Diapycnal Eddy Diffusivity Research Articles

Variability of the diapycnal mixing coefficient in coastal oceans investigated with direct microstructure measurements

Mass and heat fluxes in the ocean are important for understanding global ocean dynamics and ecosystems. Estimates of the diapycnal diffusivity (Kρ) are required for quantifying these fluxes. In this regard, one of the key parameters that is required to estimate the diapycnal eddy diffusivity is the “mixing coefficient” (Γ). The diapycnal diffusivity is estimated from a combination of the rate of dissipation of turbulent kinetic energy ε, the buoyancy frequency N (a measure of background density stratification) and Γ. This study investigates how the mixing coefficient (Γ) may be inferred from field measurable parameters using in-situ direct microstructure measurements in coastal oceans. Four microstructure data sets were analyzed to investigate the variability of Γ and associated parameters. While Γ is found to vary widely within a range of O(10−3−101), it can be parameterized using a ratio of relevant turbulent length scales: the Ellison scale (LE, which is approximately equivalent to the Thorpe scale) and the Ozmidov scale (LO). When LE/LO is less than unity, the results show that Γ is proportional to (LE/LO)4/3, consistent with previous observations. On the other hand, when LE/LO exceeds unity, Γ is approximately a constant with no discernable dependence on LE/LO, consistent with a recent theoretical and numerical study.

Swimming sheet in a density-stratified fluid

In this work, we theoretically investigate the swimming velocity of a Taylor swimming sheet immersed in a linearly density-stratified fluid. We use a regular perturbation expansion approach to estimate the swimming velocity up to second order in wave amplitude. We divide our analysis into two regimes of low ($\ll O(1)$) and finite Reynolds numbers. We use our solution to understand the effect of stratification on the swimming behaviour of organisms. We find that stratification significantly influences motility characteristics of the swimmer such as the swimming speed, hydrodynamic power expenditure, swimming efficiency and the induced mixing, quantified by mixing efficiency and diapycnal eddy diffusivity. We explore this dependence in detail for both low and finite Reynolds number and elucidate the fundamental insights obtained. We expect our work to shed some light on the importance of stratification in the locomotion of organisms living in density-stratified aquatic environments.

Turbulence and hypoxia contribute to dense biological scattering layers in a Patagonian fjord system

Abstract. The aggregation of plankton species along fjords can be linked to physical properties and processes such as stratification, turbulence and oxygen concentration. The goal of this study is to determine how water column properties and turbulent mixing affect the horizontal and vertical distributions of macrozooplankton along the only northern Patagonian fjord known to date, where hypoxic conditions occur in the water column. Acoustic Doppler current profiler moorings, scientific echo-sounder transects and in situ plankton abundance measurements were used to study macrozooplankton assemblages and migration patterns along Puyuhuapi Fjord and Jacaf Channel in Chilean Patagonia. The dissipation of turbulent kinetic energy was quantified through vertical microstructure profiles collected throughout time in areas with high macrozooplankton concentrations. The acoustic records and in situ macrozooplankton data revealed diel vertical migrations (DVM) of siphonophores, chaetognaths and euphausiids. In particular, a dense biological backscattering layer was observed along Puyuhuapi Fjord between the surface and the top of the hypoxic boundary layer (∼100 m), which limited the vertical distribution of most macrozooplankton and their DVM, generating a significant reduction of habitat. Aggregations of macrozooplankton and fishes were most abundant around a submarine sill in Jacaf Channel. In this location macrozooplankton were distributed throughout the water column (0 to ∼200 m), with no evidence of a hypoxic boundary due to the intense mixing near the sill. In particular, turbulence measurements taken near the sill indicated high dissipation rates of turbulent kinetic energy (ε∼10-5 W kg−1) and vertical diapycnal eddy diffusivity (Kρ∼10-3 m2 s−1). The elevated vertical mixing ensures that the water column is well oxygenated (3–6 mL L−1, 60 %–80 % saturation), creating a suitable environment for macrozooplankton and fish aggregations. Turbulence induced by tidal flow over the sill apparently enhances the interchange of nutrients and oxygen concentrations with the surface layer, creating a productive environment for many marine species, where the prey–predator relationship might be favored.

Can We Infer Diapycnal Mixing Rates from the World Ocean Temperature–Salinity Distribution?

