Double-diffusive Processes Research Articles

Patterns of Turbulent and Double-Diffusive Phenomena: Observations from a Rapid-Profiling Microconductivity Probe

Abstract Throughout much of the ocean interior, the diapycnal buoyancy flux is maintained by both mechanical and double-diffusive processes. Assessing the relative roles of each is a challenge, particularly in complex coastal environments. During February–March 1995, a repeat-profiling CTD system, equipped with a dual-needle microconductivity probe, was deployed off the central California coast (35°N, 121°W) from the research platform FLIP. The probe’s vertical resolution (8 cm) appears sufficient to resolve the low wavenumbers of the turbulent inertial subrange. This paper presents depth–time maps, spanning 12 days and 100–400 m, of temperature dissipation rate χ, and Cox number Ĉ. High χ and Ĉ values tend to occur in layers, on a variety of spatial scales. Simultaneously, finescale (6.4-m) Richardson number, effective strain rate, and Turner angle are measured. The occurrence of intense microstructure fluctuations is correlated with all three quantities, affirming that both mechanical turbulence and d...

Laboratory studies of double-diffusive sources in closed regions

Various observations of layering and intrusions in the ocean strongly suggest that such structures and motions are produced and driven by horizontal and vertical gradients of temperature and salinity, i.e. by double-diffusive processes. Much of the laboratory work in this field has concentrated on one-dimensional problems, with the neglect of two-dimensional phenomena. The latter are addressed explicitly in the present paper, using the salt–sugar analogue system in a simple geometry, but with the aim of establishing some more widely applicable general principles. Two sources of salt or sugar solution were fed in at opposite ends of a 750 mm long tank, with an overflow tube drawing fluid from a point at the centre of the tank. With two salt sources of different concentrations and densities, a stratification built up through the ‘filling box’ process, and the total density range lay within that of the input solutions. For one salt and one sugar source, a much larger density gradient could be set up, with the range lying outside that of the inputs. The flows were monitored using various experimental techniques: photographs of dye streaks with still and video cameras; a polarimeter to monitor sugar concentration; and the withdrawal of samples for the measurement of density and refractive index, from which the separate contributions of salt and sugar to the density could be calculated.Three related experiments with simple input conditions were particularly instructive, and these will be described first. Both inputs and the withdrawal tube were located at mid-depth, and the tank fluid and the salt and sugar supplies had the same density. The only difference between runs was the initial composition of the solution in the tank: pure salt, pure sugar, and a 50[ratio ]50 mixture of the two. Following an initial transient response which was different in the three experiments, they all tended to the same asymptotic distributions of salt, sugar and density after about 100 h, with a sharp central interface and weakly stratified upper and lower layers. This state corresponded approximately to the one-dimensional ‘rundown’ of a layer of salt solution above sugar solution, with a slightly higher, unstable concentration of salt in the top layer compared to the bottom and a very stable sugar distribution, with a much larger concentration in the bottom layer than in the top one. This distribution cannot be produced by ‘finger’ rundown, and it corresponds to the maximum release of potential energy. It was, however, achieved through the action of many intrusions, which remained active in the dynamic final state, and maintained a strong communication between the two ends of the tank. A comparable experiment was carried out using a tank 1820 mm long. With this larger aspect ratio there was a predominantly local influence of the sources at each end of the tank. Other runs have explored a variety of geometries of the sources and sinks, and the final state has been shown to be sensitive to these boundary conditions.

Dianeutral mixing, transformation and transport of Antarctic Intermediate Water in the South Atlantic Ocean

