The Diffusive Regime in Double Diffusive Convection: Observational Aspects

 
 
Emin Özsoy
Institute of Marine Sciences, Middle East Technical University,
P. O. Box 28, Erdemli, Içel 33731 Turkey. e-mail: ozsoy@ims.metu.edu.tr
 
 

Introduction

In this section, a brief survey is made of the observations concerning the diffusive regime of double-diffusive convection, expected to occur when a destabilizing temperature gradient competes with a statically stable salinity gradient (e.g. when both temperature and salinity increase with depth). Laboratory convective layers under similar conditions of a salinity gradient heated from below have been studied extensively (e.g., Turner, 1968; Huppert and Linden, 1979; Fernando, 1987), and many oceanographic and limnological examples are known (Turner, 1969; Fernando, 1989). Double diffusive convection is often triggered by horizontal contrasts (e.g. boundaries, or fronts) and by buoyancy sources (e.g. sources/sinks of heat or salt) in stratified environments with two diffusing properties, leading to interleaving layers characterized by a series of alternating diffusive / fingering interfaces (Turner, 1973, 1978; Huppert and Turner, 1980; Tsinober et al., 1983; Tanny and Tsinober, 1988; Jeevaraj and Imberger, 1991).

Double diffusive convection is often studied for its own sake, i.e. as a curiousity of fluid dynamics, applied to specific conditions. It has long been debated whether the small scale double diffusion process can have significant impacts on the large scale properties or dynamics of the marine system. In particular, one would like to answer the following questions through more extensive observations and theoretical / experimental insights: what is the overall significance of double-diffusive convection in transporting mass, momentum, energy and other properties in the ocean ? Does it modify the time scales of motion, or the structure of the thermohaline circulation in specific ocean basins ? Can it modify large scale oceanic processes or is it only important for isolated features such as fronts, eddies, etc. ? What is its relative contribution to mixing, as compared to turbulence ? Does it modify large scale mixing / water mass formation processes ? How does double-diffusive convection modify effective coefficients of diffusivity ? How is its effects supplemented in the presence of shear and turbulence ?

A description of observational evidence of diffusive contribution to meso-scale and basin-scale processes is given based on frontline examples.
 

The Black Sea

The Black Sea (see reviews by Özsoy and Ünlüata, 1997 and 1998) is the largest land-locked basin of the world with a positive surface water budget. Its effective isolation, despite the existence of the two-way exchange through the Turkish Straits, has led to stagnant conditions and anoxia in its deep waters, the average age of water increasing to more than two thousand years near the bottom (Östlund, 1974; Grasshoff, 1975). The warm and saline Mediterranean Water is the historical source of the deep waters, evolving since the end of the last ice age (more than 10,000 years ago), when it first penetrated into the fresh water lake known today as Black Sea (Stanley and Blanpied, 1980).

The Black Sea is probably one of the best places to observe the large scale effects of double diffusive convection, where it occurs in connection with (i) the warm, saline Mediterranean water intruding from the Bosphorus (ii) a diffusive interface capping the bottom convection layer, and (iii) vertical fluxes in the deep waters.

The historical evolution of the deep waters has resulted in a peculiar distribution of the 'density ratio' $R_\rho = (\beta dS/dz)/(\alphadT/dz$ such that the entire water column is formally in the diffusive instability range, changing from minimum values ( $R_\rho > 2$) at the top (below the mixed layer) and bottom (above the bottom convective layer), to marginally stable values ( $R_\rho \to \infty$) at a depth of $\sim 500 m$ (Özsoy et al 1993).

The dense bottom water of Mediterranean origin (modified in the Turkish Straits and across the continental shelf) cascading down the continental slope degenerates into discrete layers (depth range 100-500m) of double diffusive convection penetrating into the interior (Özsoy et al., 1993, Özsoy and Besiktepe, 1995). The unstable interior is expected to enhance the convection (e.g. Turner, 1978), in addition to the effects of sidewall buoyancy source (heat and salt) introduced into the stratified environment (e.g. Tsinober et al., 1983; Tanny and Tsinober, 1988).

Boundary mixing (e.g. Garrett, 1990; Woods, 1991), in this case driven by the double diffusive convection (Özsoy et al., 1993, Özsoy and Besiktepe, 1995), appears to be the dominant ventilation mechanism across the permanent halocline of the Black Sea, as it has been amply demonstrated by transport of shelf-derived materials, including dissolved nutrients, Chernobyl tracers and inorganic particulates (Buesseler et al., 1991; Buesseler and Livingston, 1997, Codispoti et al., 1991; Özsoy et al., 1991, 1993). The relatively rapid penetration of tracers across the halocline, contrasting with almost none in the deep water has been confirmed by Tritium (Top et al., 1991, Top, 1997, Rank et al., 1997) and Carbon-14 (Östlund, 1974, 1986) measurements. Plume parameterization of vertical mixing in general circulation models (Stanev and Staneva, 1996) has significantly improved the simulation of ventilation and tracer distributions in the Black Sea.

