Name: evolution of staircase structures in diffusive convection
Uploaded: 2018-09-05T15:30:00
Description: Watch this Scientific Journal Video about Evolution of Staircase Structures in Diffusive Convection at JoVE.com

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

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...

<ol>
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E., Tanny, J., Ozsoy, E. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+diffusive+regime+of+double+diffusive+convection.">The diffusive regime of double diffusive convection.</a> Progress in Oceanography. 56, 461-481 (2003).</li><li>Timmermans, M. L., Toole, J., Krishfield, R., Winsor, P. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Ice-Tethered+Profiler+observations+of+the+double-diffusive+staircase+in+the+Canada+Basin+thermocline.">Ice-Tethered Profiler observations of the double-diffusive staircase in the Canada Basin thermocline.</a> Journal of Geophysical Research: Oceans. 113, 1-10 (2008).</li><li>Zhou, S. Q., Lu, Y. 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T., Neshyba, S., Denner, W. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Thermal+stratification+in+the+Arctic+Ocean.">Thermal stratification in the Arctic Ocean.</a> Science. 166 (3903), 373-374 (1969).</li><li>Padman, L., Dillon, T. M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Vertical+heat+fluxes+through+the+Beaufort+Sea+thermohaline+staircase.">Vertical heat fluxes through the Beaufort Sea thermohaline staircase.</a> Journal of Geophysical Research: Oceans. 92 (C10), 10799-10806 (1987).</li><li>Sirevaag, A., Fer, I. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Vertical+heat+transfer+in+the+Arctic+Ocean:+The+role+of+double-diffusive+mixing.">Vertical heat transfer in the Arctic Ocean: The role of double-diffusive mixing.</a> Journal of Geophysical Research: Oceans. 117 (C7), (2012).</li><li>Guthrie, J. 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M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Spatial+variability+of+the+Arctic+Ocean's+double-diffusive+staircase.">Spatial variability of the Arctic Ocean's double-diffusive staircase.</a> Journal of Geophysical Research: Oceans. 122 (2), 980-994 (2017).</li><li>Schmid, M., Busbridge, M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Double-diffusive+convection+in+Lake+Kivu.">Double-diffusive convection in Lake Kivu.</a> Limnology and Oceanography. 55 (1), 225-238 (2010).</li><li>Sommer, T., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Interface+structure+and+flux+laws+in+a+natural+double-diffusive+layering.">Interface structure and flux laws in a natural double-diffusive layering.</a> Journal of Geophysical Research: Oceans. 118 (11), 6092-6106 (2013).</li><li>Carpenter, J. 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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...

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 almost half of the global ocean, and it has important effects on oceanic multi-scale processes and even climatic changes9.
There are two primary modes for DDC: salt finger (SF) and diffusive convection (DC). SF occurs when a warm, salty water mass overlies cooler, fresher water in the stratified environment. When the warm and salty water lies below the cold and fresh water, the DC will form. The remarkable feature of the DC is that the vertical profiles of temperature, salinity and density are staircase-like, composed by alternant homogenous convecting layers and thin, strongly stratified interfaces. DC mainly occurs in high latitude oceans and some interior salt lakes, such as the Arctic and Antarctic Oceans, the Okhotsk Sea, the Red Sea and African Kivu Lake10. In the Arctic Ocean, there exist basin-wide and persistent DC staircases in the upper and deep oceans11,12. It has an important effect on diapycnal mixing in the upper ocean and may significantly influence the ice-melting, which recently arouses more and more interests in the oceanography community13.
The DC staircase structure was first discovered in the Arctic Ocean in 196914. After that, Padman &#38; Dillon15, Timmermans et al.11, Sirevaag &#38; Fer16, Zhou &#38; Lu12, Guthrie et al.17, Bebieva &#38; Timmermans18, and Shibley et al.19 measured the DC staircases in different basins of the Arctic Ocean, including the vertical and horizontal scales of the convecting layer and interface, the depth and total thickness of the staircase, the vertical heat transfer, the DC processes in mesoscale eddy and the temporal and spatial changes of the staircase structures. Schmid et al.20 and Sommer et al.21 observed the DC staircases by using a microstructure profiler in Kivu Lake. They reported the main structure features and heat fluxes of DC and compared the measured heat fluxes with the existing parametric formula. With computer processing speeds improving, the numerical simulations of DC have recently been done, for example, to examine the interface structure and instability, heat transfer through interface, layer merging event, and so on22,23,24.
Field observation has greatly enhanced the understanding of ocean DC for oceanographers, but the measurement is strongly limited by indeterminate oceanic flow environments and instruments. For example, the DC interface has an extremely small vertical scale, thinner than 0.1 m in some lakes and oceans25, and some special high-resolution instruments are needed. The laboratory experiment shows its unique advantages in exploring the fundamental dynamic and thermodynamic laws of DC. With a laboratory experiment, one can observe the evolution of the DC staircase, measure the temperature and salinity, and propose some parameterizations for the oceanic applications26,27. Furthermore, in a laboratory experiment, the controlled parameters and conditions are readily adjusted as required. For example, Turner first simulated the DC staircase in the laboratory in 1965 and proposed a heat transfer parameterization across the diffusive interface, which was frequently updated and extensively used in the in situ oceanic observations28.
In this paper, a detailed experimental protocol is described to simulate the evolution process of the DC staircase, including the generation, development and disappearance, in stratified saline water heated from below. The temperature and salinity are measured by a micro-scale instrument as well as the DC staircases being monitored with the shadowgraph technique. The experimental setup, evolution process, data analysis, and discussion of results are described in detail. By altering the initial and boundary conditions, the present experimental setup and method can be used to simulate other oceanic phenomena, such as the oceanic horizontal convection, deep-sea hydrothermal eruptions, surface mixed layer deepening, the effect of submarine geothermal on ocean circulation, and so on.

