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## Abstract

Two interpretations of microstructure patches measured in the main thermocline of the North Pacific by Gregg (1980) are questioned. He concludes that the observed microstructure is not fossil-temperature turbulence and that the observed Cox numbers imply vertical diffusivities by turbulent mixing which am about 10^{−2} times smaller than canonical values of order 10^{−4} m^{2} s^{−1}. The first conclusion that the micro-structure is not fossil depends on an unnecessary assumption that in order to be fossil the microstructure must not be moving: actually, fossil-turbulence microstructure must always have internal wave and laminar restratification motions. The second conclusion depends on the first. The pattern of Thorpe-displacement scales for the patches containing zero temperature gradients implies they were produced by turbulence with vertical scales as large as several meters. However, the large distances separating the zero-gradient points implies that the microstructure is fossil at all scales at the time of observation. Because the microstructure is fossil it follows that the observed Cox numbers C are small compared to their previous values C_{0} when the microstructure was actively turbulent at all scales. Model calculations give C_{0} ≈ 0.2 *L _{T}
*

^{2}

*N*/

*D*values in the patches as large as 4 × 10

^{5}compared to observed

*C*values less than 10

^{3}, where

*L*is the maximum Thorpe displacement. The data sample is apparently too small to include representative active turbulent regions because such regions are so intermittent in time and patchy in space. Turbulent vertical diffusivity estimates corrected for undersampling are well within the canonical range of values.

_{T}## Abstract

Two interpretations of microstructure patches measured in the main thermocline of the North Pacific by Gregg (1980) are questioned. He concludes that the observed microstructure is not fossil-temperature turbulence and that the observed Cox numbers imply vertical diffusivities by turbulent mixing which am about 10^{−2} times smaller than canonical values of order 10^{−4} m^{2} s^{−1}. The first conclusion that the micro-structure is not fossil depends on an unnecessary assumption that in order to be fossil the microstructure must not be moving: actually, fossil-turbulence microstructure must always have internal wave and laminar restratification motions. The second conclusion depends on the first. The pattern of Thorpe-displacement scales for the patches containing zero temperature gradients implies they were produced by turbulence with vertical scales as large as several meters. However, the large distances separating the zero-gradient points implies that the microstructure is fossil at all scales at the time of observation. Because the microstructure is fossil it follows that the observed Cox numbers C are small compared to their previous values C_{0} when the microstructure was actively turbulent at all scales. Model calculations give C_{0} ≈ 0.2 *L _{T}
*

^{2}

*N*/

*D*values in the patches as large as 4 × 10

^{5}compared to observed

*C*values less than 10

^{3}, where

*L*is the maximum Thorpe displacement. The data sample is apparently too small to include representative active turbulent regions because such regions are so intermittent in time and patchy in space. Turbulent vertical diffusivity estimates corrected for undersampling are well within the canonical range of values.

_{T}## Abstract

Turbulence and turbulent mixing in the ocean are strongly intermittent in amplitude, space and time. The degree of intermittency is measured by the “intermittency factor” σ^{2}, defined as either σ^{2}
_{lnε}, the variance of the logarithm of the viscous dissipation rate ε, or σ^{2}
_{lnχ}, the variance of the logarithm of the temperature dissipation rate χ. Available data suggest that the cumulative distribution functions of ε and χ in stratified layers are approximately lognormal with large σ^{2} values in the range 3–7. Departures from lognormality are remarkably similar to those for Monte Carlo generated lognormal distributions contaminated with simulated noise and undersampling effects.

Confidence limits for the maximum likelihood estimator of the mean of a lognormal random variable are determined by Monte Carlo techniques and by theoretical modeling. They show that such large σ^{2} values cause large uncertainty in estimates of the mean unless the number of data samples is extremely large. To obtain estimates of mean dissipation rates ¯ε and ¯χ with ±10% accuracy at the 95% confidence level in the seasonal thermocline, the main thermocline or Pacific equatorial undercurrent (all stratified layers with large internmittency) requires 2600 or 10 000 independent data samples for σ^{2} = 3 or 7, respectively.

If intermittency is ignored and the data are treated as if normally distributed, mean dissipation rates will probably be underestimated from a small number of samples. For example, it is generally accepted that canonical estimates of the main thermocline vertical eddy diffusivity of order 1 cm^{2} s^{−1}, based on bulk property models, are inconsistent with much smaller values inferred, ignoring intermittency effects, from themocline microstructure measurements. However, after accounting for the intermittent lognomality of the data, no statistically significant discrepancy exists.

Intermittency may cause qualitative as well as quantitative undersampling errors: minimum values in the vertical profiles of mean dissipation rates are commonly inferred from individual profiles at the seasonal thermocline depth and the equatorial undercurrent high-velocity core depth where maxima may actually exist. From the new confidence intervals, such minima are shown to be artifacts of the extreme intermittency in these strongly stratified layers.

## Abstract

Turbulence and turbulent mixing in the ocean are strongly intermittent in amplitude, space and time. The degree of intermittency is measured by the “intermittency factor” σ^{2}, defined as either σ^{2}
_{lnε}, the variance of the logarithm of the viscous dissipation rate ε, or σ^{2}
_{lnχ}, the variance of the logarithm of the temperature dissipation rate χ. Available data suggest that the cumulative distribution functions of ε and χ in stratified layers are approximately lognormal with large σ^{2} values in the range 3–7. Departures from lognormality are remarkably similar to those for Monte Carlo generated lognormal distributions contaminated with simulated noise and undersampling effects.

