Mixing Efficiency in the Ocean

Seasonal productivity of the equatorial Atlantic shaped by distinct wind-driven processes

The eastern equatorial Atlantic hosts a productive marine ecosystem that depends on upward supply of nitrate, the primary limiting nutrient in this region. The annual productivity peak, indicated by elevated surface chlorophyll levels, occurs in the Northern Hemisphere summer, roughly coinciding with strengthened easterly winds. For enhanced productivity in the equatorial Atlantic, nitrate-rich water must rise into the turbulent layer above the Equatorial Undercurrent. Using data from two trans-Atlantic equatorial surveys, along with extended time series from equatorial moorings, we demonstrate how three independent wind-driven processes shape the seasonality of equatorial Atlantic productivity: (1) the nitracline shoals in response to intensifying easterly winds; (2) the depth of the Equatorial Undercurrent core, defined by maximum eastward velocity, is controlled by an annual oscillation of basin-scale standing equatorial waves; and (3) mixing intensity in the shear zone above the Equatorial Undercurrent core is governed by local and instantaneous winds. The interplay of these three mechanisms shapes a unique seasonal cycle of nutrient supply and productivity in the equatorial Atlantic, with a productivity minimum in April due to a shallow Equatorial Undercurrent and a productivity maximum in July resulting from a shallow nitracline coupled with enhanced mixing.

Interacting internal waves explain global patterns of interior ocean mixing

Across the stable density stratification of the abyssal ocean, deep dense water is slowly propelled upward by sustained, though irregular, turbulent mixing. The resulting mean upwelling determines large-scale oceanic circulation properties like heat and carbon transport. In the ocean interior, this turbulent mixing is caused mainly by breaking internal waves: generated predominantly by winds and tides, these waves interact nonlinearly, transferring energy downscale, and finally become unstable, break and mix the water column. This paradigm, long parameterized heuristically, still lacks full theoretical explanation. Here, we close this gap using wave-wave interaction theory with input from both localized and global observations. We find near-ubiquitous agreement between first-principle predictions and observed mixing patterns in the global ocean interior. Our findings lay the foundations for a wave-driven mixing parameterization for ocean general circulation models that is entirely physics-based, which is key to reliably represent future climate states that could differ substantially from today's.

Advection surface-flux balance controls the seasonal steric sea level amplitude

Along with the mean sea level rise due to climate change, the sea level exhibits natural variations at a large number of different time scales. One of the most important is the one linked with the seasonal cycle. In the Northern Hemisphere winter, the sea level is as much as 20 cm below its summer values in some locations. It is customary to associate these variations with the seasonal cycle of the sea surface net heat flux which drives an upper-ocean thermal expansion creating a positive steric sea level anomaly. Here, using a novel framework based on steric sea level variance budget applied to observations and to the Estimating the Circulation and Climate of the Ocean state estimate, we demonstrate that the steric sea level seasonal cycle amplitude results from a balance between the seasonal sea surface net heat flux and the oceanic advective processes. Moreover, for up to 50% of the ocean surface, surface heat fluxes act to damp the seasonal steric sea level cycle amplitude, which is instead forced by oceanic advection processes. We also show that eddies play an important role in damping the steric sea level seasonal cycle. Our study contributes to a better understanding of the steric sea level mechanisms which is crucial to ensure accurate and reliable climate projections.

The deepwater oxygen deficit in stratified shallow seas is mediated by diapycnal mixing

Seasonally stratified shelf seas are amongst the most biologically productive on the planet. A consequence is that the deeper waters can become oxygen deficient in late summer. Predictions suggest global warming will accelerate this deficiency. Here we integrate turbulence timeseries with vertical profiles of water column properties from a seasonal stratified shelf sea to estimate oxygen and biogeochemical fluxes. The profiles reveal a significant subsurface chlorophyll maximum and associated mid-water oxygen maximum. We show that the oxygen maximum supports both upward and downwards O2 fluxes. The upward flux is into the surface mixed layer, whilst the downward flux into the deep water will partially off-set the seasonal O2 deficit. The results indicate the fluxes are sensitive to both the water column structure and mixing rates implying the development of the seasonal O2 deficit is mediated by diapcynal mixing. Analysis of current shear indicate that the downward flux is supported by tidal mixing, whilst the upwards flux is dominated by wind driven near-inertial shear. Summer storminess therefore plays an important role in the development of the seasonal deep water O2 deficit.

