Double-diffusive Processes Research Articles

Double diffusive thermogravitational convection in a convex U-shaped porous chamber filled with radiative ternary hybrid nanoliquid

This research deals with the intricate dynamics of double diffusive thermogravitational convection within a convex U-shaped porous chamber and sheds light on the use of a radiative ternary hybrid nanoliquid. In this configuration, the lower flat boundary is assumed to be thermally hot and densely concentrated while the curved lateral boundaries remain cold and dilute. The other boundaries of the enclosure are kept under adiabatic conditions. The governing Navier–Stokes equations along with thermal and species equations are effectively solved by employing a higher order compact technique. The developed in-house program has been rigorously verified against experimental and computational benchmark results. The research meticulously examines the impact of several pivotal parameters, including the Lewis number (1≤Le≤20), buoyancy ratio (0≤N≤10), Darcy number (10−4≤Da≤10−2), Rayleigh number (104≤Ra≤106), volumetric heat source/sink coefficient (−10≤q≤10), radiation parameter (1≤Rd≤5), aspect parameter of the U-shaped chamber (0.2≤AR≤0.6), and solid particles concentration (0.0≤ϕthnp≤0.04) of the ternary hybrid nanofluid. The findings are eloquently portrayed through graphical representations by showcasing streamlines, iso-solutals, isotherms, and the dimensionless Nusselt (Nuavg) and Sherwood (Shavg) parameters. Our investigation demonstrates that the ternary hybrid nanofluid outperforms both hybrid and mono nanofluids in facilitating double diffusion processes. Moreover, optimal heat transfer efficiency is achieved under conditions characterized by an aspect ratio of AR = 0.2, Rayleigh number Ra=106, Darcy number Da=10−2, buoyancy ratio N = 10, Lewis number Le = 1, and solid volume fraction ϕthnp=0.04.

The sub-microscale dynamics of double-diffusive convection

This study investigates the dynamics of fingering convection on scales much smaller than the typical size of individual salt fingers. On such scales, salinity patterns exhibit the spontaneous emergence of sharp fronts induced by finger-scale strain. In contrast, velocity and temperature fields are largely devoid of sub-microscale variability, which is attributed to the rapid molecular dissipation of heat and momentum. The presence of fine salinity structures fundamentally limits the efficiency of direct numerical simulations (DNS) of double-diffusive processes. In the oceanographic context, the computational cost of resolving sub-microscale salinity features exceeds that of temperature-only DNS by up to four orders of magnitude, severely restricting the types of double-diffusive systems that can be studied numerically. To address this complication, we introduce the sub-microscale filtering (SMF) algorithm, which resolves temperature and velocity while parameterizing the sub-microscale dynamics of salinity. The proposed closure draws inspiration from the Smagorinsky scheme, which represents unresolved processes by the downgradient strain-dependent momentum flux. The SMF model is successfully validated through fully resolved simulations.

Diapycnal Mixing and Double Diffusion over the Continental Slope in the Northern Sea of Japan in the Warm Half-Year

This study investigates double diffusion processes responsible for diapycnal mixing in the Primorye current in the northern Sea of Japan. The results of processing and analysis of a long time series of data from regular Aqualog-profiler measurements of thermohaline characteristics and current velocity over the continental slope between the horizons of 60 and 420 m from April to October 2015. Using the Osborne-Cox parameterization (1972) and Gregg’s (1989) parameterization, we estimated heat and salt diffusivities, as well as the buoyancy flux. To reveal the processes of double diffusion, the Turner angle was estimated. We estimated contributions of diffusive convection and salt fingers into the buoyancy flux. Due to double diffusion, the intense vertical mixing covered the layer from 80 to 170 m. From mid-spring to early May, diffusive convection penetrated to a horizon of 250 m, and then a process like salt fingers played a leading role. Shear instability caused by the weakly nonlinear interaction of internal waves prevailed in the underlying layers.