<table border="0" cellpadding="0" cellspacing="0" width="623">
	<tbody>
		<tr height="28">
			<td height="28" style="height:28px;width:185px;">Rectangular tank</td>
			<td style="width:152px;"></td>
			<td style="width:119px;"></td>
			<td style="width:167px;">Custom made part</td>
		</tr>
		<tr height="28">
			<td height="28" style="height:28px;width:185px;">Plexiglas</td>
			<td style="width:152px;"></td>
			<td style="width:119px;"></td>
			<td>Custom made part</td>
		</tr>
		<tr height="26">
			<td height="26" style="height:27px;width:185px;">Electric heating pad</td>
			<td style="width:152px;"></td>
			<td style="width:119px;"></td>
			<td>Custom made part</td>
		</tr>
		<tr height="26">
			<td height="26" style="height:27px;width:185px;">Distilled water</td>
			<td style="width:152px;"></td>
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			<td style="width:167px;">Multiple suppliers</td>
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			<td height="26" style="height:27px;width:185px;">Optical table</td>
			<td style="width:152px;">Liansheng Inc.</td>
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			<td height="29" style="height:29px;width:185px;">Thermiostors</td>
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			<td style="width:119px;"></td>
			<td>Custom made part</td>
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			<td height="29" style="height:29px;width:185px;">Digital multimeter</td>
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			<td height="63" style="height:63px;width:185px;">Micro-scale conductivity and temperature instrument (MSCTI)</td>
			<td style="width:152px;">PME. Inc.</td>
			<td style="width:119px;">Model 125</td>
			<td></td>
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			<td height="42" style="height:42px;width:185px;">Multifunction data acquisition (MDA)</td>
			<td style="width:152px;">MCC. Inc.</td>
			<td style="width:119px;">USB-2048</td>
			<td></td>
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			<td height="42" style="height:42px;width:185px;">Motorized precision translation stage (MPTS)</td>
			<td style="width:152px;">Thorlabs Inc.</td>
			<td style="width:119px;">LTS300</td>
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		<tr height="29">
			<td height="29" style="height:29px;width:185px;">Tracing paper</td>
			<td style="width:152px;"></td>
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			<td style="width:167px;">Multiple suppliers</td>
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			<td height="28" style="height:28px;width:185px;">LED lamp</td>
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			<td height="28" style="height:28px;width:185px;">Camcorder</td>
			<td style="width:152px;">Sony Inc.</td>
			<td style="width:119px;">XDR-XR550</td>
			<td></td>
		</tr>
		<tr height="28">
			<td height="28" style="height:28px;width:185px;">De-gassed fresh water</td>
			<td style="width:152px;"></td>
			<td style="width:119px;"></td>
			<td>Custom made part</td>
		</tr>
		<tr height="28">
			<td height="28" style="height:28px;width:185px;">Saline water</td>
			<td style="width:152px;"></td>
			<td style="width:119px;"></td>
			<td>Custom made part</td>
		</tr>
		<tr height="30">
			<td height="30" style="height:31px;width:185px;">Flexible tube</td>
			<td style="width:152px;"></td>
			<td style="width:119px;"></td>
			<td style="width:167px;">Multiple suppliers</td>
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			<td height="30" style="height:31px;width:185px;">Electric magnetic stirrer&#160;</td>
			<td style="width:152px;">Meiyingpu Inc.</td>
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			<td height="28" style="height:28px;width:185px;">Plastic soft tube</td>
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			<td height="42" style="height:42px;width:185px;">Direct-current power supply</td>
			<td style="width:152px;">GE Inc.</td>
			<td style="width:119px;">GPS-3030</td>
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			<td height="32" style="height:32px;width:185px;">Matlab</td>
			<td style="width:152px;">MathWorks Inc.</td>
			<td style="width:119px;">R2012a</td>
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	</tbody>
</table>

evolution of staircase structures in diffusive convection

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.