AbstractThe turbulent diapycnal mixing in the ocean is currently obtained from microstructure and finestructure measurements, dye experiments, and inverse models. This study presents a new method that infers the diapycnal mixing from low-resolution numerical calculations of the World Ocean whose temperatures and salinities are restored to the climatology. At the difference of robust general circulation ocean models, diapycnal diffusion is not prescribed but inferred. At steady state the buoyancy equation shows an equilibrium between the large-scale diapycnal advection and the restoring terms that take the place of the divergence of eddy buoyancy fluxes. The geography of the diapycnal flow reveals a strong regional variability of water mass transformations. Positive values of the diapycnal flow indicate an erosion of a deep-water mass and negative values indicate a creation. When the diapycnal flow is upward, a diffusion law can be fitted in the vertical and the diapycnal eddy diffusivity is obtained throughout the water column. The basin averages of diapycnal diffusivities are small in the first 1500 m [O(10−5) m2 s−1] and increase downward with bottom values of about 2.5 × 10−4 m2 s−1 in all ocean basins, with the exception of the Southern Ocean (50°–30°S), where they reach 12 × 10−4 m2 s−1. This study confirms the small diffusivity in the thermocline and the robustness of the higher canonical Munk’s value in the abyssal ocean. It indicates that the upward dianeutral transport in the Atlantic mostly takes place in the abyss and the upper ocean, supporting the quasi-adiabatic character of the middepth overturning.

Assessment of intraseasonal variabilities in China Ocean Reanalysis (CORA)

A regional reanalysis product—China Ocean Reanalysis (CORA)—has been developed for the China’s seas and the adjacent areas. In this study, the intraseasonal variabilities (ISVs) in CORA are assessed by comparing with observations and two other reanalysis products (ECCO2 and SODA). CORA shows a better performance in capturing the intraseasonal sea surface temperatures (SSTs) and the intraseasonal sea surface heights (SSHs) than ECCO2 and SODA do, probably due to its high resolution, stronger response to the intraseasonal forcing in the atmosphere (especially the Madden-Julian Oscillation), and more available regional data for assimilation. But at the subsurface, the ISVs in CORA are likely to be weaker than reality, which is probably attributed to rare observational data for assimilation and weak diapycnal eddy diffusivity in the CORA model. According to the comparison results, CORA is a good choice for the study related to variabilities at the surface, but cares have to be taken for the study focusing on the subsurface processes.

Biogenic mixing induced by intermediate Reynolds number swimming in stratified fluids.

We study fully resolved motion of interacting swimmers in density stratified fluids using an archetypal swimming model called “squirmer”. The intermediate Reynolds number regime is particularly important, because the vast majority of organisms in the aphotic ocean (i.e. regions that are 200 m beneath the sea surface) are small (mm-cm) and their motion is governed by the balance of inertial and viscous forces. Our study shows that the mixing efficiency and the diapycnal eddy diffusivity, a measure of vertical mass flux, within a suspension of squirmers increases with Reynolds number. The mixing efficiency is in the range of O(0.0001–0.04) when the swimming Reynolds number is in the range of O(0.1–100). The values of diapycnal eddy diffusivity and Cox number are two orders of magnitude larger for vertically swimming cells compared to horizontally swimming cells. For a suspension of squirmers in a decaying isotropic turbulence, we find that the diapycnal eddy diffusivity enhances due to the strong viscous dissipation generated by squirmers as well as the interaction of squirmers with the background turbulence.

Turbulence and internal waves in Patricia Bay, Saanich Inlet, British Columbia

The physical environment in Patricia Bay of Saanich Inlet, British Columbia, is characterized. Turbulence and internal waves were measured over September 2010 using a moored Acoustic Doppler velocimeter and Acoustic Doppler Current Profiler, while diel vertical migration of zooplankton was recorded with an echosounder to test for possible biological generation of turbulence. The average turbulent dissipation rate 〈ϵ〉 was O(10−8Wkg−1) with the corresponding diapycnal eddy diffusivity K of ~5×10−6m2s−1. Barotropic velocities responded to forcing outside Saanich Inlet in the Strait of Georgia and Haro Strait. Subtidal baroclinic velocities were southward at the surface and northward at mid-depth during spring tides, the reverse during neaps. Mode-2 M4 frequency in cross-inlet velocity u was more energetic than any mode-1 diurnal or semidiurnal frequencies in both u and v, which may be a signature of cross-inlet seiches. Spectral energy levels of baroclinic velocities and shear were weakly correlated with ϵ. No relation was found between turbulent events and diel vertical migration.