Turbulent disruption of density staircases in stratified shear flows

The formation of step-like ‘density staircase’ distributions induced by stratification and turbulence has been widely studied, and can be explained by the ‘instability’ of a sufficiently strongly stably stratified turbulent flow due to the decrease of the turbulent density flux with increasing stratification via the ‘Phillips mechanism’ (Phillips, Deep Sea Research and Oceanographic Abstracts, vol. 19, 1972, pp. 79–81. Elsevier). However, such density staircases are not often observed in ocean interiors, except in regions where double-diffusion processes are important, leading to thermohaline staircases. Using reduced-order models for the evolution of velocity and density gradients, we analyse staircase formation in stratified and sheared turbulent flows. Under the assumption of inertial scaling $\epsilon \sim U^3/L$ for the kinetic energy dissipation rate $\epsilon$ , where $U$ and $L$ are characteristic velocity and length scales, we determine ranges of bulk Richardson numbers ${Ri}_{b}$ and turbulent Prandtl numbers ${Pr}_{T}$ for which staircases can potentially form and show that the Phillips mechanism only survives in the limit of sufficiently small turbulent Prandtl numbers. For relevant oceanic parameters, a range of turbulent Prandtl numbers above which the system is not prone to staircases is found to be ${Pr}_T \simeq 0.5\unicode{x2013}0.8$ . Since several studies indicate that the turbulent Prandtl number in stably stratified turbulence and in ocean interiors is usually above this threshold, this result supports the empirical observation that staircases are not favoured in ocean interiors in the presence of relatively homogeneous and sustained turbulence. We also show that our analysis is robust to other scalings for $\epsilon$ (such as the more strongly stratified scaling $\epsilon \sim U^{2}N_{c}$ , where $N_{c}$ is a characteristic value of the buoyancy frequency), supporting our results in both shear-dominated and buoyancy-dominated turbulent regimes as well as in weakly and strongly stratified regimes.

An inventory of salty and warm subsurface intrusions in the South Brazil Bight

Subsurface intrusions of salty and warm waters onto the shelf can potentially impact the thermodynamics and biogeochemistry of these relatively shallow water environments. Such thermohaline intrusions are usually associated with double diffusive processes and can enhance the vertical and lateral fluxes. In this work, we characterized subsurface intrusions of Tropical Waters (TW) at the South Brazil Bight (SBB) - a mid-latitude continental shelf, which were detected based on salinity vertical profiles from a historical dataset. We found the intrusions tend to follow the pycnocline and are relatively common year-round, occurring at 27% of the dataset, with a maximum salinity highly correlated with the maximum stratification. Intrusions have different along-shelf characteristics, varying with the shelf width and depth. North of São Sebastião Island (SSI) – at the central portion of the SBB –, intrusions were thicker, saltier, and shallower than the ones found at the south of SSI. These differences could be related to the variations of the Coastal Water (CW) and South Atlantic Central Water (SACW) volume along the shelf and throughout the year. We found that intrusions’ thickness presents an inverse correlation with stratification, resulting in thinner intrusions in more stratified environments. This inverse correlation suggests double-diffusively driven intrusions. We apply the Turner Angle method to investigate whether the environment is susceptible to double diffusive processes. This analysis suggests that thermohaline intrusions in the SBB might not be primarily double diffusive. However, the dominance of different double diffusion processes - diffusive convection (salt fingering) at the upper (lower) layer - suggests that these processes influence intrusion growth, steady-state, and erosion. Nonetheless, the mechanism responsible for the initial density perturbation remains unknown and further studies are needed to explore the relationship between the Brazil Current dynamics and thermohaline warm and salty subsurface intrusions.

A Glider View of the Spreading and Mixing Processes of Antarctic Intermediate Water in the Northeastern Subtropical Atlantic

The Antarctic Intermediate Water (AAIW), one of the most important global intermediate water masses, spreads over the world ocean. Its propagation limit at the Northeast Subtropical Atlantic is characterized by its encounter with the Mediterranean Water (MW), which presents dissimilar thermohaline properties. Previous studies of the AAIW in this region have been based on traditional oceanographic cruise observations, which were later complemented by observations using autonomous systems such as ARGO floats. However, these observations present limitations for the study of processes occurring at mesoscale and smaller scales. In this study, we used high-resolution observations made by cutting edge platforms such as underwater gliders. Specifically, a meridional glider section realized in spring 2016 between the islands of Madeira and Gran Canaria has been used. The temperature, salinity and dissolved oxygen minima have allowed the detection of the AAIW signal north of the Canarian archipelago and significantly westward from its main northward propagation pathway in this region. The results of this work have shown that the encounter of AAIW and MW generates thermohaline intrusions or interleaving layers. It is suggested that double diffusion processes may play a role in the development of these structures, which may be important for water masses mixing and, therefore, in determining the northward spreading boundary of AAIW. The use of the high-resolution glider observations combined with other data products is essential for the study of water masses and dynamics when relevant processes have a wide range of scales.