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...

Watch this Scientific Journal Video about Evolution of Staircase Structures in Diffusive Convection at JoVE.com

Evolution of Staircase Structures in Diffusive Convection

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 ...

This method can be used to explore the key issues in the dynamic processes of diffusive convection staircase structures, such as their generation, development, and disappearance. With the present experimental setup, we can clearly see the evolution of diffusive convection, which is very difficult, if it is not impossible, to observe directly in the ocean. Gather the components of the working tank.These include copper top and bottom plates and an acrylic sidewall assembly. The top plate is electroplated and encloses a water chamber accessible by tubes. It also has places for thermistors.The bottom plate is also electroplated and has slots for thermistors. It contains a heating pad. Use distilled water to carefully clean the copper plates and the acrylic sidewalls.When done, assemble the tank using screws to ensure it is water-tight. This completed tank is 257 millimeters in length and height and 65 millimeters wide. At an optical table, set up a stainless-steel supporting frame.On top of the frame, place an insulating slab. With everything in place, place the assembled tank on the slab. Insert thermistors into the top and bottom plates, and connect them to the data acquisition system.A thermistor monitors the temperature of the plate into which it is placed. Next, move a precision vertical translation stage into place for mounting a probe. Through the top plate, place a micro scale conductivity and temperature instrument sensor into the tank.Fix the instrument to the precision translation stage. Now, set up software for sensor data acquisition and thermistor readings. Return to the tank to adjust the position of the conductivity and temperature sensor.Set the initial position of the sensor at its lowest point, here, 20 millimeters above the bottom of the tank. Then, set the parameters of the motion for the translation stage for the experiment. Use the shadowgraph technique to monitor the experiment.For this, attach a piece of tracing paper on the outside of one side of the tank. On the opposite side of the tank, about five meters away, place a light source. To produce a nearly collimated beam, use a narrow beam LED as a light source.Place a high-speed camcorder about a meter in front of the tracing paper in the beam path. With the lamp and camcorder on, adjust their positions for a clear image. Obtain two identical rectangular tanks for the working fluid.The tanks are the same size as the working tank. Join them at their base with a clamped flexible tube, 10 centimeters in length. Place the two tanks at the same height.Arrange for one tank to have an electric stirrer in it. Next, clamp a flexible 50-centimeter tube into a peristaltic pump. Use the tube to join the tank with the stirrer to the working tank.Fill the tank that has no stirrer with saline solution of 60 grams per kilogram concentration. Fill the other tank with an equal volume of degassed fresh water. Once the tanks are filled, unclamp the connecting tube.Continuously homogenize the mixing water with the electric stirrer. Control the flow rate in the working tank with the peristaltic pump. The working tank takes approximately three hours to fill and be ready for the experiment.For an experiment, use a refrigerated circulator to set the top plate boundary conditions. At the top plate, connect the water chamber to the refrigerated circulator using eight soft plastic tubes. At the circulator, set the temperature for the top plate to the room temperature.Now, connect the bottom plate's heating pad to a DC power supply, and set its power level. Turn on the camcorder to record the flow pattern. Begin monitoring temperature and salinity data.Then, start vertical motion of the sensor. Finally, turn on the refrigerated circulator and the DC power supply to achieve the working fluid boundary conditions. This is an example of a shadowgraph image taken when the top plate is at the room temperature and the bottom plate is being heated.There are three convecting layers in the image, where the fluid density is homogeneous. There are also three interface layers, where large density gradients exist. This intensity fluctuation profile has three peaks that correspond to the interfaces.Here is the evolution of the intensity fluctuation profile in time, which reveals layer generation, development, and disappearance associated with the diffusive convection staircase. The temperature profile and the salinity profile provide other views of the evolution in time of the system. In these profiles, each continuous line represents data collected over 404 seconds.The data sets in the temperature profile are each offset by 1.5 degrees Celsius from the one before. For the salinity profile, each data set is offset by three grams per kilogram from the previous set. This method can also be applied to simulate other phenomenon in oceans, such as global oceanic circulation, mixed layer deepening, and hydrothermal plume eruption.If you want to try this procedure, please do remember to initially adjust the conductivity and temperature sensors to the lowest position of the translation stage to prevent the sensor for crashing on the bottom plate. With the presented results, we can further develop new parameterization of layer thickness, heat flux, and add diffusivity in diffusive convection, which would pave the way for the community of physical oceanography to study the phenomena in the oceanic application.

Research

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Environment

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