JoVE Logo
Faculty Resource Center

Sign In





Representative Results






Evolution of Staircase Structures in Diffusive Convection

Published: September 5th, 2018



1State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences

Diffusive convection (DC) widely occurs in natural processes and engineering applications, characterized by a series of staircases with homogeneous convecting layers and stratified interfaces. An experimental procedure is described to simulate the evolution process of the DC staircase structure, including the generation, development and disappearance, in a rectangular tank.

Diffusive convection (DC) occurs when the vertical stratified density is controlled by two opposing scalar gradients that have distinctly different molecular diffusivities, and the larger- and smaller- diffusivity scalar gradients have negative and positive contributions for the density distribution, respectively. The DC occurs in many natural processes and engineering applications, for example, oceanography, astrophysics and metallurgy. In oceans, one of the most remarkable features of DC is that the vertical temperature and salinity profiles are staircase-like structure, composed of consecutive steps with thick homogeneous convecting layers and relatively thin and high-gradient interfaces. The DC staircases have been observed in many oceans, especially in the Arctic and Antarctic Oceans, and play an important role on the ocean circulation and climatic change. In the Arctic Ocean, there exist basin-wide and persistent DC staircases in the upper and deep oceans. The DC process has an important effect on diapycnal mixing in the upper ocean and may significantly influence the surface ice-melting. Compared to the limitations of field observations, laboratory experiment shows its unique advantage to effectively examine the dynamic and thermodynamic processes in DC, because the boundary conditions and the controlled parameters can be strictly adjusted. Here, a detailed protocol is described to simulate the evolution process of DC staircase structure, including its generation, development and disappearance, in a rectangular tank filled with stratified saline water. The experimental setup, evolution process, data analysis, and discussion of results are described in detail.

Double diffusive convection (DDC) is one of the most important vertical mixing processes. It occurs when the vertical density distribution of the stratified water column is controlled by two or more scalar components gradients of opposite directions, where the components have distinctly different molecular diffusivities1. It widely occurs in oceanography2, the atmosphere3, geology4, astrophysics5, material science6, metallurgy7, and architectural engineering8. DDC is present in a....

Log in or to access full content. Learn more about your institution’s access to JoVE content here

1. Working Tank

Note: The experiment is carried out in a rectangular tank. The tank includes top and bottom plates and a side wall. The top and bottom plates are made of copper with electroplated surfaces. There is a water chamber within the top plate. An electric heating pad is inserted in the bottom plate. The side wall is made of transparent Plexiglas. The tank size is Lx = 257 mm (length), Ly = 65 mm (width) and Lz = 257 mm (height). The thickness of the side.......

Log in or to access full content. Learn more about your institution’s access to JoVE content here

Figure 1 shows the schematic of the experimental setup. Its components are described in the protocol. The main parts are shown in Figure 1a and the detailed working tank is shown in Figure 1b. Figure 2 shows the temperature changes at the bottom (Tb, the red curve) and top (Tt, the black curve) plates. It is indicated that the temperature of the two plates are almost the same as th.......

Log in or to access full content. Learn more about your institution’s access to JoVE content here

In this paper a detailed experimental protocol is described to simulate the thermohaline DC staircase structures in a rectangular tank. An initial linear density stratification of working fluid is constructed using the two-tank method. The top plate is kept at a constant temperature and the bottom one at constant heat flux. The whole evolution process of the DC staircase, including its generation, development, mergence, and disappearance, are visualized with the shadowgraph technique, and the variances of the temperature.......

Log in or to access full content. Learn more about your institution’s access to JoVE content here

This work was supported by the Chinese NSF grants (41706033, 91752108 and 41476167), Grangdong NSF grants (2017A030313242 and 2016A030311042) and LTO grant (LTOZZ1801).


Log in or to access full content. Learn more about your institution’s access to JoVE content here

Name Company Catalog Number Comments
Rectangular tank Custom made part
Plexiglas Custom made part
Electric heating pad Custom made part
Distilled water Multiple suppliers
Optical table Liansheng Inc. MRT-P/B
Thermiostors Custom made part
Digital multimeter Keithley Inc Model 2700
Micro-scale conductivity and temperature instrument (MSCTI) PME. Inc. Model 125
Multifunction data acquisition (MDA) MCC. Inc. USB-2048
Motorized precision translation stage (MPTS) Thorlabs Inc. LTS300
Tracing paper Multiple suppliers
LED lamp Multiple suppliers
Camcorder Sony Inc. XDR-XR550
De-gassed fresh water Custom made part
Saline water Custom made part
Flexible tube Multiple suppliers
Electric magnetic stirrer  Meiyingpu Inc. MYP2011-100
Peristaltic pump Zhisun Inc. DDBT-201
Refrigerated circulator Polyscience Inc. Model 9702
Plastic soft tube Multiple suppliers
Direct-current power supply GE Inc. GPS-3030
Matlab MathWorks Inc. R2012a