A bottom convection layer, with a thickness of $\sim 450m$ forms the largest known example in the world ocean. A destabilizing geothermal heat flux of $\sim 40mW/m^2$ at the bottom acts against an otherwise stable salinity stratification. The transport between the bottom convective layer and the overlying waters occurs through a single diffusive interface. The observed features and the parametric setting suggest that the convective layer is far from the initial phase of growth proportional to t1/2 (e.g., Turner, 1968; Huppert and Linden, 1979, Fernando, 1987; Fernando, 1989), and corresponds with the long time limit of the 'low stability regime' of Fernando (1987, 1989) and Fernando and Ching (1991), in which the interfacial entrainment, and therefore layer growth become negligibly small (Özsoy et al., 1991; Özsoy and Besiktepe, 1995). The heat flux at the the stable Black Sea interface ( $Ri_\star \simeq 600$), estimated from the Huppert and Linden (1971) and Fernando (1989) models were about 5-8 times larger than the geothermal heat flux from the bottom, since these models typically overestimate fluxes when the Richardson number $Ri_\star = \Delta b h_s / w_*^2 >240$ (Fernando, 1989, $\Delta b$ is the buoyancy step, hs the layer thickness and ws a vertical velocity scale for convection), and most probably do not apply in the long time limit not adequately investigated in the laboratory studies on which they are based.

The bottom convective layer is expected to have a similar age as the deep waters (few thousands of years). The observed homogenisation of water properties vertically and across the basin inside the convective layer is expected to occur in about 40 years, which may also have bearing on the homogeneity in deposition/diagenesis of bottom sediments (Özsoy et al., 1991; Özsoy and Besiktepe, 1995).

Based on comparison of flux ratios above the diffusive interface and the water column, double diffusion is most likely to be the main vertical transport mode for heat and salt in the deep waters extending from the lower part of the pynocline to the diffusive interface above the bottom convective layer (Özsoy et al., 1991; Murray et al., 1991). The observed 'S-shape' of the $\theta-S$ curves in the Black Sea deep waters also leads one to expect that it has been generated by the different diffusivities of salt and heat (Mamayev, 1975, 1995).
 

Polar Seas

Double diffusive staircases have frequently been observed at polar seas, where cold, low salinity surface waters affected by surface cooling and fresh water from rivers and glacial ice, overlying warmer more saline waters entering from other ocean basins create a suitable environment. Because some parts of these ice covered seas are low-energy environments, especially at the central gyre areas, double diffusion can play a significant role compared to shear and turbulence effects, especially in the internal redistribution of heat and other properties.

Foster and Carmack (1976) have found staircase structures in the Weddell Sea in the Antarctic, where both double diffusive and cabelling intabilities appeared to be important. Muench, et al. (1990) also found similar, unstable staircases ( $R_\rho < 2$ in both papers), and also showed that the heat transported vertically by the deeper, 'Type B' staircases below the pycnocline ( $\sim 15 W/m^2$) was close to the independent estimates of heat transported ( $\sim 18 W/m^2$) through the pycnocline by budget considerations. Robertson, et al. (1995) observed step structures during part of their measurements from a drifting ice station in Weddell Sea, and estimated heat fluxes of 2 W/m2 at the permanent pycnocline, which were larger than the contribution of shear instabilities (1 W/m2), but still much less than the 19 W/m2 required by the gyre scale heat budget.

Although diffusive staircases have also been observed in the Arctic Sea (Padman and Dillon, 1987, 1989), the estimated fluxes were much smaller than the Antarctic, on the order of 0.1 W/m2, which was not sufficient to explain basin average fluxes of heat between waters of Arctic and Atlantic origin. Other processes such as benthic and boundary stirring were invoked. During a survey of the central Arctic Sea in summer 1996, Muench, et al. (1997) found steplike features of up to 100m in thickness, conserving their features for more than a distance of 500km, yet containing water of ages differing by a few years.
 

'Saline' Lakes

In some lakes, total dissolved constitute the 'salinity', and salt stratification can be sufficient to stabilize the lake against the action of bottom heating. An example of such a lake is Lake Vanda in Antarctica (Fernando, 1989, and references cited therein). Newman (1976) found a similar situation in Lake Kivu, where he also observed double diffusive steps. The estimated heat flux ( $\sim 1 W/m^2$) was an order of magnitude larger than the bottom heat flux from sediments, and is conjectured to balance with other possible sources of heat, from bottom hot springs or bacterial activity. The $R_\rho$ values were in the range 1.3-2.1, suggesting unstable layers, while the estimated and observed layer thickness values were close to each other.
 