Recently obtained World Ocean Circulation Experiment (WOCE) sections combined with a specially prepared pre-WOCE South Atlantic data set are used to study the dianeutral (across neutral surface) mixing and transport achieving Antarctic Intermediate Water (AAIW) being transformed to be part of the North Atlantic Deep Water (NADW) return cell. Five neutral surfaces are mapped, encompassing the AAIW from 700 to 1100 db at the subtropical latitudes. Coherent and significant dianeutral upwelling is found in the western boundary near the Brazil coast north of the separation point (about 25°S) between the anticyclonic subtropical and cyclonic south equatorial gyres. The magnitude of dianeutral upwelling transport is 10 -3 Sv (1 Sv=10 6 m 3 s -1) for 1°×1° square area. It is found that the AAIW sources from the southwestern South Atlantic and southwestern Indian Ocean do not rise significantly into the Benguela Current. Instead, they contribute to the NADW return formation by dianeutral upwelling into the South Equatorial Current. In other words, the AAIW sources cannot obtain enough heat/buoyancy to rise until they return to the western boundary region but north of the separation point. The basin-wide integration of dianeutral transport shows net upward transports, ranging from 0.25 to 0.6 Sv, across the lower and upper boundary of AAIW north of 40°S. This suggests that the equatorward AAIW is a slow rising water on a basin average. Given one order of uncertainty in evaluating the along-neutral-surface and dianeutral diffusivities from the assumed values, K=10 3 m 2 s -1 and D=10 -5 m 2 s -1, the integrated dianeutral transport has an error band of about 10–20%. The relatively weak integrated dianeutral upwelling transport compared with AAIW in other oceans implies much stronger lateral advection of AAIW in the South Atlantic. Mapped Turner Angle in diagnosing the double-diffusion processes shows that the salty Central Water can flux salt down to the upper half of AAIW layer through salt-fingering. Therefore, the northward transition of AAIW can gain salt either through along-neutral-surface advection and diffusion or through salt fingering from the Central Water and heat through either along-neutral-surface advection and diffusion or dianeutral upwelling. Cabbeling and thermobaricity are found significant in the Antarctic frontal zone and contribute to dianeutral downwelling with velocity as high as −1.5×10 -7 m s -1. A schematic AAIW circulation in the South Atlantic suggests that dianeutral mixing plays an essential role in transforming AAIW into NADW return formation.

Dead Sea water trajectories in the T–S space

The Dead Sea water column is composed, to a first approximation, of two water bodies: the deep waters, constituting most of the lake's volume, and a shallow upper layer a few meters thick. The temperature and salinity profiles can both be either stabilizing or destabilizing, depending on the regime and the season; if salinity is destabilizing, and double-diffusive processes are attained, the two water bodies mix at a much faster rate than normal turbulent diffusion can account for. The trajectories of the Dead Sea brines since 1977 belong to one of three different categories: upper layer under a meromictic regime, upper layer under a holomictic regime, and lower layer under a holomictic regime. The lower layer during the meromictic regime of 1979– 82 remained constant in its properties and its trajectory is thus represented by one single point.

Interpreting Conductivity Microstructure: Estimating the Temperature Variance Dissipation Rate

A simple model of the conductivity gradient spectrum is developed and used to interpret oceanic conductivity microstructure observations. A principal goal is to estimate the correction factor E for inferring the temperature variance dissipation rate χr′, over a wide range of temperature and salinity gradients. The correction factor is defined as E≡χc′/χr′, where χc′, is the temperature variance dissipation rate inferred directly by integrating the measured conductivity spectrum. Three spectral forms of temperature and salinity fluctuations are used to model E: the Batchelor spectrum, a white dissipation spectrum, and a growing salt finger spectrum. Model results show that E depends on 1) the local temperature-salinity (T−S) relation m=ds/dT, 2) the spatial response function of the conductivity probe, 3) the degree of T−S correlation at high wavenumbers, 4) the forms of temperature and salinity spectra, and 5) the kinetic energy dissipation rate ε. Results also indicate that E can diverge significantly from unity, particularly when m is negative, ε is large, and temperature and salinity gradients are stable. For example. when m=−0.3 psu°C−1 and ε=10−6m2 s−3,E is in the range 0.05–0.6, depending on the spectral form and T−S correlation. For growing salt finger spectra, E is in the range 1.2–2,4 over the range of density ratio 1.2≤Rρ≤2.0, based on parameters from the area of the North Atlantic Tracer Release Experiment (NATRE). A general method is outlined for determining E from observations of conductivity microstructure and is applied to a dataset obtained during NATRE using the Cartesian diver profiler. Observed profiles exhibit high variability in T, S, m, and conductivity microstructure on vertical scales of a few meters. Because conductivity microstructure. at the NATRE site can result from either shear-driven turbulence or double-diffusive processes, a wide variety of spectral shapes is possible. These physical uncertainties lead to alternative possible estimates of E, hence χr′, which vary by factors of 10–20 for a few profile segments. However, χr′, is more typically constrained to within a factor of 2.

