### Significance Statement

Rain is an indispensable process in forecasting the intensity and path of tropical cyclones. However, its role in the air–sea interaction is still poorly understood, and its parameterization in numerical models is still in development. In this work, we analyzed sound measurements made by hydrophones on board Lagrangian floats beneath tropical cyclones. We find that wind, rain, and breaking waves each have distinctive signatures in underwater ambient sound. We suggest that the air–sea dynamic processes in tropical cyclones can be explored by listening to ambient sound using hydrophones beneath the sea surface.

## Abstract

The calibration accuracy and stability of three Aanderaa 3835 optodes and three Sea-Bird Electronics SBE-43 oxygen sensors were evaluated over four years using in situ and laboratory calibrations. The sensors were mostly in storage, being in the ocean for typically only a few weeks per year and operated for only a few days per year. Both sensors measure partial pressure of oxygen, or equivalently saturation at standard pressure; results are expressed in this variable. It is assumed that sensor drift occurs in the oxygen sensitivity of the sensors, not the temperature compensation; this is well justified for the SBE-43 based on multiple calibrations. Neither sensor had significant long-term drift in output when sampling anoxic water. Sensor output at 100% saturation differed from the factory calibrations by up to ±6% (averaging −2.3% ± 3%) for the SBE-43 and up to −12.6% for the optodes. The optode output at 100% saturation is well described by a single decaying exponential with a decay constant of approximately 2 yr and an amplitude of 28%. The mechanism of this drift is unknown but is not primarily due to sensor operation. It may be different from that experienced by sensors continuously deployed in the ocean. Thus, although the optodes in this study did not have a stable calibration, their drift was stable and, once calibrated, allowed optode and SBE-43 pairs mounted on the same autonomous floats to be calibrated to an accuracy of ±0.4% over a 4-yr period.

## Abstract

The calibration accuracy and stability of three Aanderaa 3835 optodes and three Sea-Bird Electronics SBE-43 oxygen sensors were evaluated over four years using in situ and laboratory calibrations. The sensors were mostly in storage, being in the ocean for typically only a few weeks per year and operated for only a few days per year. Both sensors measure partial pressure of oxygen, or equivalently saturation at standard pressure; results are expressed in this variable. It is assumed that sensor drift occurs in the oxygen sensitivity of the sensors, not the temperature compensation; this is well justified for the SBE-43 based on multiple calibrations. Neither sensor had significant long-term drift in output when sampling anoxic water. Sensor output at 100% saturation differed from the factory calibrations by up to ±6% (averaging −2.3% ± 3%) for the SBE-43 and up to −12.6% for the optodes. The optode output at 100% saturation is well described by a single decaying exponential with a decay constant of approximately 2 yr and an amplitude of 28%. The mechanism of this drift is unknown but is not primarily due to sensor operation. It may be different from that experienced by sensors continuously deployed in the ocean. Thus, although the optodes in this study did not have a stable calibration, their drift was stable and, once calibrated, allowed optode and SBE-43 pairs mounted on the same autonomous floats to be calibrated to an accuracy of ±0.4% over a 4-yr period.

## Abstract

Simultaneous measurements of temperature, salinity, their vertical gradients, and the vertical gradient of velocity across a 1.4-m-long Lagrangian float were used to investigate the accuracy with which the dissipation of scalar variance *χ* can be computed using inertial subrange methods from such a neutrally buoyant float. The float was deployed in a variety of environments in Puget Sound; *χ* varied by about 3.5 orders of magnitude. A previous study used an inertial subrange method to yield accurate measurements of *ɛ*, the rate of dissipation of kinetic energy, from this data. Kolmogorov scaling predicts a Lagrangian frequency spectrum for the rate of change of a scalar as Φ_{
D
σ/Dt
}(*ω*) = *β*
_{
s
}
*χ*, where *β _{s}
* is a universal Kolmogorov constant. Measured spectra of the rate of change of potential density

*σ*were nearly white at frequencies above

*N*, the buoyancy frequency. Deviations at higher frequency could be modeled quantitatively using the measured deviations of the float from perfect Lagrangian behavior, yielding an empirical nondimensional form Φ

_{ D σ/Dt }=

*β*

_{ s }

*χ*

*H*(

*ω*/

*ω*

_{ L }) for the measured spectra, where

*L*is half the float length,

*ω*

^{3}

_{ L }=

*ɛ*/

*L*

^{2}, and

*H*is a function describing the deviations of the spectrum from Kolmogorov scaling. Using this empirical form, estimates of