Circum-Antarctic bottom water formation mediated by tides and topographic waves

The downslope plumes of dense shelf water (DSW) are critical for the formation of Antarctic Bottom Water (AABW), and thus to the exchange of heat and carbon between surface and abyssal ocean. Previous studies have shown that tides and overflow-forced topographic Rossby waves (TRWs) may have strong impact on the downslope transport of DSW, but it remains unclear how the combined action of these two processes influence the descent processes of DSW, and of the resulting AABW properties. Here, with a synthesis of historical in situ observations and a set of numerical model experiments, we show that tides and TRWs play comparable roles in AABW formation: they both act to accelerate DSW descent to the abyss, leading to the formation of colder and denser AABW. Yet, tides have little impact on AABW formation unless the continental slope is steep enough to suppress TRW generation. We further characterize the dynamical regimes of dense overflows around the entire Antarctic continent based on the relative importance of TRWs versus tides. These findings highlight the pervasive role of high-frequency processes, which are not well represented in the present climate models, in the formation of AABW, and thus in the global overturning circulation.

Coastal trapped waves and tidal mixing control primary production in the tropical Angolan upwelling system

Eastern boundary upwelling systems are hotspots of marine life and primary production. The strength and seasonality of upwelling in these systems are usually related to local wind forcing. However, in some tropical upwelling systems, seasonal maxima of productivity occur when upwelling favorable winds are weak. Here, we show that in the tropical Angolan upwelling system (tAUS), the seasonal productivity maximum is due to the combined effect of coastal trapped waves (CTWs) and elevated tidal mixing on the shelf. During austral winter, the passage of an upwelling CTW displaces the nitracline upward by more than 50 m. Thereby, nitrate-rich waters spread onto the shelf, where elevated vertical mixing causes a nitrate flux into the surface mixed layer. Interannual variability of the productivity maximum is strongly correlated to the amplitude of the upwelling CTW as seen in sea level data. Given that CTWs are connected to equatorial forcing, a predictability of the strength of the productivity maximum is suggested.

Energy Spectra of Nonlocal Internal Gravity Wave Turbulence

Starting from the classical formulation of the weak turbulence theory in a density stratified fluid, we derive a simplified version of the kinetic equation of internal gravity wave turbulence. This equation allows us to uncover scaling laws for the spatial and temporal energy spectra of internal wave turbulence which are consistent with typical scaling exponents observed in the oceans. The keystone of our description is the assumption that the energy transfers are dominated by a class of nonlocal resonant interactions, known as the "induced diffusion" triads, which conserve the ratio between the wave frequency and vertical wave number. Our analysis remarkably shows that the internal wave turbulence cascade is associated to an apparent constant flux of wave action.

Bolgiano-Obukhov spectrum and mixing efficiency in stably stratified turbulence

In this paper, using a shell model, we simulate highly turbulent stably stratified flow for weak to moderate stratification at unitary Prandtl number. We investigate the energy spectra and fluxes of velocity and density fields. We observe that for moderate stratification, in the inertial range, the kinetic energy spectrum E_{u}(k) and the potential energy spectrum E_{b}(k) show dual scaling-Bolgiano-Obukhov scaling [E_{u}(k)∼k^{-11/5} and E_{b}(k)∼k^{-7/5}] for k<k_{B}, where k_{B} is the Bolgiano wave number, and Kolmogorov scaling (∼k^{-5/3}) for k>k_{B}. In addition, we find that the mixing efficiency η_{mix} varies as η_{mix}∼Ri for weak stratification, whereas η_{mix}∼Ri^{1/3} for moderate stratification, where Ri is the Richardson number.