Stability dependent parameterisations of vertical mixing in ocean general circulation models

Parameterisations of mixing induced through shear instability, internal wave breaking, and double diffusion are investigated in simulations of ocean climate using a global ocean general circulation model (OGCM). Focus is placed on the sensitivity of the large scale circulation, water mass formation and transport of heat as measures of the model's ability to represent current climate. The model resolution is typical of OGCMs being coupled to atmospheric. GCMs in climate models and the parameterisations investigated are all computationally inexpensive enough to allow for integrations on long time scales. Under the assumption of constant vertical eddy coefficients (the control case), the model climatology displays acceptable values of North Atlantic Deep Water formation, Antarctic Circumpolar Current (ACC) transport, and Indonesian through-flow but an excessively deep and diffuse pycnocline structure with weak stratification in the deep ocean. It is found that various circulation and water mass properties are sensitive to the choice of parameterisation of vertical mixing and that determining a scheme which works satisfactorily over all regions (tropical, mid-latitude, and polar) of the domain is not straightforward. Parameterisations of internal wave breaking or upper ocean shear instability lead to some improvements in the model water mass formation. ACC and poleward heat transport when compared to the control case whereas parameterisations of double diffusive processes did not. Based on these and other results, various recommendations are made for mixing parameterisations in ocean climate models.

Isopycnal and Diapycnal Mixing at the Cape Verde Frontal Zone

The Cape Verde Frontal Zone separates the North and the South Atlantic Central Waters in the eastern North Atlantic. It also represents the boundary between the ventilated subtropical gyre and the quasi-stagnant shadow zone in the southeast. The thermohaline front is nearly compensated with respect to density, and density parameters RP, suggest the existence of double-diffusive processes. Datasets from three cruises to the region, approximately one year apart each, are used to determine the effects of double-diffusive diapycnal versus isopycnal mixing. For this purpose results from the usual temperature-salinity analysis assuming isopycnal mixing are compared to results from a multiparameter analysis where nutrient and oxygen data are also used. Significant diapycnal fluxes are found in the frontal zone between 200 and 300 m, with water mass contents being changed by more than 20% through diapycnal mixing. The associated buoyancy fluxes have a similar magnitude as surface fluxes in the area and thus represent an important contribution to the vertical balances of heat and salt.

Mixing of shelf, slope and Gulf Stream water over the continental slope of the Middle Atlantic Bight

A combination of water masses was observed over the continental slope between Cape Hatteras and Hudson Canyon following the passage of a Gulf Stream meander. It was largely made up of fluid discharged from the Gulf Stream in the wake of the meander and also contained intrusions of Middle Atlantic Bight (MAB) shelf water and slope water. Its most prominent dynamical feature was an anticyclonic eddy that had an initial diameter of about 100 km but contained relatively weak currents, not greater than 30 cm s −1 in magnitude. Discharged Gulf Stream water made up the eddy's core, and a band of entrained shelf water circulated at its margin. This band was connected with another entrained shelf water band that flowed along the northern margin of the Gulf Stream. Transport of the shelf water at the edge of the eddy was estimated to be 1.3 × 10 5 m 3 s −1, which is comparable with the estimated alongshore transport of water over the MAB shelf. Vigorous mixing of both shelf water bands with surrounding discharged Gulf Stream water is indicated by the large differences of the latter's T/S properties from those found within the Gulf Stream. These differences were used to estimate salt fluxes into the shelf water band at the edge of the anticyclonic eddy, with results in the range of 1.9–6.6 × 10 −6 g salt cm −2 s −2. Density ratios and Richardson numbers determined from hydrographic data suggest that these salt fluxes were primarily the result of mixing by double diffusive processes, and that shear-induced turbulence combined with double diffusion to effect vertical mixing at the margins of the shelf water band next to the Gulf Stream.

