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T. M. Dillon and D. R. Caldwell

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W. D. Smyth, J. N. Moum, and D. R. Caldwell

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The time evolution of mixing in turbulent overturns is investigated using a combination of direct numerical simulations (DNS) and microstructure profiles obtained during two field experiments. The focus is on the flux coefficient Γ, the ratio of the turbulent buoyancy flux to the turbulent kinetic energy dissipation rate ϵ. In observational oceanography, a constant value Γ = 0.2 is often used to infer the buoyancy flux and the turbulent diffusivity from measured ϵ. In the simulations, the value of Γ changes by more than an order of magnitude over the life of a turbulent overturn, suggesting that the use of a constant value for Γ is an oversimplification. To account for the time dependence of Γ in the interpretation of ocean turbulence data, a way to assess the evolutionary stage at which a given turbulent event was sampled is required. The ratio of the Ozmidov scale L O to the Thorpe scale L T is found to increase monotonically with time in the simulated flows, and therefore may provide the needed time indicator. From the DNS results, a simple parameterization of Γ in terms of L O/L T is found. Applied to observational data, this parameterization leads to a 50%–60% increase in median estimates of turbulent diffusivity, suggesting a potential reassessment of turbulent diffusivity in weakly and intermittently turbulent regimes such as the ocean interior.

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D. Hebert, J. N. Moum, and D. R. Caldwell

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In spite of the effects of several form of temporal variability that tend to mask geographical patterns in turbulence intensity, our evidence indicates that the turbulence is enhanced above the equatorial undercurrent in comparison to latitudes north and south of it. This evidence consists of three meridional transects of micro-structure observations across the equator (at 140°W in 1984 and 1987. and at 110°W in 1987) along with an equatorial station at 140°W and a longitudinal transect along the equator from 140°W to 110°W. All three meridional transects show a peak in averaged estimates of the turbulent kinetic energy dissipation rates, ε, at the equator, although in 1984 the peak was not significant at the 95% level. The major sources a temporal variability were the diurnal buoyancy flux variation and the wind stress variations, which had a typical period of a few days. After the diurnal variability is removed by averaging, it can be shown that, for similar wind stress, ε is larger over the undercurrent than away from it. Examination of the 16-m, 1-hour averaged ε, in terms of the vertical shear of horizontal velocity and the stratification (determined over similar space and time scales), indicated a tendency of this mean ε to vary with the Richardson number, Ri, when Ri<1. However, closer examination showed that the dependence of ε on Ri varied with depth. Therefore, a simple parameterization for mixing rates on Ri is not valid for all depth.

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D. R. Caldwell, T. M. Dillon, and J. N. Moum

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Evaluation of the Rapid-Sampling Vertical Profiler, which was developed for sampling the hydrophysical fields in the upper ocean from a moving vessel, shows that the instrument is useful for near-microscale measurements of temperature and salinity and also for turbulent kinetic energy dissipation measurements with airfoil probes. A depth of 200 meters is reached from a ship moving at 6 knots. The vertical resolution is 3 cm, the temperature resolution is 0.5 millidegrees, the salinity resolution is 0.6 parts per million, and the sigma-t resolution is 0.0004. (The estimates given for resolution are 99% confidence limits on series of 3-cm samples.) The instrument falls with a speed uniform within 20% in an orientation within a few degrees of vertical. Vibrations within the dissipation range of turbulence are sufficiently small to permit the measurement of turbulence with airfoil probes in many regions of the ocean.

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J. N. Moum, D. R. Caldwell, J. D. Nash, and G. D. Gunderson

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Observations of mixing over the continental slope using a towed body reveal a great lateral extent (several kilometers) of continuously turbulent fluid within a few hundred meters of the boundary at depth 1600 m. The largest turbulent dissipation rates were observed over a 5 km horizontal region near a slope critical to the M 2 internal tide. Over a submarine landslide perpendicular to the continental slope, enhanced mixing extended at least 600 m above the boundary, increasing toward the bottom. The resulting vertical divergence of the heat flux near the bottom implies that fluid there must be replenished.

Intermediate nepheloid layers detected optically contained fluid with θS properties distinct from their surroundings. It is suggested that intermediate nepheloid layers are interior signitures of the boundary layer detachment required by the near-bottom flux divergance.

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J. N. Moum, D. Hebert, C. A. Paulson, and D. R. Caldwell

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High correlations between turbulent dissipation rates and high-wavenumber internal waves and the high values of turbulent dissipation associated with internal wave activity suggest that internal waves are the main direct source of mixing in the thermocline above the core of the Equatorial Undercurrent. An extensive dataset obtained using a microstructure profiler and thermistor chain towed along the equator was analyzed to examine the correspondence between turbulent mixing and high-wavenumber internal waves. In the low Richardson number (Ri) thermocline below the mixed layer but above the core of the Equatorial Undercurrent, and when winds were moderate and steadily westward, it was found that:

• the spectrum of vertical isotherm displacement was dominated by a narrow wavenumber band (corresponding to 150–250-m zonal wavelength) of internal waves;

• both turbulence and internal waves varied diurnally—hourly averaged values of turbulent dissipation rate and wave potential energy were greater by a factor of 100 at night; and

• correlations between turbulent dissipation rate and several measures of internal wave activity (wave isotherm displacement, wave slope, and wave potential energy) were high.

Little or no high wavenumber internal wave activity was observed when winds were light or eastward: Superposing plane waves with the observed characteristics on the observed background field suggests that they are inherently unstable to both adjective and shear instability above the core of the Equatorial Undercurrent. These waves are due either to locally generated internal gravity waves or to Kelvin-Helmholz-type instabilities generated in the shear flow; from our measurements these two phenomena could not be distinguished.