Double-diffusive layering and mixing in Patagonian fjords

Double-diffusive layering was quantified for the first time in the Chilean Patagonian fjords region (41.5–56°S). Approximately 600 temperature and salinity profiles collected during 1995–2012 were used to study water masses, quantify diffusive layering and compute the vertical diffusivity of heat. Development of “diffusive-layering” or simply “layering” was favored by relatively fresh–cold waters overlying salty–warm waters. Fresh waters are frequently derived from glacial melting that influences the fjord either directly or through rivers. Salty waters are associated with Modified Subantarctic (MSAAW) and Subantarctic Water (SAAW). Double-diffusive convection occurred as layering in 40% of the year-round data and as salt fingering in <1% of the time. The most vigorous layering, was found at depths between 20 and 70m, as quantified by (a) Turner angles, (b) density ratios, and (c) heat diffusivity (with maximum values of 5×10−5m2s−1). Diffusive-layering events presented a meridional gradient with less layering within the 41–47°S northern region, relative to the southern region between 47° and 56°S. Layering occupied, on average, 27% and 56% of the water column in the northern and southern regions, respectively. Thermohaline staircases were detected with microprofile measurements in Martinez and Baker channels (48°S), showing homogeneous layers (2–4m thick) below the pycnocline (10–40m). Also in this area, increased vertical mixing coincided with the increased layering events. High values of Thorpe scale (LT∼7m), dissipation rate of TKE (ε=10−5–10−3Wkg−1) and diapycnal eddy diffusivity (Kρ=10−6–10−3m−2s−1) were associated with diffusive layering. Implications of these results are that diffusive layering should be taken into account, together with other mixing processes such as shear instabilities and wind-driven flows, in biological and geochemical studies.

Weak Vertical Diffusion Allows Maintenance of Cold Halocline in the Central Arctic

In spring preceding the record minimum summer ice cover detailed microstructure measurements were made from drifting pack ice in the Arctic Ocean, 110 km from the North Pole. Profiles of hydrography, shear, and temperature microstructure collected in the upper water column covering the core of the Atlantic Water are analyzed to determine the diapycnal eddy diffusivity, the eddy diffusivity for heat, and the turbulent flux of heat. Turbulence in the bulk of the cold halocline layer was not strong enough to generate significant buoyancy flux and mixing. Resulting turbulent heat flux across the upper cold halocline was not significantly different than zero. The results show that the low levels of eddy diffusivity in the upper cold halocline lead to small vertical turbulent transport of heat, thereby allowing the maintenance of the cold halocline in the central Arctic.

Inferences and Observations of Turbulent Dissipation and Mixing in the Upper Ocean at the Hawaiian Ridge

Abstract The Hawaiian Ridge is one of the most energetic generators of internal tides in the pelagic ocean. The density and current structure of the upper ocean at the Hawaiian Ridge were observed using SeaSoar and Doppler sonar during a survey extending from Oahu to Brooks Banks and up to 200 km from the ridge peak. Survey observations are used to quantify spatial changes in internal-wave-induced turbulent dissipation and mixing. The turbulent dissipation rate of kinetic energy ɛ and diapycnal eddy diffusivity Kρ are inferred from an established parameterization using internal wave shear as input. At the Kauai Channel (KC) and French Frigate Shoals/Brooks Banks sites, ɛ and Kρ decay away from the ridge with maxima exceeding minima by 5 times. At both sites, average Kρ is everywhere greater than the canonical open-ocean value of 10−5 m2 s−1. Along the ridge, ɛ and Kρ vary by up to 100 times and are largest at sites of largest numerical model internal tide energy density. In the eastern KC, Kρ &amp;gt; 10−3 m2 s−1 is typical in a patch more than 200 m thick located above the path of an M2 internal tide ray. An upper limit on the dissipation rate from M2 internal tides to turbulence within 50 km of the Hawaiian Ridge is roughly estimated to be in the range of 4–9 GW. At KC, the depth-integrated internal wave energy density and dissipation rate are positively correlated. Potential density inversions occur near the main ridge axis at significant topographic features. Average Kρ is larger inside inversions.