Effect of Rϱ on double diffusive interleaving

The role of the density ratio during double diffusive interleaving is investigated experimentally. A sharp vertical front is created by lifting a barrier separating two stratified compartments of different T- S composition but similar density. The environment is either stably stratified in both components or double diffusively stratified in the diffusive sense. Interleaving layers driven entirely by double diffusive processes start to form and to propagate horizontally. The observed thickness of the intrusions agrees well with the predicted vertical scale of Ruddick and Turner [ Deep-Sea Research, 26, 903–913 (1979)] when the stratification is doubly stable, and is found to be smaller in the diffusive case, as can be predicted from Linden's [ Deep-Sea Research, 23, 895–908 (1976)] formula. The cross-frontal flux is independent of the stability of the environment except when the environment is double diffusively stratified in the diffusive sense and the gradient of the unstable component is at least 66% that of the stable component. In this latter case the cross-frontal flux is larger than for a double stable environment, as an extra source of potential energy is already present in the unstably stratified component. A parametrization of the cross-frontal flux is given in terms of the vertical finger flux. These results are applied to oceanic Meddies and to the survival of the core region of a Meddy against lateral intrusions.

Anomalous sound propagation influenced by Mediterranean water

Sound propagation in the Northeast Atlantic is strongly influenced by the outflow of saline water from the Mediterranean. The resulting sound profiles are characterized by a double channel structure separated by an intermediate sound‐speed maximum. A propagation experiment was conducted in 1988 in the Tage Abyssal plain over a 280‐km path, with source and receiver placed in the deep channel. Supporting hydrographic data indicated that although the sound‐speed perturbations with respect to some mean were not very large, significant variability combined with the particular profile shape gave rise to unusual propagation conditions. The problem of how to characterize the overall shape of the profile, the variability of the depth and magnitude of the intermediate maximum, and the presence of strong fine structure is considered in particular. Angle depth and angle time of arrival plots are useful as characterizations of the channel; it is shown how they are related to the phase integral. Range variability of the intermediate sound‐speed maximum can lead to leaking from the deep to the shallow channel. In those conditions it is illusory to attempt to make range‐dependent predictions of arrivals. Even range‐independent predictions can be unstable. The fine structure is related to internal waves and to the double diffusive processes evident in the area. An attempt to quantify them is made and the effect of various degrees of smoothing on the profiles is evaluated. A tomography experiment is presently being conducted in the Bay of Biscay by SHOM and IFREMER. Some comments on the feasibility of tomography in this region will be made.

The formation of the doubly stable stratification in the Mediterranean Outflow

The Mediterranean Outflow as it exits from the Strait of Gibraltar can be seen as a gravity current flowing down the slope and mixing with Atlantic Water until it reaches its own density level. Typical salinity and temperature profiles through the core region of a Meddy show that the bottom of the core is colder and saltier than the top, leading to a stably stratified core with respect to double-diffusive processes. The bottom of the core is also more enriched with Mediterranean Water than the top, and this behaviour can be explained by a reduced mixing of the source water with the environment close to the rigid bottom. Although the mechanism involved is different from the actual case, we have successfully produced these doubly stable gradient in some laboratory experiments which incorporate the “filling-box” mechanism. Salt and sugar were used as laboratory analogues of temperature and salt, respectively. The laboratory experiments consisted of supplying a dense input fluid at the surface of a linearly salt stratified environment. We suggest that r eq, the ratio of the initial volume flux at the source to the volume flux at the equilibrium level, is an important parameter, and that in our experiments this must be in general smaller than 0.1 in order to produce a doubly stable region of salt and sugar. The most relevant experiments had a mixed sugar/salt input which is the analogue of the Mediterranean Outflow as it mixes with Atlantic Water outside the Strait of Gibraltar.

The stability chart of parallel shear flows with double diffusive processes—approximate derivation by a first-order Galerkin method

The stability of an infinite fluid layer subject to arbitrary horizontal shear flow and to arbitrary vertical temperature and salinity distributions is considered. Linear stability analysis is used to investigate the stability under general three-dimensional (3-D) perturbations. A first approximation Galerkin method is used to derive the characteristic equation ; then conditions for stability are obtained and the marginal stability lines can be found. The method is applied in an example with a parabolic velocity distribution and linear temperature and salinity profiles. The stability chart in the plane of the Rayleigh numbers is found to include various stable and unstable regions, depending on the Reynolds number. The results obtained here are compared with previous results derived by a general Galerkin method. A region is found where the flow in stable for two-dimensional (2-D) transverse perturbations but unstable with respect to general 3-D disturbances.