Observational evidence of salt finger in the diurnal thermocline

Due to strong turbulent mixing, the ocean surface boundary layer region is generally not conducive to double diffusion. However, vertical microstructure profiles observations in the northeastern Arabian Sea during May 2019 imply the formation of salt fingers in the diurnal thermocline (DT) region during the daytime. In the DT layer, conditions are favorable for salt fingering: Turner angle values are between 50 and 55° with both temperature and salinity decreasing with depth; shear-driven mixing is weak with a turbulent Reynolds number of about 30. The presence of salt fingering in the DT is confirmed by the presence of staircase-like structures with step sizes larger than the Ozmidov length and by the dissipation ratio that is larger than the mixing coefficient. The unusual daytime salinity maximum in the mixed layer that supports salt fingering is primarily due to a daytime reduction in vertical entrainment of fresh water along with minor contributions from evaporation and horizontal advection and a significant contribution from detrainment processes.

Tracking a Rain-Induced Low-Salinity Pool in the South China Sea Using Satellite and Quasi-Lagrangian Field Observations

A low-salinity pool (LSP) was observed in the northeastern South China Sea on 8–10 August 2018. Employing satellite and field observations, as well as widely used HYbrid Coordinate Ocean Model (HYCOM) Analysis data, we investigated the distribution, origin and evolution of the LSP. A bowl-like structure of the LSP was observed from field observations and is also indicated by the HYCOM Analysis data. Spatially, the LSP extended 20 m deep vertically and spread at least 45 km laterally. Particle tracking simulations using satellite-observed precipitation and surface currents revealed the origin and evolution of the LSP. It is found that the LSP was induced by a heavy rainfall event two days prior to the field observations, evidenced by the significant correlation between the rainfall and salinity anomaly. The vertical expansion of the LSP was favored by nocturnal convection, but was restricted by the strong stratification at its base, which appeared to have prohibited development of convective instabilities as indicated by the observed vertical variation of the turbulent dissipation rate. The formation of a barrier layer due to the LSP restricted vertical heat exchanges, and as a result a thin temperature inversion layer was formed as the surface temperature dropped due to the nighttime cooling and mixing with the cold rainwater. The thermohaline structure favored development of diffusive convection, which is evidenced by the observation that the diapycnal diffusivity for heat (KT) was one order of magnitude larger than that for density (Kρ). Overall, this study provides novel insights into how the upper ocean responds to rainfall with satellite and field observations.

A multi-site, year-round turbulence microstructure atlas for the deep perialpine Lake Garda

A multi-site, year-round dataset comprising a total of 606 high-resolution turbulence microstructure profiles of shear and temperature gradient in the upper 100 m depth is made available for Lake Garda (Italy). Concurrent meteorological data were measured from the fieldwork boat at the location of the turbulence measurements. During the fieldwork campaign (March 2017-June 2018), four different sites were sampled on a monthly basis, following a standardized protocol in terms of time-of-day and locations of the measurements. Additional monitoring activity included a 24-h campaign and sampling at other sites. Turbulence quantities were estimated, quality-checked, and merged with water quality and meteorological data to produce a unique turbulence atlas for a lake. The dataset is open to a wide range of possible applications, including research on the variability of turbulent mixing across seasons and sites (demersal vs pelagic zones) and driven by different factors (lake-valley breezes vs buoyancy-driven convection), validation of hydrodynamic lake models, as well as technical studies on the use of shear and temperature microstructure sensors.

Log-Skew-Normality of Ocean Turbulence

The statistics of intermittent ocean turbulence is the key link between physical understanding of turbulence and its global implications. The log-normal distribution is the standard but imperfect assumed distribution for the turbulent kinetic energy dissipation rate. We argue that as turbulence is often generated by multiple changing sources, a log-skew-normal (LSN) distribution is more appropriate. We show the LSN distribution agrees excellently and robustly with observations. The heavy tail of the LSN distribution has important implications for sampling of turbulence in terrestrial and extraterrestrial analogous systems.