Observations of turbulence in a tidal beam and across a coastal ridge

During a microstructure survey off California in Monterey Bay, we found a midwater beam of strong turbulence emanating from the shelf break along the ray path of the semidiurnal M2 internal tide. Within the 50‐m‐thick beam the turbulence kinetic energy dissipation rate ε exceeded 10−6 W kg−1, and the diapycnal eddy diffusivity Kρ was &gt;0.01 m2 s−1. The beam extended 4 km off the shelf break. Several factors suggest that this beam of strong turbulence resulted from the breaking of semidiurnal internal tides: the beam appeared to originate from the shelf break, which is a potential generation site for semidiurnal internal tides; the beam closely followed the ray path of the semidiurnal internal tide; the average ε off the shelf break varied by a factor of 100 with a semidiurnal tidal periodicity; the isopycnal displacement confirmed the presence of semidiurnal internal tides. Processes associated with the breaking of internal tides are intermittent and sporadic. At the same location we also observed equally intense turbulence in a ∼100‐m‐thick layer of stratified water across the ridge of a sea fan. This layer of strong turbulence was separated from the bottom and was clearly not generated by bottom friction. Although less well resolved in time, the strong turbulence above the bottom seemed to vary with the semidiurnal tide and existed at the lee of the ridge, where the isopycnal surface dipped and rebounded in a pattern resembling that of internal hydraulic jumps. On the basis of the behavior of the density field, we believe that the deep mixing was most likely produced by the across‐ridge current of internal tides. The breaking of internal tides at middepth, where the Richardson number is close to the critical value, is likely due to shear instability. The presence of the coastal ridge provides an alternative pathway for converting energy from internal tides to turbulence via internal hydraulics. Multiplying the average ε in the midwater beam by the length of the global coastline gives 31 GW, only a small fraction of the estimated 360 GW dissipated globally by M2 internal tides. Our observations suggest that either most internal tides are generated away from shelf breaks or most internal tides generated at shelf breaks propagate away from their generation sites, rather than dissipate locally, and eventually contribute to pelagic mixing.

Mixing of a tracer in the pycnocline

A patch of sulfur hexafluoride was released in May 1992 in the eastern North Atlantic on an isopycnal surface near 300 m depth and was surveyed over a period of 30 months as it dispersed across and along isopycnal surfaces. The diapycnal eddy diffusivity K estimated for the first 6 months was 0.12±0.02 cm2/s, while for the subsequent 24 months it was 0.17±0.02 cm2/s. The vertical tracer distribution remained very close to Gaussian for the full 30 months, as the root mean square (rms) dispersion grew from 5 to 50 m. Lateral dispersion was measured on several scales. The growth of the rms width of the tracer streaks from less than 100 m to approximately 300 m within 2 weeks implies an isopycnal diffusivity of 0.07 m2/s at scales of 0.1 to 1 km, larger than expected from the interaction between vertical shear of the internal waves and diapycnal mixing. Teasing of the overall patch, initially about 25 km across, into streaks with an overall length of 1800 km within 6 months supports predictions of exponential growth by the mesoscale strain field at a rate of 3±0.5 × 10−7 s−1. The rms width of these streaks, estimated as 3 km and maintained in the face of the streak growth, indicates an isopycnal diffusivity of 2 m2/s at scales of 1 to 10 km, much greater than expected from internal wave shear dispersion. The patch was painted in, albeit streakily, by 12 months, confirming expectations from analytical and numerical models. Homogenization of the patch continued during the subsequent 18 months, while the patch continued to spread with an effective isopycnal eddy diffusivity on the order of 1000 m2/s, acting at scales of 30 to 300 km.

A tracer study of mixing in the Santa Cruz Basin

A tracer release experiment to study diapycnal and isopycnal mixing was performed in Santa Cruz Basin in 1988–1989. Approximately 1450 g of sulfur hexafluoride were injected close to an isopycnal surface at 1500 m depth in May 1988. This depth is midway between the bottom of the basin at 1920 m and the sill at 1084 m. The diapycnal dispersion measured during the first few months, while the tracer was still mixing to the walls of the basin, yielded a diapycnal eddy diffusivity of 1.0 cm2 s−1, within a factor of 1.5. This is approximately 4 times larger than the diffusivity found by Ledwell and Watson (1991) in the interior of Santa Monica Basin, where the buoyancy frequency was 5 times greater. The tracer was well mixed to the walls 6 months after the injection, and at that time the diapycnal spread of the tracer was greater near the walls than in the interior. The rate of diapycnal dispersion of the tracer increased dramatically after the tracer had mixed to the walls of the basin, indicating enhanced boundary mixing. An effective basin‐wide diapycnal diffusivity of 10 cm2 s−1 would be required to support the fluxes of tracer observed. A one‐dimensional model for tracer and heat diffusion does not simulate the results very well, however, probably because of the finite mixing time between the boundary region and interior and because of the complexity of the processes in the boundary region.