Double Diffusion and the Distribution of the Density Ratio in the Mediterranean Waterfront Southeast of the Azores

Abstract Temperture and salinity (T–S) finestructure on vertical scales of 10 db and larger is examined in a 500 by 500 km grid located southeast of the Azores in the North Atlantic. The convergence of several water masses dominated by the Mediterranean Water (MW) at mid-depth (1000 m) leads to variety of T–S finestructure which is unstable to double diffusive processes. By forming histograms of the density ratio Rρ, a fundamental parameter in controlling double diffusive processes, it is found that 71% of the volume is unstable to salt fingering while only 5% is unstable to diffusive layering, the other double diffusive instability. In about 24% of the volume, Rρ is less than 2 in the salt fingering sense and at these low values salt fingers grow rapidly. This suggests that salt fingering may be an important diapycnal mixing process in much of the region. Two primary salt fingering regions are found: a near-surface region from about 100 to 500 db with a modal Rρ of 2.0 and a deeper region from about 1000...

Stratification background conditions for development of double-diffusion processes in the North Pacific

Based on mean multiyear temperature and salinity data structural zones and layers are isolated. Within their limits there are favourable conditions for the development of processes such as layer convection and salt fingers. It is shown that distribution of their parameters is conditioned by location of intermediate water mass boundaries and front interfaces. Stability of the density ratio valueRϱ for various areas is revealed. The obtained results are in good agreement with STD=sounding data. Compared are profiles ofRϱ and local estimates of heat and salt fluxes for various structural zones.

Fine structures in the seasonal thermocline during JASIN

Fine structures and their generating processes observed in the seasonal thermocline of the northeast Atlantic during JASIN were analysed. A comparison of the temperature and density fields as well as the stratification parameters showed the dominance of vertical processes, particularly internal wave strain or turbulent mixing. Intrusive and double-diffusive processes were seldom observed. In comparison to numerous intrusions in the main thermocline of the JASIN area, the vertical scales of the fine structure in the seasonal thermocline were smaller. The ratio of the vertical to the horizontal scales was 1:100. To discriminate between reversible and irreversible fine structure, data sets were compared with different theoretical models. The measurements from R.V. Meteor along an oceanic front showed numerous irreversible fine structures, while the observations of R.V. Planet outside the front showed more reversible structures.

The stability chart of double-diffusive processes with parallel flows ? construction by the Galerkin and continuation methods

The stability of an infinite fluid layer subject to arbitrary horizontal flow and to arbitrary vertical temperature and salinity distributions is considered. Linear stability analysis is used to investigate the stability under general three-dimensional perturbations.

Double-diffusive convection in partially molten silicate systems: Its role during magma production and in magma chambers

In this paper, two problems involving double-diffusive convection in partially molten, silicate systems are investigated mathematically. The first problem concerns the role of double-diffusive convection during magma production. The systems Di-An and Di-An-Ab are used as examples. The calculations show that, in a growing layer of partial melt, heated from below, the thickness of the layer at which convection initiates depends strongly upon the bulk composition. For example, assuming reasonable values of the physical parameters, in a Di-rich system, convection will occur when the layer is ∼ 800 m thick, whereas in an An-rich system convection, driven by the destabilizing compositional gradient, will begin in a layer only centimeters thick. A qualitative investigation of the Di-An-Ab system suggests similar results, depending upon whether the bulk composition lies in the diopside or the plagioclase field, respectively. Moreover, if one considers a two-component, one-dimensional diapir of Di-An, an examination of the phase diagram indicates that vigorous compositional convection will occur in the partially molten diapir as it ascends, regardless of whether the bulk composition is Di-rich or An-rich. These results suggest that during magma production, convective processes will tend to homogenize the melt before it segregates from the source zone; however, the vigor of mixing is dependent upon the bulk composition of the source, among several other factors. Models of melt segregation should be modified to include double-diffusive processes. The second problem concerns the structure of a porous boundary layer that forms as a result of side-wall crystallization in a convecting magma chamber. An examination of the steady-state boundary layer equations for flow through a porous medium shows that the boundary layer structure may be of two types. If the residual melt fraction, upon crystallization at the wall, has negative compositional buoyancy, or if the negative thermal buoyancy at the cold wall exceeds the positive compositional buoyancy of the residual melt, the flow across the entire boundary layer will be downward. If the residual melt fraction has negative compositional buoyancy, the magma chamber will become stratified as a result of accumulation of a layer of dense, cold liquid on the floor; whereas if the melt fraction has positive compositional buoyancy, the boundary layer fluid will tend to be remixed into the interior of the magma chamber. If, however, the positive compositional buoyancy exceeds the negative thermal buoyancy, counterflowing boundary layers will occur; and the compositionally buoyant liquid will tend to be fractionated towards the top of the magma chamber. An examination of the Di-An and Di-An-Ab systems suggests that both types of boundary layer structures may occur in magma chambers. An approximate calculation of the rate of fractionation suggests that, for a range of parameters that may be representative of basaltic magmas, the flow in the compositional boundary layer may transport ∼ 10 −3 km 3/yr of low-density liquid to the top of the magma chamber.