Variations in Ocean Mixing from Seconds to Years

Over the past several decades, there has developed a community-wide appreciation for the importance of mixing at the smallest scales to geophysical fluid dynamics on all scales. This appreciation has spawned greater participation in the investigation of ocean mixing and new ways to measure it. These are welcome developments given the tremendous separation in scales between the basins, [Formula: see text]) m, and the turbulence, [Formula: see text]) m, and the fact that turbulence that leads to thermodynamically irreversible mixing in high-Reynolds-number geophysical flows varies by at least eight orders of magnitude in both space and time. In many cases, it is difficult to separate the dependencies because measurements are sparse, also in both space and time. Comprehensive shipboard turbulence profiling experiments supplemented by Doppler sonar current measurements provide detailed observations of the evolution of the vertical structure of upper-ocean turbulence on timescales of minutes to weeks. Recent technical developments now permit measurements of turbulence in the ocean, at least at a few locations, for extended periods. This review summarizes recent and classic results in the context of our expanding knowledge of the temporal variability of ocean mixing, beginning with a discussion of the timescales of the turbulence itself (seconds to minutes) and how turbulence-enhanced mixing varies over hours, days, tidal cycles, monsoons, seasons, and El Niño-Southern Oscillation timescales (years).

Turbulence and Coral Reefs

The interaction of coral reefs, both chemically and physically, with the surrounding seawater is governed, at the smallest scales, by turbulence. Here, we review recent progress in understanding turbulence in the unique setting of coral reefs-how it influences flow and the exchange of mass and momentum both above and within the complex geometry of coral reef canopies. Flow above reefs diverges from canonical rough boundary layers due to their large and highly heterogeneous roughness and the influence of surface waves. Within coral canopies, turbulence is dominated by large coherent structures that transport momentum both into and away from the canopy, but it is also generated at smaller scales as flow is forced to move around branches or blades, creating wakes. Future work interpreting reef-related observations or numerical models should carefully consider the influence that spatial variation has on momentum and scalar flux.

Quantitative Experimental Observation of Weak Inertial-Wave Turbulence

We report the quantitative experimental observation of the weak inertial-wave turbulence regime of rotating turbulence. We produce a statistically steady homogeneous turbulent flow that consists of nonlinearly interacting inertial waves, using rough top and bottom boundaries to prevent the emergence of a geostrophic flow. As the forcing amplitude increases, the temporal spectrum evolves from a discrete set of peaks to a continuous spectrum. Maps of the bicoherence of the velocity field confirm such a gradual transition between discrete wave interactions at weak forcing amplitude and the regime described by weak turbulence theory (WTT) for stronger forcing. In the former regime, the bicoherence maps display a near-zero background level, together with sharp localized peaks associated with discrete resonances. By contrast, in the latter regime, the bicoherence is a smooth function that takes values of the order of the Rossby number in line with the infinite-domain and random-phase assumptions of WTT. The spatial spectra then display a power-law behavior, both the spectral exponent and the spectral level being accurately predicted by WTT at high Reynolds number and low Rossby number.

Mixing in Turbulent Flows: An Overview of Physics and Modelling

Turbulent flows featuring additional scalar fields, such as chemical species or temperature, are common in environmental and industrial applications. Their physics is complex because of a broad range of scales involved; hence, efficient computational approaches remain a challenge. In this paper, we present an overview of such flows (with no particular emphasis on combustion, however) and we recall the major types of micro-mixing models developed within the statistical approaches to turbulence (the probability density function approach) as well as in the large-eddy simulation context (the filtered density function). We also report on some trends in algorithm development with respect to the recent progress in computing technology.

