Douglas R. Caldwell

The Efficiency of Mixing in Turbulent Patches: Inferences from Direct Simulations and Microstructure Observations

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 G, the ratio of the turbulent buoyancy flux to the turbulent kinetic energy dissipation rate e .I n observational oceanography, a constant value G5 0.2 is often used to infer the buoyancy flux and the turbulent diffusivity from measured e. In the simulations, the value of G changes by more than an order of magnitude over the life of a turbulent overturn, suggesting that the use of a constant value for G is an oversimplification. To account for the time dependence of G 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 LO to the Thorpe scale LT 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 G in terms of LO/ LT 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.

Observations of Boundary Mixing over the Continental Slope

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 ove ra5k mhorizontal region near a slope critical to the M2 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 u‐S 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.

Heat and salt transport through a diffusive thermohaline interface

An investigation of a thermohaline diffusive interface between convecting layers, with heat fluxes more similar to natural ones than in previous studies, shows that the formula suggested by Huppert (Deep-Sea Research, 18, 1005–1021, 1971) for the dependence of heat flux on interface stability should not be extrapolated to stability numbers higher than five and a new formula is proposed. The non-dimensional ratio of salt flux to heat flux increases from the value 0.15 found by Turner (International Journal of Heat and Mass Transfer, 8, 759–767, 1965) as the heat flux is lowered. The interface migrates vertically, whereas Hupperts analysis of the stability of a pair of diffusive interfaces assumed stationary interfaces. The migration rate depends on both stability number and heat flux. For oceanic values of the heat flux, the thickness of the interface was in the range observed for the layered system of microstructure in the Arctic Ocean.

Turbulence and Internal Waves at the Equator. Part I: Statistics from Towed Thermistors and a Microstructure Profiler

Abstract 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...

A laboratory study of the turbulent ekman layer

Abstract Comparing characteristics of a turbulent Ekman boundary layer in a rotating apparatus with atmospheric observations and theories, we find that the similarity relations derived by Kazanski and Monin, and others, scale both laboratory and field data quite well, especially considering that the Coriolis parameter is larger by a factor of 105 in the experiment than it is in the atmosphere. Eddy viscosity models and Deardorffs numerical model predict the properties of both with varying degrees of success. High frequency spectra of velocity fluctuations scale with the Kolmogoroff length and time scales. Both magnitude and direction of the surface shear stress were measured directly, with a heated film stress gauge.

Turbulence variability at the equator in the central Pacific at the beginning of the 1991-1993 El Nino

A 38-day, 5990-cast microstructure study on the equator performed during the onset of the 1991–1993 El Nino shows the effect on small-scale activity at 140°W of an equatorial Kelvin wave. By using two ships, data were taken continuously from November 4 to December 12, 1991, near the National Oceanic and Atmospheric Administration Pacific Marine Environmental Laboratory mooring at O°N, 140°W. The ships occupied the station sequentially with a 3.5-day overlap for intercalibration. Variability in currents was observed on tidal periods, and periods of 4 days (presumably equatorially trapped internal gravity waves), 8 days (cause unknown), 20 days (tropical instability waves), and longer (Kelvin waves). Variation in water structure occurred most prominently on the timescale of Kelvin waves. The diurnal cycle typical of that location was observed: nocturnal deepening of the surface mixed layer was accompanied by a “deep cycle,” bursts of turbulence penetrating into the stratified region below the nighttime mixed layer. During the observational period, one Kelvin wave trough and one crest passed through the site. Changes accompanying the phase change in the Kelvin wave included a reversal of the near-surface current, a deepening of the thermocline, and a change of water mass. Changes in small-scale activity included a tenfold decrease of the thermal dissipation rate and a fourfold decrease of the rate of heat transport downward from the mixed layer. The nighttime mixed layer deepened from 30 to 60 m. The thickness of the stratified region in which nocturnal turbulence bursts occurred, the deep cycle region, thinned from 40 to 20 m because it was confined between the bottom of the nighttime mixed layer and the low-shear region near the core of the undercurrent. The decrease in downward heat flux observed at this passage of the downwelling Kelvin wave front could explain the rapid sea surface temperature (SST) increase seen at El Nino onsets. The magnitude of the change in vertical flux is similar to the magnitude of the change in horizontal advection. This process would produce a warmer SST much more quickly than could the advection of warm waters eastward.

Structure and Dynamics of a Coastal Filament

Repeated microstructure transects across filaments in the coastal transition zone (CTZ) have revealed fundamental structure and dynamics of the complicated features. The measurements allow detailed momentum and vorticity analyses and provide a possible explanations for structural asymmetry of the fronts. Observations made between July 2 and July 23, 1988, along the central meridional CTZ survey line were used to estimate terms in the meridional momentum equation. The analysis indicates geostrophic flow along the axes of the fronts with the acrosg-fr0nt pressure gradient explaining as much as 87% of the variance in the balance. Significant ageostrophic flow in the across-front coordinate was found, with the along-front pressure gradient explaining only 7!% of the variance in the momentum balance. The fronts were found to be asymmetric in relative vorticity, with stronger positive vorticity on the cooler side of the front and weaker negative vorticity on the warm side. Mean vertical velocities were estimated from the repeated transects of acoustic Doppler current profiles and the rapid sampling vertical profiler hydrographic and turbulence measurements. Regions of upwelling and downwelling are likely associated with adjustments in the relative vorticity, resulting in maximum vertical velocities of 40 m d -l . Asymmetry in the near-surface temperature and salinity extrema are explained by cross-frontal exchang e. This cross-frontal exchange modifies the relative roles of salinity and temperature in determining the density away from the coastal upwelling region, a dynamically important characteristic not revealed by advanced very high resolution radiometer imagery.

Turbulence and Internal Waves at the Equator. Part II: Details of a Single Event

Abstract 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, t...

Zonal Momentum Balance at the Equator

Abstract 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 measu...

The maximum density points of pure and saline water

Abstract Measurements of the temperature-pressure-salinity points at which the density of saline water is a maximum can be made more directly than previously by determining conditions under which compressive heating vanishes. These measurements show that the density formulas of Chen and Millero (Deep-Sea Research, 23, 595–612, 1976) and the expression for maximum-density temperature, Tm of Gebhart and Mollendorf (Deep-Sea Research, 24, 831–848, 1977) give eatimates of Tm several tenths of a degree too high for saline water. Disagreement is observed at temperatures below 0°C where density measurements have not been made, andso may indicate caution should be used in extrapolating the various equations of state to these temperatures. The recent pure-water equation of Chen, Fine and Millero (Journal of Chemical Physics, 66, 2142–2144, 1977) predicts the observed Tm within 0.04°C. The dependence of Tm on pressure is non-linear at higher pressures. The formula Tm=T0−AS−BP(1+CS)(1+DP) represents these data for Tm as a function of salinity in parts per thousand (S) and pressure in bars (P with a root-mean-square deviation of 0.044°C if T0=3.982, A=0.2229, B=0.02004, C=0.00376 and D=0.000402.