The stability chart of parallel shear flows with double-diffusive processes ? general properties

The stability of an infinite fluid layer is considered, subject to horizontal flow and arbitrary initial vertical temperature and salinity distributions. Linear stability analysis is applied, using three-dimensional perturbations. A method is outlined for the construction of a general stability chart; parts of the chart are marginal-stability lines obtained by using the Squire theorem, where disturbances in the flow direction are the most unstable; necessary conditions for the theorem to be valid are developed. These conditions are shown to be sufficient in certain cases. A technique is presented to obtain the stability boundary even when these conditions are not satisfied. The results show that an increase in the Reynolds number cannot increase the stability domain.

Time and space scales of vertical mixing and advection of phytoplankton in the upper ocean

The dependence of phytoplankton photosynthesis on light intensity may be altered by the range and frequency of variations in light intensity recently experienced by the organisms. A major source of the fluctuations in light intensity experienced by phytoplankton in the upper ocean is vertical motion. We estimate time and space scales for vertical displacements of phytoplankton caused by turbulent mixing, internal waves, Langmuir circulations, and double diffusive processes. In the surface layer, depending on windspeed, current shear and stratification, we find that time scales for cycling of phytoplankton by turbulent eddies and mixing vary from about 0.5 h to hundreds of hours for vertical displacements of the order of 10 m. In the seasonal thermocline, turbulent diffusive time scales for displacements as small as several meters are weeks to months, whereas similar displacements by internal waves occur over periods of several minutes to several hours, according to the strength of the density stratification, and are then dominant. Langmuir cells seem to scale as the large turbulent eddies and need not be treated separately, and double diffusive processes seem to be of minor importance. The formulation used here of a vertical turbulent diffusion coefficient Kz as a function of observable quantities—ε the rate of dissipation of turbulent kinetic energy, arid N the local buoyancy frequency—should also be useful for estimating vertical fluxes of nutrients. In addition, this formulation is reversible in time and can be used to estimate the recent depth and light history of phytoplankton taken from the upper ocean.

Water-Mass Distributions at Intermediate Layers off the Somali Coast during the Onset of the Southwest Monsoon, 1979

Hydrographic observations at intermediate depth in the Somali Basin have been made during and after the transition from the northeast monsoon to the southwest monsoon, 1979. The data are discussed in relation to measurements of absolute currents during the same time period. Earlier water-mass identification by Warren et al. (1966) is confirmed and extended by introducing a well-defined Equatorial Water Mass. The distribution of water masses and its temporal evolution with the changing monsoonal wind field is analyzed on three different spatial scales. Equatorial and near-coastal undercurrents are an important factor in the large-scale redistribution of water masses in the intermediate layers. Cross-equatorial exchange of water, in particular highly saline Red Sea water, is largely confined to a narrow region off the East African Coast. No obvious response of these currents to the onset of the southwest monsoon is detected. In the mesoscale range anticyclonic subsurface eddies containing Equatorial Water are observed in the northern and southern Somali Basin. A possible formation mechanism of these features through equatorial westward subsurface jets in discussed. Double-diffusive intrusions with vertical scales of over 100 m are observed near strong fronts. Their characteristics compare well with theoretical predictions (Ruddick and Turner, 1979). A stability analysis for the upper and lower boundaries of these intrusions shows significantly that double-diffusive processes are acting also on these intrusions themselves.