Coupling Large Eddies and Waves in Turbulence: Case Study of Magnetic Helicity at the Ion Inertial Scale

In turbulence, for neutral or conducting fluids, a large ratio of scales is excited because of the possible occurrence of inverse cascades to large, global scales together with direct cascades to small, dissipative scales, as observed in the atmosphere and oceans, or in the solar environment. In this context, using direct numerical simulations with forcing, we analyze scale dynamics in the presence of magnetic fields with a generalized Ohm’s law including a Hall current. The ion inertial length ϵ H serves as the control parameter at fixed Reynolds number. Both the magnetic and generalized helicity—invariants in the ideal case—grow linearly with time, as expected from classical arguments. The cross-correlation between the velocity and magnetic field grows as well, more so in relative terms for a stronger Hall current. We find that the helical growth rates vary exponentially with ϵ H , provided the ion inertial scale resides within the inverse cascade range. These exponential variations are recovered phenomenologically using simple scaling arguments. They are directly linked to the wavenumber power-law dependence of generalized and magnetic helicity, ∼ k − 2 , in their inverse ranges. This illustrates and confirms the important role of the interplay between large and small scales in the dynamics of turbulent flows.

Estimation of Turbulence Parameters in the Lower Troposphere from ShUREX (2016–2017) UAV Data

Turbulence parameters in the lower troposphere (up to ~4.5 km) are estimated from measurements of high-resolution and fast-response cold-wire temperature and Pitot tube velocity from sensors onboard DataHawk Unmanned Aerial Vehicles (UAVs) operated at the Shigaraki Middle and Upper atmosphere (MU) Observatory during two ShUREX (Shigaraki UAV Radar Experiment) campaigns in 2016 and 2017. The practical processing methods used for estimating turbulence kinetic energy dissipation rate ε and temperature structure function parameter C T 2 from one-dimensional wind and temperature frequency spectra are first described in detail. Both are based on the identification of inertial (−5/3) subranges in respective spectra. Using a formulation relating ε and C T 2 valid for Kolmogorov turbulence in steady state, the flux Richardson number R f and the mixing efficiency χ m are then estimated. The statistical analysis confirms the variability of R f and χ m around ~ 0.13 − 0.14 and ~ 0.16 − 0.17 , respectively, values close to the canonical values found from some earlier experimental and theoretical studies of both the atmosphere and the oceans. The relevance of the interpretation of the inertial subranges in terms of Kolmogorov turbulence is confirmed by assessing the consistency of additional parameters, the Ozmidov length scale L O , the buoyancy Reynolds number R e b , and the gradient Richardson number Ri. Finally, a case study is presented showing altitude differences between the peaks of N 2 , C T 2 and ε , suggesting turbulent stirring at the margin of a stable temperature gradient sheet. The possible contribution of this sheet and layer structure on clear air radar backscattering mechanisms is examined.

Asymptotic Dynamics of High Dynamic Range Stratified Turbulence

Direct numerical simulations of homogeneous sheared and stably stratified turbulence are considered to probe the asymptotic high dynamic range regime suggested by Gargett et al. J. Fluid Mech. 144, 231 (1984)10.1017/S0022112084001592 and Shih et al. J. Fluid Mech. 525, 193 (1999)10.1017/S0022112004002587. We consider statistically stationary configurations of the flow that span three decades in dynamic range defined by the separation between the Ozmidov length scale L_{O}=sqrt[ε/N^{3}] and the Kolmogorov length scale L_{K}=(ν^{3}/ε)^{1/4}, up to Re_{b}≡(L_{O}/L_{K})^{4/3}=ε/(νN^{2})∼O(1000), where ε is the mean turbulent kinetic energy dissipation rate, ν is the kinematic viscosity, and N is the buoyancy frequency. We isolate the effects of Re_{b}, particularly on irreversible mixing, from the effects of other flow parameters of stratified and sheared turbulence. Specifically, we evaluate the influence of dynamic range independent of initial conditions. We present evidence that the flow approaches an asymptotic state for Re_{b}⪆300, characterized both by an asymptotic partitioning between the potential and kinetic energies and by the approach of components of the dissipation rate to their expected values under the assumption of isotropy. As Re_{b} increases above 100, there is a slight decrease in the turbulent flux coefficient Γ=χ/ε, where χ is the dissipation rate of buoyancy variance, but, for this flow, there is no evidence of the commonly suggested Γ∝Re_{b}^{-1/2} dependence when 100≤Re_{b}≤1000.