Evidence for enhanced boundary mixing in the Santa Monica Basin

Transients in the heat content in Santa Monica and San Pedro Basins imply a basin‐wide diapycnal eddy diffusivity greater than 1 cm2/s. This is significantly larger than the value for SF6 of 0.25±0.08 cm2/s determined for the interior of Santa Monica Basin for September 1985 to February 1986 by Ledwell and Watson (1991). However, the exodus of SF6 from Santa Monica Basin after February 1986, by which time the tracer had mixed to the boundaries of the basin, was fast enough to be consistent with a greatly enhanced vertical flux. Since the kinetic energy in the basin had not changed significantly, it is unlikely that a temporal increase in forcing resulted in enhanced fluxes in the interior of the basin. The most likely interpretation is that diapycnal fluxes in the basin are dominated by processes in the boundary regions. Temperature and SF6 profiles from near the edges of the basin do not give conclusive evidence either for or against such enhanced mixing.

Parameter space exploration of an ocean general circulation model using an isopycnal mixing parameterization

ABSTRACT In this study we have employed statistical methods to efficiently design experiments and analyze output of an ocean general circulation model that uses an isopycnal mixing parameter- ization. Full ranges of seven inputs are explored using 51 numerical experiments. Fifteen of the cases fail to reach satisfactory equilibria. These are attributable to numerical limitations specific to the isopycnal model. Statistical approximating functions are evaluated using the remaining cases to determine the dependency of each of the six scalar outputs on the inputs. With the exception of one output, the approximating functions perform well. Known sensitivities, particularly the importance of diapycnal (vertical) eddy diffusivity and wind stress, are reproduced. The sensitivities of the model to two numerical constraints specific to the isopycnal parameterization, maximum allowable isopycnal slope and horizontal back- ground eddy diffusivity, are explored. Isopycnal modelling issues, convection reduction and the Veronis effect, are examined and found to depend crucially on the isopycnal modelling constraints.

Estimates of Diapycnal Mixing in the Abyssal Ocean

Profiles of diapycnal eddy diffusivity to a maximum depth of 4000 meters were derived from ocean velocity and temperature microstructure data obtained in conjunction with separate experiments in the Northeast Pacific and Northeast Atlantic oceans. These profiles indicate that in the ocean interior where the internal wave field is at background intensity, the diapycnal eddy diffusivity is small (on the order of 0.1 x 10(-4) meters squared per second) and independent of depth, in apparent contradiction with large-scale budget studies. Enhanced dissipation is observed in regions of elevated internal wave energy, particularly near steeply sloping boundaries (where the eddy diffusivity estimates exceed 1 x 10(-4) meters squared per second). These results suggest that basin-averaged mixing rates may be dominated by processes occurring near the ocean boundaries.

The Relative Roles of Diapycnal and Isopycnal Mixing on Subsurface Water Mass Conversion

Abstract Fluid motion in the sea is known to occur predominantly along quasi-horizontal neutral surfaces but the very small diapycnal (i.e., across isopycnal) velocities often make a significant contribution to the conversation equations of heat, salt and tracer. By eliminating the diapycnal advection term between the conservation equations for (i) heat and (ii) salt, an equation is derived for the rate of change (Lagrangian derivative) of potential temperature θ on a neutral surface which has terms caused by (a) turbulent mixing along isopycnal surfaces (i.e., isopycnal mixing), (b) diapycnal turbulent mixing and (c) double-diffusive convection. Bemuse of the nature of the isopycnal reference frame, the diapycnal mixing terms do not take their expected forms. For example, the diapycnal turbulent mixing term is proportional to the diapycnal eddy diffusivity D multiplied by the curvature of the θ-S curve, d2S/dθ2, rather than the usual form (Dθx)x. If the θ−S curve is locally straight, small-scale turbulen...