Confidence limits for the maximum likelihood estimator of the mean of a lognormal random variable are determined by Monte Carlo techniques and by theoretical modeling. They show that such large σ^{2} values cause large uncertainty in estimates of the mean unless the number of data samples is extremely large. To obtain estimates of mean dissipation rates ¯ε and ¯χ with ±10% accuracy at the 95% confidence level in the seasonal thermocline, the main thermocline or Pacific equatorial undercurrent (all stratified layers with large internmittency) requires 2600 or 10 000 independent data samples for σ^{2} = 3 or 7, respectively.

If intermittency is ignored and the data are treated as if normally distributed, mean dissipation rates will probably be underestimated from a small number of samples. For example, it is generally accepted that canonical estimates of the main thermocline vertical eddy diffusivity of order 1 cm^{2} s^{−1}, based on bulk property models, are inconsistent with much smaller values inferred, ignoring intermittency effects, from themocline microstructure measurements. However, after accounting for the intermittent lognomality of the data, no statistically significant discrepancy exists.

Intermittency may cause qualitative as well as quantitative undersampling errors: minimum values in the vertical profiles of mean dissipation rates are commonly inferred from individual profiles at the seasonal thermocline depth and the equatorial undercurrent high-velocity core depth where maxima may actually exist. From the new confidence intervals, such minima are shown to be artifacts of the extreme intermittency in these strongly stratified layers.

## Abstract

Measurements of small-scale fluctuations of temperature are used to estimate turbulent parameters such as viscous dissipation rate (ε), dissipation rate of temperature variance (χ), and turbulent diffusion coefficients of momentum (ν*
_{T}
*) and temperature (

*D*). Results from two locations are reported: one in the center of the undercurrent (ON 150W) and one toward the northern edge (IN 150W); both at depths of about 100 m where high vertical shear and high vertical stability are found. Universal similarity and local isotropy assumptions were used to determine the dissipation rates from measured spectra. While ε(∼0.08 cm

_{T}^{2}sec

^{−3}) was about the same at both locations, χ at ON [7 × 10

^{−5}(°C)

^{2}sec

^{−1}] was larger by a factor of 9. Even greater differences were found in

*D*: 27 cm

_{T}^{2}sec

^{−1}at ON vs 0.52 cm

^{2}sec

^{−1}at 1N indicating large vertical mixing at the equator. From two independent methods ν

*yielded about the same results within 15%: 12 cm*

_{T}^{2}sec

^{−1}at 1N and 25 cm

^{2}sec

^{−1}at ON.

## Abstract

Measurements of small-scale fluctuations of temperature are used to estimate turbulent parameters such as viscous dissipation rate (ε), dissipation rate of temperature variance (χ), and turbulent diffusion coefficients of momentum (ν*
_{T}
*) and temperature (

*D*). Results from two locations are reported: one in the center of the undercurrent (ON 150W) and one toward the northern edge (IN 150W); both at depths of about 100 m where high vertical shear and high vertical stability are found. Universal similarity and local isotropy assumptions were used to determine the dissipation rates from measured spectra. While ε(∼0.08 cm

_{T}^{2}sec

^{−3}) was about the same at both locations, χ at ON [7 × 10

^{−5}(°C)

^{2}sec

^{−1}] was larger by a factor of 9. Even greater differences were found in

*D*: 27 cm

_{T}^{2}sec

^{−1}at ON vs 0.52 cm

^{2}sec

^{−1}at 1N indicating large vertical mixing at the equator. From two independent methods ν

*yielded about the same results within 15%: 12 cm*

_{T}^{2}sec

^{−1}at 1N and 25 cm

^{2}sec

^{−1}at ON.

## Abstract

Measurements of turbulent wind velocity, humidity and temperature spectra for stable and unstable stratification in the atmospheric surface layer obtained during an experiment over the North Pacific Ocean are presented. The velocity field appears to be in a state of local isotropy as measured by the ratio of vertical to streamwise velocity spectra *S*
_{u}(*n>*/ *S*
_{u}(*n>* at the measurement height of 29 m above the sea surface. Using Monin-Obukhov scaling, spectral shapes for humidity are similar to those for overland temperature. Evidence is presented which suggests that previous departures of marine temperature measurements from Monin-Obukhobzv similarity may be due to humidity sensitivity of salt-spray-contaminated temperature probes. Overland humidity data from the AFCRL-UCSD 1973 Minnesota Experiment (Champagne *et al*., 1977) were analyzed and also found to exhibit Monin-Obukhov similarity.

## Abstract

Measurements of turbulent wind velocity, humidity and temperature spectra for stable and unstable stratification in the atmospheric surface layer obtained during an experiment over the North Pacific Ocean are presented. The velocity field appears to be in a state of local isotropy as measured by the ratio of vertical to streamwise velocity spectra *S*
_{u}(*n>*/ *S*
_{u}(*n>* at the measurement height of 29 m above the sea surface. Using Monin-Obukhov scaling, spectral shapes for humidity are similar to those for overland temperature. Evidence is presented which suggests that previous departures of marine temperature measurements from Monin-Obukhobzv similarity may be due to humidity sensitivity of salt-spray-contaminated temperature probes. Overland humidity data from the AFCRL-UCSD 1973 Minnesota Experiment (Champagne *et al*., 1977) were analyzed and also found to exhibit Monin-Obukhov similarity.