Self-organized criticality in geophysical turbulence

Turbulence in geophysical flows tends to organize itself so that the mean flow remains close to a stability boundary in parameter space. That characteristic suggests self-organized criticality (SOC), a statistical property that has been identified in a range of complex phenomena including earthquakes, forest fires and solar flares. This note explores the relationship between the properties of forced, sheared, stratified turbulence (as found in oceans, atmospheres and other geophysical fluids) and those of SOC. Self-organization to the critical state is demonstrated in a wide range of cases drawn mostly (but not entirely) from in situ observations of ocean turbulence. Turbulent events in the ocean also exhibit a second characteristic associated with SOC: their sizes follow a power-law distribution indicating self-similarity. These results suggest SOC as a new conceptual foundation for the study of geophysical turbulence, an explanation for the mixing efficiency of ocean turbulence and a potential for cross-fertilization with other areas of geophysics.

Biologically Generated Mixing in the Ocean

This article assesses the contribution to ocean mixing by the marine biosphere at both high and low Reynolds numbers Re= uℓ/ ν. While back-of-the-envelope estimates have suggested that swimming marine organisms might generate as much high-Reynolds-number turbulence as deep-ocean tide- and wind-generated internal waves, and that turbulent dissipation rates of O(10^-5 W kg^-1) (Re ∼ 10⁵) could be produced by aggregations of organisms ranging from O(0.01 m) krill to O(10 m) cetaceans, comparable to strong wind and buoyancy forcing near the surface, microstructure measurements do not find consistently elevated dissipation associated with diel vertically migrating krill. Elevated dissipation rates are associated with schools of O(0.1- 1 m) fish but with low mixing coefficients ( γ ∼ 0.002-0.02, as compared with γ ∼ 0.2 for geophysical turbulence). Likewise, viscously induced drift at low Reynolds numbers produces little mixing of temperature, solutes, dissolved nutrients, and gases when realistic swimmers and molecular scalar diffusion are taken into account. The conclusion is that, while the marine biosphere can generate turbulence, it contributes little ocean mixing compared with breaking internal gravity waves.

The Global Overturning Circulation

In this article, I use the Estimating the Circulation and Climate of the Ocean version 4 (ECCO4) reanalysis to estimate the residual meridional overturning circulation, zonally averaged, over the separate Atlantic and Indo-Pacific sectors. The abyssal component of this estimate differs quantitatively from previously published estimates that use comparable observations, indicating that this component is still undersampled. I also review recent conceptual models of the oceanic meridional overturning circulation and of the mid-depth and abyssal stratification. These theories show that dynamics in the Antarctic circumpolar region are essential in determining the deep and abyssal stratification. In addition, they show that a mid-depth cell consistent with observational estimates is powered by the wind stress in the Antarctic circumpolar region, while the abyssal cell relies on interior diapycnal mixing, which is bottom intensified.

Climate Process Team on Internal Wave-Driven Ocean Mixing

Diapycnal mixing plays a primary role in the thermodynamic balance of the ocean and, consequently, in oceanic heat and carbon uptake and storage. Though observed mixing rates are on average consistent with values required by inverse models, recent attention has focused on the dramatic spatial variability, spanning several orders of magnitude, of mixing rates in both the upper and deep ocean. Away from ocean boundaries, the spatio-temporal patterns of mixing are largely driven by the geography of generation, propagation and dissipation of internal waves, which supply much of the power for turbulent mixing. Over the last five years and under the auspices of US CLIVAR, a NSF- and NOAA-supported Climate Process Team has been engaged in developing, implementing and testing dynamics-based parameterizations for internal-wave driven turbulent mixing in global ocean models. The work has primarily focused on turbulence 1) near sites of internal tide generation, 2) in the upper ocean related to wind-generated near inertial motions, 3) due to internal lee waves generated by low-frequency mesoscale flows over topography, and 4) at ocean margins. Here we review recent progress, describe the tools developed, and discuss future directions.