Brine 'Lakes'

The other example of diffusive interfaces occurs at small pockets of saline water trapped near the ocean bottom in the form of 'trenches' or 'lakes', where there is also a supply of geothermal heat either from sediments or hot vents. Swallow and Crease (1965) found sharp interfaces bounding layers of hot salty water at the bottom of the Red Sea. Turner (1969) calculated the geothermal heat flux to be 215 mW/m2 and found interfacial $R_\rho$ values in the range of 9-25. The average age of the water in the brine layer was estimated to be 30 years. Brine 'lakes' were also found in the deep eastern Mediterranean basin by Boldrin and Rabitti (1990), where the density ratio was very high, $R_\rho \simeq 600$, and the interfacial heat flux was estimated to be of the same order as the geothermal flux of 46 mW/m2. Both these estimates and isotopic composition (Stenni and Longinelli, 1990) suggested that the water in the bottom layer was of 'fossil' origin, probably developed about 4500 years or earlier. Similar features were found in other Eastern Mediterranean brine lakes (MEDRIFF Consortium, 1995), which also showed the recent invasion of a new dense water mass of Aegean Sea origin (Roether, 1996). The warmer more saline deep waters after the renewal event are warmer but less saline than the fossil water below the interface, making the interface stable. It appears that brine lakes can memorize the deep water history of a basin, if the information they hold can be correctly interpreted.

McDougall (1984) investigated brine layers capped by a double diffusive interface and supplied by hot saline plumes in a depression, as in the case of the Red Sea brine layers, and found the system to converge to a stablle fixed point in T-S space, which may explain their stationary character.
 

REFERENCES

Boldrin, A. and S. Rabitti, 1990. Hydrography of the Brines in the Bannock and Tyro Anoxic Basins (eastern Mediterranean), Marine Chemistry, 31, 21-33.

Buesseler, K. O., Livingston, H. D., and S. Casso, 1991. Mixing Between Oxic and Anoxic Waters of the Black Sea as Traced by Chernobyl Cesium Isotopes, Deep-Sea Res., 38, S725 - S745.

Buesseler, K. O. and H. D. Livingston, 1997. Time-Series Profiles of 134Cs, 137Cs and 90Sr in the Black Sea, in: E. Özsoy and A. Mikaelyan (editors), Sensitivity to Change: Black Sea, Baltic Sea and North Sea, NATO ASI Series, Kluwer Academic Publishers.

Fernando, H. J. S., 1987. The Formation of Layered Structure when a Stable Salinity Gradient is Heated from Below, J. Fluid Mech., 182, 525-541.

Fernando, H. J. S., 1989. Oceanographic Implications of Laboratory Experiments on Diffusive Interfaces, J. Phys. Oceanogr., 19, 1707-1715.

Fernando, H. J. S., and C. Y. Ching, An Experimental Study on Thermohaline Staircases, 1991. In: Double Diffusion in Oceanography, Proceedings of a Meeting, September 26-29, 1989, R. W. Schmitt (editor), Technical Report, Woods Hole Oceanographic Institution, 141-149.

Foster, T. D. and E. C. Carmack, 1976. Temperature and Salinity Structure in the Weddell Sea, J. Phys. Oceanogr., 6, 36-44.

Garrett, C., 1990. The Role of Secondary Circulation in Boundary Mixing, J. Geophys. Res., 95, 3181-3188.

Grasshoff, K., 1975. The Hydrochemistry of Landlocked Basins and Fjords, In: Chemical Oceanography, J. P. Riley and G. Skirrow (editors), Academic Press, New York, 2, 647 pp.

Huppert, H. E. and P. F. Linden, 1979. On Heating a Salinity Gradient from Below, J. Fluid Mech., 95, 431-464.

Huppert, H. E. and J. S. Turner, 1980. Ice Blocks Melting Into a Salinity Gradient, J. Fluid Mech., 100, 367-384.

Mamayev, O. I., 1975. Temperature - Salinity Analysis of World Ocean Waters, Elsevier, Amsterdam, 374 pp.

Mamayev, O. I., 1995. The Black Sea: The Double-Diffusive Process in the light of the Analytical Theory of T,S Curves, Oceanology, 35(2), 153-160.

McDougall, T. J. 1984. Fluid Dynamical Implications for Massive Sulphide Deposits of Hot Saline Fluid Flowing into a Submarine Depression from Below, Deep-Sea Res., 31, 145-170.

MEDRIFF Consortium, 1995. Three Brine Lakes Discovered in the Seafloor of the Eastern Mediterranean, EOS, 76(33), 313-318.

Muench, R. D. H. J. S. Fernando and G. R. Stegen, 1990. Temperature and Salinity Staircases in the Northwestern Weddell Sea, J. Phys. Oceanogr., 20, 295-306.