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J. N. Moum, D. Hebert, C. A. Paulson, D. R. Caldwell, M. J. McPhaden, and H. Peters

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Appearing in this issue of the Journal of Physical Oceanography are three papers that present new observations of a distinct, narrow band, and diurnally varying signal in temperature records obtained in the low Richardson number shear flow above the core of the equatorial undercurrent. Moored data suggest that the intrinsic frequency of the signal is near the local buoyancy frequency, while towed data indicate that the horizontal wavelength in the zonal direction is 150–250 m. Coincident microstructure profiling shows that this signal is associated with bursts of turbulent mixing, it seems that this narrowband signal represents the signature of instabilities that ultimately cause the turbulence observed in the equatorial thermocline. Common problems in interpreting the physics behind the signature are discussed here.

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D. Hebert, J. N. Moum, C. A. Paulson, and D. R. Caldwell

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In the low Richardson number shear flow above the Pacific Equatorial Undercurrent, a single vertical microstructure profile intersected the overturning crest of a packet of high horizontal wavenumber waves. The observed dissipation rates within the overturning wave were so high that if they were representative of the volume-averaged rate, the total wave energy would have been dissipated within a single buoyancy period. The chaotic structure (and temperature fluctuations with horizontal scales less than 2 m) of the two wave crests and troughs west of the overturning wave crest suggest that recent mixing had occurred there. Wave crests and troughs east of the overturning wave crest showed little or no sign of turbulent mixing.

Similar high horizontal wavenumber waves, believed to be shear-instability waves, have been observed in low Richardson number regions of the midlatitude seasonal thermocline. Although the equatorial waves have a horizontal wavelength appropriate for shear-instability waves, their vertical scale is much larger than the vertical extent of the low Richardson region, unlike that found for simple shear-instability waves.

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D. R. Caldwell, R-C. Lien, J. N. Moum, and M. C. Gregg

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Although the process of restratification of the ocean surface layer at the equator following nighttime convection is similar in many ways to the process at midlatitudes, there are important differences. A composite day calculated from 15 days of consistent conditions at 140°W on the equator was compared with midlatitude observations by Brainerd and Gregg. In the depth range of 20–40 m, 1) minimum nighttime stratification was similar [N 2 of 1.2–3.2 (× 10−6 s−2) vs 0.4–1.7 (× 10−6 s−2)], 2) maximum daytime stratification was significantly larger, as might be expected from the greater surface heat input [N 2 of 8–21 (× 10−6 s−2 vs 3–7 (× 10−6 s−2)], and 3) minimum nighttime shear was similar [shear-squared was 1.4–4.6 (× 10−6 s−2) vs 0.8–1.9 (× 10−6 s−2)], but the maximum daytime shear was much larger [shear-squared of 24–41 (× 10−6 s−2) vs 3–7 (× 10−6 s−2)].

For much of the surface layer, the dominant identifiable cause of restratification in both cases was the divergence of the penetrating shortwave radiation, although at the equator the divergence of turbulent flux was important from 10 to 25 m. In both cases the divergence of vertical fluxes accounted for only 60%–70% of the restratification; relaxation of lateral gradients was probably the source for the rest. At the equator, the shear in the upper 40 m was restored in the daytime by turbulent transport of momentum injected by the wind.

In the region convectively mixed at night, turbulence decayed exponentially in the daytime in both cases, the e-folding time, τ ε, being 1.7 ± 0.2 h at the equator, 1.5 h in midlatitude. A dimensionless decay time, N τ ε, was 7.2–9.3 compared with 6.0 in the midlatitude case. In both cases the vertical scale of the turbulence was controlled by the Ozmidov scale, and the turbulence remained active throughout the day.

At the equator “deep-cycle” nighttime turbulence was generated in the always-stratified water at depth 60–80 m never reached by nighttime convection. Neither shear nor stratification varied significantly diurnally. The decay of this turbulence was similar to that above in that its vertical scale was controlled by the Ozmidov scale and remained active throughout the day, but the e-folding timescale was much longer, 3.5 h (N τ ε = 66–96). For the turbulence to persist this long, turbulence production must be a large proportion of ε.

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T. M. Dillon, J. N. Moum, T. K. Chereskin, and D. R. Caldwell

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The conventional view of equatorial dynamics requires that the zonal equatorial wind stress be balanced, in the mean, by the vertical integral of “large-scale” terms, such as the zonal pressure gradient, mesoscale eddy flux, and mean advection, over the upper few hundred meters. It is usually presumed that the surface wind stress is communicated to the interior by turbulent processes. Turbulent kinetic energy dissipation rates measured at 140°W during the TROPIC HEAT I experiment and a production rate–dissipation rate balance argument have been used to calculate the zonal turbulent stress at 30 to 90 m depth. The calculated turbulent stress at 30 m depth amounts to only 20% of the wind stress and decreases exponentially with depth below 30 m. Typical large-scale estimates of the zonal pressure gradient, mesoscale eddy flux, and advection have a depth scale larger than the turbulent stress, and are inconsistent with the vertical divergence of the stress as estimated from the dissipation rate measurements. It is concluded that either 1) the measured estimates of dissipation rate are too small, 2) the actual large-scale zonal pressure gradient, mesoscale eddy flux, and advection during our observation period were highly atypical and had a very shallow depth scale, 3) some process other than the simple diffusion of momentum through shear instabilities is transporting the momentum, or 4) the assumption of a production-dissipation balance in the turbulent kinetic energy budget is incorrect. The first two possibilities are unlikely.

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