*χ*were computed and compared with estimates derived from

*ɛ*. The required mixing efficiency was computed from the turbulent Froude number

*ω*

_{0}/

*N*, where

*ω*

_{0}is the large-eddy frequency. The results are consistent over a range of

*ɛ*from 10

^{−8}to 3 × 10

^{−5}W kg

^{−1}implying that

*χ*can be estimated from float data to an accuracy of least a factor of 2. These methods for estimating

*ɛ*,

*χ*, and the Froude number from Lagrangian floats appear to be unbiased and self-consistent for

*ɛ*> 10

^{−8}W kg

^{−1}. They are expected to fail in less energetic turbulence both for instrumental reasons and because the Reynolds number typically becomes too small to support an inertial subrange. The value of

*β*

_{ s }is estimated at 0.6 to within an uncertainty of less than a factor of 2.

## Abstract

Simultaneous measurements of temperature, salinity, their vertical gradients, and the vertical gradient of velocity across a 1.4-m-long Lagrangian float were used to investigate the accuracy with which the dissipation of scalar variance *χ* can be computed using inertial subrange methods from such a neutrally buoyant float. The float was deployed in a variety of environments in Puget Sound; *χ* varied by about 3.5 orders of magnitude. A previous study used an inertial subrange method to yield accurate measurements of *ɛ*, the rate of dissipation of kinetic energy, from this data. Kolmogorov scaling predicts a Lagrangian frequency spectrum for the rate of change of a scalar as Φ_{
D
σ/Dt
}(*ω*) = *β*
_{
s
}
*χ*, where *β _{s}
* is a universal Kolmogorov constant. Measured spectra of the rate of change of potential density

*σ*were nearly white at frequencies above

*N*, the buoyancy frequency. Deviations at higher frequency could be modeled quantitatively using the measured deviations of the float from perfect Lagrangian behavior, yielding an empirical nondimensional form Φ

_{ D σ/Dt }=

*β*

_{ s }

*χ*

*H*(

*ω*/

*ω*

_{ L }) for the measured spectra, where

*L*is half the float length,

*ω*

^{3}

_{ L }=

*ɛ*/

*L*

^{2}, and

*H*is a function describing the deviations of the spectrum from Kolmogorov scaling. Using this empirical form, estimates of

*χ*were computed and compared with estimates derived from

*ɛ*. The required mixing efficiency was computed from the turbulent Froude number

*ω*

_{0}/

*N*, where

*ω*

_{0}is the large-eddy frequency. The results are consistent over a range of

*ɛ*from 10

^{−8}to 3 × 10

^{−5}W kg

^{−1}implying that

*χ*can be estimated from float data to an accuracy of least a factor of 2. These methods for estimating

*ɛ*,

*χ*, and the Froude number from Lagrangian floats appear to be unbiased and self-consistent for

*ɛ*> 10

^{−8}W kg

^{−1}. They are expected to fail in less energetic turbulence both for instrumental reasons and because the Reynolds number typically becomes too small to support an inertial subrange. The value of

*β*

_{ s }is estimated at 0.6 to within an uncertainty of less than a factor of 2.

## Abstract

The effects of upward buoyancy on the accuracy with which Lagrangian floats can measure the Eulerian mean variance 〈*ww*〉*
_{E}
* and skewness

*S*of vertical fluid velocity

_{w}^{E}*w*in the wind-driven upper-ocean boundary layer is investigated using both simulated floats in large-eddy simulation (LES) models and two float datasets. Nearly neutrally buoyant floats are repeatedly advected by the turbulent velocities across the boundary layer. Their vertical position

*Z*is determined from pressure measurements; their

*W*variance 〈

*WW*〉

*and skewness*

_{F}*S*are determined from the time series of float

_{W}^{E}*W*=

*dZ*/

*dt*. If the float buoyancy is small, then the simulated floats measure the Eulerian velocity accurately; that is,

*δW*

^{2}= 〈

*WW*〉

*− 〈*

_{F}*ww*〉

*and*

_{E}*δS*=

_{W}*S*−

_{W}^{F}*S*are small compared to 〈

_{w}^{E}*ww*〉

*and*

_{E}*S*respectively. If the floats are buoyant, and thus have an upward vertical velocity