Muench, R. D., B. Rudels, G. Bjork and U. Schauer, 1997. Basin Scale Double-Diffusive Layering in the Arctic Ocean, Abstracts booklet, 'Marine Turbulence Revisited', 29th International Liege Colloquium on Ocean Hydrodynamics, Liege, May 5-9, 1997.

Murray, J. W., Z. Top and E. Özsoy, 1991. Hydrographic Properties and Ventilation of the Black Sea, Deep-Sea Res., 38, Suppl. 2, S663-S689.

Newman, F. C., 1976. Temperature Steps in Lake Kivvu: A Bottom Heated Saline Lake, J. Phys. Oceanogr., 6, 157-163.

Östlund, H. G., 1974. Expedition Odysseus 65: Radiocarbon Age of Black Sea Water, In: The Black Sea - Geology, Chemistry and Biology, E. T. Degens and D. Ross (editors), The American Association of Petroleum Geologists, Memoir No. 20.

Östlund, H. G. and D. Dyrssen, 1986. Renewal Rates of the Black Sea Deep Water, In: The Chemical and Physical Oceanography of the Black Sea, Univ. of Göteborg, Rep. on the Chemistry of the Sea XXXIII. Presented in the Meeting on the Chemical and Physical Oceanography of the Black Sea, Göteborg, Sweden, June 1986.

Özsoy E., Z. Top, G. White and J. W. Murray, 1991. Double Diffusive Intrusions, Mixing and Deep Convective Processes in the Black Sea, In: Black Sea Oceanography, NATO ASI series C - Vol. 351, E. zdar and J. W. Murray (editors), Kluwer Academic Publishers, 17-42.

Özsoy, E., Ü. Ünlüata, and Z. Top, 1993. The Mediterranean Water Evolution, Material Transport by Double Diffusive Intrusrions, and Interior Mixing in the Black Sea, Prog. Oceanogr., 31, 275-320.

Özsoy, E. and S. Besiktepe, 1995. Sources of Double Diffusive Convection and Impacts on Mixing in the Black Sea, pp. 261-274, in: Brandt, A. and H. J. S. Fernando (editors), Double-Diffusive Convection, Geophysical Monograph 94, American Geophysical Union, 334 pp.

Özsoy, E. and Ü. Ünlüata (1997). Oceanography of the Black Sea: A Review of Some Recent Results, Earth Sci. Rev., 42(4), 231-272.

Özsoy, E. and Ü. Ünlüata (1998). The Black Sea, in: A. R. Robinson and K. Brink (editors), The Sea: The Global Coastal Ocean: Regional Studies and Syntheses, 11, John Wiley and Sons, New York, pp. 889-914.

Padman, L. and T. M. Dillon, 1987. Vertical Heat Fluxes through the Beaufort Sea Thermahaline Staircase, J. Geophys. Res., 92, 10799-10806.

Padman, L. and T. M. Dillon, 1989. Thermal Microstructure and internal Waves in the Canada Basin Diffusive Staircase, Deep-Sea Res., 36, 531-542.

Robertson, R., L. Padman, and M. Levine, 1995. Fine Structure, microstructure, and Vertical Mixing Processes in the Upper Ocean in the Western Wedell Sea, J. Geophys. Res., 100, 18517-18535.

Stanley, D. J., and C. Blanpied, 1980. Late Quaternary Water Exchange between the Eastern Mediterranean and the Black Sea', Nature, 285, 537-541.

Stenni, B. and A. Longinelli, 1990. Stable Isotope Study of Water, Gypsum and Carbonate Samples from the Bannock and Tyro Basins, Eastern Mediterranean, Marine Chemistry, 31, 123-135.

Swallow, J. C. and J. Crease, 1965. Hot Salty Water at the Bottom of the Red Sea, Nature, 205, 165-166.

Tanny, J., and A. B. Tsinober, 1988. The Dynamics and Structure of Double-Diffusive Layers in Sidewall Heating Experiments, J. Fluid Mech., 196, 135-156.

Turner, J. S., 1968. The Behaviour of a Stable Salinity Gradient Heated from Below, J. Fluid Mech., 33(1), 183-200.

Turner, J. S.,1969. A Physical Interpretation of Hot Brine Layers in the Red Sea, In: Hot Brines and Recent Heavy Metal Deposits in the Red Sea, E. T. Degens and D. A. Ross (editors), Springer, New York, 164-172.

Turner, J. S., 1973. Buoyancy Effects in Fluids, Cambridge University Press, 367 pp.

Turner, J. S., 1978. Double-Diffusive Intrusions into a Density Gradient, J. Geophys. Res., 83, 2887-2901.

Woods, A. W., 1991. Boundary-Driven Mixing, J. Fluid Mech., 226, 625-654.

Emin Ozsoy

1999-10-28