  1. Turner, J. S. . Buoyancy Effects in Fluids. , 367 (1973).
  2. Schmitt, R. W. Double diffusion in oceanography. Annual Review of Fluid Mechanics. 26, 255-285 (1994).
  3. Turner, J. S., Gustafson, L. B. Fluid motions and compositional gradients produced by crystallization or melting at vertical boundaries. Journal of Volcanology and Geothermal Research. 11, 9S125 (1981).
  4. Robb, L. . Introduction to Ore-forming Processes. , 373 (2004).
  5. Chabrier, G., Baraffe, I. Heat transport in giant (exo)planets: a new perspective. The Astrophysical Journal Letters. 661, 81-84 (2007).
  6. Langlois, W. E. Buoyancy-driven flows in crystal-growth melts. Annual Review of Fluid Mechanics. 17, 191 (1985).
  7. Chen, C. -. F., Johnson, D. H. Double-diffusive convection: A report on an engineering foundation conference. Journal of Fluid Mechanics. 138, 405-416 (1984).
  8. Griffiths, R. W. Layered double-diffusive convection in porous media. Journal of Fluid Mechanics. 102, 221-248 (1981).
  9. You, Y. Z. A global ocean climatological atlas of the Turner angle: implications for double-diffusion and water-mass structure. Deep Sea Research Part I: Oceanographic Research Papers. 49, 2075-2093 (2002).
  10. Kelley, D. E., Fernando, H. J. S., Gargett, A. E., Tanny, J., Ozsoy, E. The diffusive regime of double diffusive convection. Progress in Oceanography. 56, 461-481 (2003).
  11. Timmermans, M. L., Toole, J., Krishfield, R., Winsor, P. Ice-Tethered Profiler observations of the double-diffusive staircase in the Canada Basin thermocline. Journal of Geophysical Research: Oceans. 113, 1-10 (2008).
  12. Zhou, S. Q., Lu, Y. Z. Characterization of double diffusive convection steps and heat budget in the deep Arctic Ocean. Journal of Geophysical Research: Oceans. 118 (12), 6672-6686 (2013).
  13. Turner, J. S. The melting of ice in the arctic ocean: The influence of double-diffusive transport of heat from below. Journal of Physical Oceanography. 40, 249-256 (2010).
  14. Neal, V. T., Neshyba, S., Denner, W. Thermal stratification in the Arctic Ocean. Science. 166 (3903), 373-374 (1969).
  15. Padman, L., Dillon, T. M. Vertical heat fluxes through the Beaufort Sea thermohaline staircase. Journal of Geophysical Research: Oceans. 92 (C10), 10799-10806 (1987).
  16. Sirevaag, A., Fer, I. Vertical heat transfer in the Arctic Ocean: The role of double-diffusive mixing. Journal of Geophysical Research: Oceans. 117 (C7), (2012).
  17. Guthrie, J. D., Fer, I., Morison, J. Observational validation of the diffusive convection flux laws in the Amundsen Basin, Arctic Ocean. Journal of Geophysical Research: Oceans. 120 (12), 7880-7896 (2015).
  18. Bebieva, Y., Timmermans, M. L. An examination of double-diffusive processes in a mesoscale eddy in the Arctic Ocean. Journal of Geophysical Research: Oceans. 121 (1), 457-475 (2016).
  19. Shibley, N. C., Timmermans, M. L., Carpenter, J. R., Toole, J. M. Spatial variability of the Arctic Ocean's double-diffusive staircase. Journal of Geophysical Research: Oceans. 122 (2), 980-994 (2017).
  20. Schmid, M., Busbridge, M. Double-diffusive convection in Lake Kivu. Limnology and Oceanography. 55 (1), 225-238 (2010).
  21. Sommer, T., et al. Interface structure and flux laws in a natural double-diffusive layering. Journal of Geophysical Research: Oceans. 118 (11), 6092-6106 (2013).
  22. Carpenter, J. R., Sommer, T., Wüest, A. Simulations of a double-diffusive interface in the diffusive convection regime. Journal of Fluid Mechanics. 711, 411-436 (2012).
  23. Flanagan, J. D., Lefler, A. S., Radko, T. Heat transport through diffusive interfaces. Geophysical Research Letters. 40 (10), 2466-2470 (2013).
  24. Radko, T., Flanagan, J. D., Stellmach, S., Timmermans, M. L. Double-diffusive recipes. Part II: Layer-merging events. Journal of Physical Oceanography. 44 (5), 1285-1305 (2014).
  25. Scheifele, B., Pawlowicz, R., Sommer, T., Wüest, A. Double diffusion in saline Powell Lake, British Columbia. Journal of Physical Oceanography. 44 (11), 2893-2908 (2014).
  26. Guo, S. X., Zhou, S. Q., Qu, L., Lu, Y. Z. Laboratory experiments on diffusive convection layer thickness and its oceanographic implications. Journal of Geophysical Research: Oceans. 121 (10), 7517-7529 (2016).
  27. Guo, S. X., Cen, X. R., Zhou, S. Q. New parametrization for heat transport through diffusive convection interface. Journal of Geophysical Research: Oceans. 123 (2), 1327-1338 (2018).
  28. Turner, J. S. The coupled turbulent transports of salt and heat across a sharp density interface. International Journal of Heat and Mass Transfer. 8 (5), 759-767 (1965).
  29. Hill, D. F. General density gradients in general domains: the "two-tank" method revisited. Experiments in Fluids. 32 (4), 434-440 (2002).
  30. Zhou, S. Q., Ahlers, G. Spatiotemporal chaos in electroconvection of a homeotropically aligned nematic liquid crystal. Physical Review E. 74 (4), 046212 (2006).

This article has been published

Video Coming Soon

JoVE Logo


Terms of Use





Copyright © 2024 MyJoVE Corporation. All rights reserved