_{w}^{E}*W*

_{bias}relative to the water, then

*δW*

^{2}and

*δS*can become significant. Buoyancy causes the floats to oversample both shallow depths and strong vertical velocities, leading to positive values of

_{W}*δW*

^{2}and negative values of

*δS*. The skewness

_{W}*S*

_{ Z′}

*of depth measures the degree to which shallow depths are oversampled; it is shown to be a good predictor of*

^{F}*W*

_{bias}/〈

*WW*〉

_{ F }

^{1/2},

*δW*

^{2}/〈

*WW*〉, and

_{F}*δS*/

_{W}*S*over a wide range of float buoyancies and boundary layer forcings. Float data collected during two deployments confirm these results, but averaging times of several float days are typically required to obtain stable statistics. Significant differences in the magnitude of the effect may occur between datasets from different ocean forcing regimes and float designs. Other measures of float buoyancy are also useful predictors. These results can be used to correct existing float measurements of 〈

_{W}^{F}*ww*〉

*for the effects of buoyancy and also can be used as a means to operationally assess and control float buoyancy.*

_{E}## Abstract

The effects of upward buoyancy on the accuracy with which Lagrangian floats can measure the Eulerian mean variance 〈*ww*〉*
_{E}
* and skewness

*S*of vertical fluid velocity

_{w}^{E}*w*in the wind-driven upper-ocean boundary layer is investigated using both simulated floats in large-eddy simulation (LES) models and two float datasets. Nearly neutrally buoyant floats are repeatedly advected by the turbulent velocities across the boundary layer. Their vertical position

*Z*is determined from pressure measurements; their

*W*variance 〈

*WW*〉

*and skewness*

_{F}*S*are determined from the time series of float

_{W}^{E}*W*=

*dZ*/

*dt*. If the float buoyancy is small, then the simulated floats measure the Eulerian velocity accurately; that is,

*δW*

^{2}= 〈

*WW*〉

*− 〈*

_{F}*ww*〉

*and*

_{E}*δS*=

_{W}*S*−

_{W}^{F}*S*are small compared to 〈

_{w}^{E}*ww*〉

*and*

_{E}*S*respectively. If the floats are buoyant, and thus have an upward vertical velocity

_{w}^{E}*W*

_{bias}relative to the water, then

*δW*

^{2}and

*δS*can become significant. Buoyancy causes the floats to oversample both shallow depths and strong vertical velocities, leading to positive values of

_{W}*δW*

^{2}and negative values of

*δS*. The skewness

_{W}*S*

_{ Z′}

*of depth measures the degree to which shallow depths are oversampled; it is shown to be a good predictor of*

^{F}*W*

_{bias}/〈

*WW*〉

_{ F }

^{1/2},

*δW*

^{2}/〈

*WW*〉, and

_{F}*δS*/

_{W}*S*over a wide range of float buoyancies and boundary layer forcings. Float data collected during two deployments confirm these results, but averaging times of several float days are typically required to obtain stable statistics. Significant differences in the magnitude of the effect may occur between datasets from different ocean forcing regimes and float designs. Other measures of float buoyancy are also useful predictors. These results can be used to correct existing float measurements of 〈

_{W}^{F}*ww*〉

*for the effects of buoyancy and also can be used as a means to operationally assess and control float buoyancy.*

_{E}## Abstract

This study tests the ability of a neutrally buoyant float to estimate the dissipation rate of turbulent kinetic energy *ɛ* from its vertical acceleration spectrum using an inertial subrange method. A Lagrangian float was equipped with a SonTek acoustic Doppler velocimeter (ADV), which measured the vector velocity 1 m below the float's center, and a pressure sensor, which measured the float's depth. Measurements were taken in flows where estimates of *ɛ* varied from 10^{−8} to 10^{−3} W kg^{−1}. Previous observational and theoretical studies conclude that the Lagrangian acceleration spectrum is white within the inertial subrange with a level proportional to *ɛ*. The size of the Lagrangian float introduces a highly reproducible spectral attenuation at high frequencies. Estimates of the dissipation rate of turbulent kinetic energy using float measurements *ɛ*
_{float} were obtained by fitting the observed spectra to a model spectrum that included the attenuation effect. The ADV velocity measurements were converted to a wavenumber spectrum using a variant of Taylor's hypothesis. The spectrum exhibited the expected −5/3 slope within an inertial subrange. The turbulent kinetic energy dissipation rate *ɛ*
_{ADV} was computed from the level of this spectrum. These two independent estimates, *ɛ*
_{ADV} and *ɛ*
_{float}, were highly correlated. The ratio *ɛ*
_{float}/*ɛ*
_{ADV} deviated from one by less than a factor of 2 over the five decades of *ɛ* measured. This analysis confirms that *ɛ* can be estimated reliably from Lagrangian float acceleration spectra in turbulent flows. For the meter-sized floats used here, the size of the float and the noise level of the pressure measurements sets a lower limit of *ɛ*
_{float} > 10^{−8} W kg^{−1}.