Double Diffusion in the Arabian Sea during Winter and Spring

Abstract Microstructure measurements from two cruises during winter and spring 2019 documented the importance of double-diffusion processes for small-scale mixing in the upper 400 m of the open-ocean region of the eastern Arabian Sea (EAS) below the mixed layer. The data indicated that shear-driven mixing rates are weak, contributing diapycnal diffusivity (Kρ) of not more than 5.4 × 10−6 m2 s−1 in the EAS. Instead, signatures of double diffusion were strong, with the water column favorable for salt fingers in 70% of the region and favorable for diffusive convection in 2%–3% of the region. Well-defined thermohaline staircases were present in all the profiles in these regions that occupied 20% of the water column. Strong diffusive convection favorable regime occurred in ∼45% of data in the barrier layer region of the southern EAS (SEAS). Comparison of different parameterizations of double diffusion with the measurements of vertical heat diffusivity (KT) found that the Radko and Smith salt fingering scheme and the Kelley diffusive convection scheme best match with the observations. The estimates based on flux law show that the combination of downward heat flux of approximately −3 W m−2 associated with salt fingering in the thermocline region of the EAS and the upward heat flux of ∼5 W m−2 due to diffusive convection in the barrier layer region of the SEAS cools the thermocline.

Direct Measurements of Turbulence in the Upper Western Pacific North Equatorial Current over a 25-h Period.

Measurements of the turbulent kinetic energy dissipation rate (ε) were conducted by a free-fall microstructure profiler in the western Pacific North Equatorial Current (WPNEC) during a continuous period of 25 h, from the sea surface to about 160 m depth. In the mixed layer (ML), ε values were typically on the order of 10−8∼10−7 W kg−1, and an obvious diurnal cycle existed in the upper 40 m of the surface mixing layer. Below the ML, ε was reduced to 10−9∼10−8 W kg−1 with some patches of high ε reaching 10−7.5 W kg−1. The barrier layer was identified in the nighttime with a maximum thickness of 20 m, and it was eroded by the advection of freshwater within the lower part of the isothermal layers associated with an anticyclonic eddy in the afternoon. A simple scaling relevant to shear (S2) instability and stratification (N2) that can predict turbulent dissipation rates in the transition layer, between the well-mixed layer and the thermocline below, was obtained through the scaling . Besides turbulence, double-diffusive processes also contributed to the vertical mixing levels in the upper WPNEC.

Double Diffusion, Shear Instabilities, and Heat Impacts of a Pacific Summer Water Intrusion in the Beaufort Sea

AbstractPacific Summer Water eddies and intrusions transport heat and salt from boundary regions into the western Arctic basin. Here we examine concurrent effects of lateral stirring and vertical mixing using microstructure data collected within a Pacific Summer Water intrusion with a length scale of ∼20 km. This intrusion was characterized by complex thermohaline structure in which warm Pacific Summer Water interleaved in alternating layers ofm thickness with cooler water, due to lateral stirring and intrusive processes. Along interfaces between warm/salty and cold/freshwater masses, the density ratio was favorable to double-diffusive processes. The rate of dissipation of turbulent kinetic energy (ε) was elevated along the interleaving surfaces, with values up to 3 × 10−8W kg−1compared to backgroundεof less than 10−9W kg−1. Based on the distribution ofεas a function of density ratioRρ, we conclude that double-diffusive convection is largely responsible for the elevatedεobserved over the survey. The lateral processes that created the layered thermohaline structure resulted in vertical thermohaline gradients susceptible to double-diffusive convection, resulting in upward vertical heat fluxes. Bulk vertical heat fluxes above the intrusion are estimated in the range of 0.2–1 W m−2, with the localized flux above the uppermost warm layer elevated to 2–10 W m−2. Lateral fluxes are much larger, estimated between 1000 and 5000 W m−2, and set an overall decay rate for the intrusion of 1–5 years.