## Abstract

This study tests the ability of a neutrally buoyant float to estimate the dissipation rate of turbulent kinetic energy *ɛ* from its vertical acceleration spectrum using an inertial subrange method. A Lagrangian float was equipped with a SonTek acoustic Doppler velocimeter (ADV), which measured the vector velocity 1 m below the float's center, and a pressure sensor, which measured the float's depth. Measurements were taken in flows where estimates of *ɛ* varied from 10^{−8} to 10^{−3} W kg^{−1}. Previous observational and theoretical studies conclude that the Lagrangian acceleration spectrum is white within the inertial subrange with a level proportional to *ɛ*. The size of the Lagrangian float introduces a highly reproducible spectral attenuation at high frequencies. Estimates of the dissipation rate of turbulent kinetic energy using float measurements *ɛ*
_{float} were obtained by fitting the observed spectra to a model spectrum that included the attenuation effect. The ADV velocity measurements were converted to a wavenumber spectrum using a variant of Taylor's hypothesis. The spectrum exhibited the expected −5/3 slope within an inertial subrange. The turbulent kinetic energy dissipation rate *ɛ*
_{ADV} was computed from the level of this spectrum. These two independent estimates, *ɛ*
_{ADV} and *ɛ*
_{float}, were highly correlated. The ratio *ɛ*
_{float}/*ɛ*
_{ADV} deviated from one by less than a factor of 2 over the five decades of *ɛ* measured. This analysis confirms that *ɛ* can be estimated reliably from Lagrangian float acceleration spectra in turbulent flows. For the meter-sized floats used here, the size of the float and the noise level of the pressure measurements sets a lower limit of *ɛ*
_{float} > 10^{−8} W kg^{−1}.

## Abstract

A three-dimensional nonhydrostatic numerical model is used to calculate nonlinear energy transfers within decaying Garrett–Munk internal wavefields. Inviscid wave interactions are calculated over horizontal scales from about 1 to 80 km and for vertical mode numbers less than about 40 in an exponentially stratified model ocean 2000 m deep. The rate of energy transfer from these scales to smaller, numerically damped scales is used to make predictions of the dissipation rate ε in the open ocean midlatitude thermocline. In agreement with the theoretical analyses based on resonant interaction and eikonal theories, the simulation results predict ε ∝ *Ē*
^{2}
*N*
^{2}, where *Ē* and *N* are the internal wave energy density and the ambient buoyancy frequency respectively. The magnitudes of the simulated dissipation rates are shown to be in good agreement with the dissipation measurements taken from six diverse sites in the midlatitude thermocline. The results suggest that the rates of dissipation and mixing in the ocean thermocline are controlled by the nonlinear dynamics of the large-scale energy-containing internal waves.

## Abstract

A three-dimensional nonhydrostatic numerical model is used to calculate nonlinear energy transfers within decaying Garrett–Munk internal wavefields. Inviscid wave interactions are calculated over horizontal scales from about 1 to 80 km and for vertical mode numbers less than about 40 in an exponentially stratified model ocean 2000 m deep. The rate of energy transfer from these scales to smaller, numerically damped scales is used to make predictions of the dissipation rate ε in the open ocean midlatitude thermocline. In agreement with the theoretical analyses based on resonant interaction and eikonal theories, the simulation results predict ε ∝ *Ē*
^{2}
*N*
^{2}, where *Ē* and *N* are the internal wave energy density and the ambient buoyancy frequency respectively. The magnitudes of the simulated dissipation rates are shown to be in good agreement with the dissipation measurements taken from six diverse sites in the midlatitude thermocline. The results suggest that the rates of dissipation and mixing in the ocean thermocline are controlled by the nonlinear dynamics of the large-scale energy-containing internal waves.