A note about density staircases in the Gulf of Naples : 20 years of persistent weak salt-fingering layers in a coastal area

This is a short communication about the inter-annual recurring presence at the coastal site in the Gulf of Naples of density staircases visible below the mixed surface layer of the water-column, from the end of summer to the beginning of winter, each year during nearly two decades of survey (2001 to 2020). We repetitively observe sequences from 1 to 4 small vertical staircases structures (~ 3 m thick) in the density profiles (~ Δ0.2 kg.m-3), located between 10 m to 50 m deep below the seasonal mixed layer depth. We interpret these vertical structures as the result of double diffusive processes that could host salt-fingering regime (SF) due to warm salty water parcels overlying on relatively fresher and colder layers. This common feature of the Mediterranean basin (i.e., the thermohaline staircases of the Tyrrhenian sea) may sign here for the lateral intrusions of nearshore water masses. These stably stratified layers are characterized by density ratio Rρ 5.0 to 10.0, slightly higher than the critical range (1.0 - 3.0) generally expected for fully developed salt-fingers. SF mixing, such as parameterized (Zhang et al., 1998), appears to inhibit weakly the effective eddy diffusivity with negative averaged value (~ - 1e-8 m2.s-1). A quasi 5-year cycle is visible in the inter-annual variability of the eddy diffusivity associated to SF, suggesting a decadal modulation of the parameters regulating the SF regime. Even contributing weakly to the turbulent mixing of the area, we hypothesis that SF could influence the seasonal stratification by intensifying the density of deep layers. Downward transfer of salt could have an impact on the nutrient supply for the biological communities, that remains to be determined.

Mixing in the Tyrrhenian Interior Due to Thermohaline Staircases

Thermohaline staircases are a well-known peculiar feature of the Tyrrhenian Sea. Generated by extensive double diffusion processes fueled by lateral intrusions, they are considered to be the most stable of all the staircases that have been detected in the world ocean, seeing their persistence of more than 40 years in the literature. Double diffusion leads to efficient vertical mixing, potentially playing a significant role in guiding the diapycnal mixing. The present study investigates this process of mixing in the case of the Tyrrhenian staircases by calculating the heat and salt fluxes in their gradient zones (interfaces) and the resulting net fluxes in adjacent layers using hydrological profiles collected from 2003 to 2016 at a station in the heart of the basin interior. The staircases favor downward fluxes of heat and salt, and the results of the calculations show that these are greater where temperature and salinity gradients are also high. This condition is more frequently encountered at thin and sharp interfaces, which sometimes appear as substructures of the thicker interfaces of the staircases. These substructures are hot spots where vertical fluxes are further accentuated. Due to the increasing salt and heat content of the Levantine Intermediate Water (LIW) during the observation period, a rise in the values of the fluxes was noted in the portion of the water column below it down to about 1800 m. The data furthermore show that internal gravity waves can modulate the structure of the staircases and very likely contribute to the mixing, too, but the sampling frequency of the time series is too large to permit a proper assessment of these processes. It is shown that, at least during the period of observation, the fluxes due to salt fingers do not reach the bottom layer but remain within the staircases.

Oriented structure design and evaluation of Fe3O4/o-MWCNTs/PVC composite membrane assisted by magnetic field

A composite polyvinyl chloride (PVC) separation membrane blending with magnetic nanoparticles (NPs) was successfully prepared via the non-solvent induced phase separation (NIPS) method assisted by magnetic field. The magnetic Fe3O4/ oxidized multi-walled carbon nanotubes (o-MWCNTs) composite NPs with excellent hydrophilicity and magnetization were synthesized by chemical co-precipitation method. Then the Fe3O4/o-MWCNTs/PVC composite membrane included the Fe3O4/o-MWCNTs/PVC functional layer and PVC support layer was fabricated under the induction of the magnetic field. The effects of the addition of magnetic Fe3O4/o-MWCNTs NPs and its directional migration under magnetic field on the structure and performance of prepared Fe3O4/o-MWCNTs/PVC composite membrane were investigated. The results showed that the addition of hydrophilic magnetic Fe3O4/o-MWCNTs NPs and its directional migration to the membrane surface under the action of magnetic field promoted the process of double diffusion and microphase separation processes, which simultaneously increased the membrane porosity, hydrophilicity, pure water flux and BSA rejection ratio. The prepared Fe3O4/o-MWCNTs/PVC composite membrane exhibited higher pure water flux (400 L·m−2·h−1) and outstanding BSA rejection ratio (89%), which was increased by 60 and 117% compared with the PVC pristine membrane, respectively.

Double-diffusive mixing makes a small contribution to the global ocean circulation

Double-diffusive processes enhance diapycnal mixing of heat and salt in the open ocean. However, observationally based evidence of the effects of double-diffusive mixing on the global ocean circulation is lacking. Here we analyze the occurrence of double-diffusive thermohaline staircases in a dataset containing over 480,000 temperature and salinity profiles from Argo floats and Ice-Tethered Profilers. We show that about 14% of all profiles contains thermohaline staircases that appear clustered in specific regions, with one hitherto unknown cluster overlying the westward flowing waters of the Tasman Leakage. We estimate the combined contribution of double-diffusive fluxes in all thermohaline staircases to the global ocean’s mechanical energy budget as 7.5 GW [0.1 GW; 32.8 GW]. This is small compared to the estimated energy required to maintain the observed ocean stratification of roughly 2 TW. Nevertheless, we suggest that the regional effects, for example near Australia, could be pronounced.

The effect of double diffusion on the dynamics of horizontal turbulent thermohaline jets

Abstract

Hydrographic and Biological Survey of a Surface‐Intensified Anticyclonic Eddy in the Caribbean Sea

AbstractIn the Caribbean Sea, mesoscale anticyclonic ocean eddies impact the local ecosystem by mixing of low salinity river outflow with the nutrient‐rich waters upwelling along the Venezuelan and Colombian coast. To gain insight into the physics and the ecological impact of these anticyclones, we performed a combined hydrographic and biological survey of one Caribbean anticyclone in February 2018. We found that the anticyclone had a radius of 90 km and was surface intensified with the strongest velocities (0.72 m/s) in the upper 150 m of the water column. Below, isopycnal displacements were found down to 700 dbar. The core of the anticyclone entrained waters from the Orinoco River plume and contained slightly elevated chlorophyll concentrations compared to the surroundings. At the edge of the anticyclone we observed higher densities of flying fish but not higher densities of predators like seabirds and cetaceans. Below the surface, a strong temperature inversion (0.98 °C) was present within a barrier layer. In addition, we found thermohaline staircases that originated from double diffusion processes within Tropical Atlantic Central Water.

An axisymmetric non-hydrostatic model for double-diffusive water systems

Abstract. The three-dimensional (3-D) modelling of water systems involving double-diffusive processes is challenging due to the large computation times required to solve the flow and transport of constituents. In 3-D systems that approach axisymmetry around a central location, computation times can be reduced by applying a 2-D axisymmetric model set-up. This article applies the Reynolds-averaged Navier–Stokes equations described in cylindrical coordinates and integrates them to guarantee mass and momentum conservation. The discretized equations are presented in a way that a Cartesian finite-volume model can be easily extended to the developed framework, which is demonstrated by the implementation into a non-hydrostatic free-surface flow model. This model employs temperature- and salinity-dependent densities, molecular diffusivities, and kinematic viscosity. One quantitative case study, based on an analytical solution derived for the radial expansion of a dense water layer, and two qualitative case studies demonstrate a good behaviour of the model for seepage inflows with contrasting salinities and temperatures. Four case studies with respect to double-diffusive processes in a stratified water body demonstrate that turbulent flows are not yet correctly modelled near the interfaces and that an advanced turbulence model is required.

Seasonal variation of the double diffusion processes at the Strait of Hormuz

Profiles of salinity and temperature were measured in the strait of Hormuz (SH) during the winter of 2012, spring and summer of 2013. To investigate the double diffusion (DD) processes, Turner (TU) angle values are calculated in all the stations in the SH. Different TU angle values correspond to salt fingering (SF), diffusive convection (DC) and stable stratification. The distributions of the two forms of DD were plotted vertically along transects in the eastern, central and western part of the SH, and corresponding DD processes were described. The results show that both SF and DC occurred in most part of the study area. Two different water masses (the Indian Ocean surface water and the Persian Gulf water) were evident at the SH, and SF and DC were evident at the interface of two water masses. Due to evaporation, SF occurred in the surface layer of most Stations throughout the year. In the eastern part of the SH, occurrences of DC were more feasible in wintertime. SF was the main phenomenon at the end of hot season. For central part, SF occurred throughout the year in water column. In the western part, water column was stable in summer and DC happened in most part of water column in winter.

Decadal variability of the Turner Angle in the Mediterranean Sea and its implications for double diffusion

The physical reanalysis component of the Mediterranean Forecasting System is used to construct a high-resolution three-dimensional atlas of the Turner Angle. An assessment of the model quality shows a maximum degree of agreement with observations in the water column between 150 and 1000m depth. The mean state of the favourable conditions for double diffusion processes is evaluated and the recent decadal variability is studied in terms of changes in the water mass properties. The results show that approximately 50% of the Mediterranean Sea is favourable to double diffusion processes, from which around 47% is associated with salt fingering. The Tyrrhenian, Ionian and southwestern Mediterranean are the most vulnerable basins to salt fingering, and the strongest processes can occur in the Tyrrhenian deep waters. Diffusive convection is most likely to occur in the Ionian, Aegean and eastern Mediterranean at vertical levels deeper than 1000m. The observed gradual warming and salinification of the Mediterranean after 1997 decreased and increased the possibilities of the occurrence of salt fingers and double diffusive convections, respectively. The climatological atlas that is presented in this paper provides a three-dimensional picture of the regions that are either doubly stable or favourable to double diffusion instability and allows for the characterization of the diffusive properties of the water masses.

The feasibility of thermal and compositional convection in Earth's inner core

Inner core convection, and the corresponding variations in grain size and alignment, has been proposed to explain the complex seismic structure of the inner core, including its anisotropy, lateral variations and the F-layer at the base of the outer core. We develop a parametrized convection model to investigate the possibility of convection in the inner core, focusing on the dominance of the plume mode of convection versus the translation mode. We investigate thermal and compositional convection separately so as to study the end-members of the system. In the thermal case the dominant mode of convection is strongly dependent on the viscosity of the inner core, the magnitude of which is poorly constrained. Furthermore recent estimates of a large core thermal conductivity result in stable thermal stratification, hindering convection. However, an unstable density stratification may arise due to the pressure dependant partition coefficient of certain light elements. We show that this unstable stratification leads to compositionally driven convection, and that inner core translation is likely to be the dominant convective mode due to the low compositional diffusivity. The style of convection resulting from a combination of both thermal and compositional effects is not easy to understand. For reasonable parameter estimates, the stabilizing thermal buoyancy is greater than the destabilizing compositional buoyancy. However we anticipate complex double diffusive processes to occur given the very different thermal and compositional diffusivities.

Tracer Stirring around a Meddy: The Formation of Layering

AbstractThe dynamics of the formation of layering surrounding meddy-like vortex lenses is investigated using primitive equation (PE), quasigeostrophic (QG), and tracer advection models. Recent in situ data inside a meddy confirmed the formation of highly density-compensated layers in temperature and salinity at the periphery of the vortex core. Very high-resolution PE modeling of an idealized meddy showed the formation of realistic layers even in the absence of double-diffusive processes. The strong density compensation observed in the PE model, in good agreement with in situ data, suggests that stirring might be a leading process in the generation of layering. Passive tracer experiments confirmed that the vertical variance cascade in the periphery of the vortex core is triggered by the vertical shear of the azimuthal velocity, resulting in the generation of thin layers. The time evolution of this process down to scales of O(10) m is quantified, and a simple scaling is proposed and shown to describe precisely the thinning down of the layers as a function of the initial tracer column’s horizontal width and the vertical shear of the azimuthal velocity. Nonlinear QG simulations were performed and analyzed for comparison with the work of Hua et al. A step-by-step interpretation of these results on the evolution of layering is proposed in the context of tracer stirring.