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 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 & Dillon15, Timmermans et al.11, Sirevaag & Fer16, Zhou & Lu12, Guthrie et al.17, Bebieva & 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.
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 sidewall is 9.5 mm.
2. Optical Apparatus
Note: During the experiment, the evolution of the DC staircase would be monitored with the shadowgraph technique, which is fulfilled with the below procedures
3. Working Fluid
4. Running the Experiment
5. Data Processing
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 the room temperature (24 °C) initially. At t = 641 s, the top-cooling and bottom-heating are applied. Then, Tb begins to increase rapidly, from 24 °C to 57 °C, while Tt is almost constant until the time reaches 7683 s. During this time range, it is expected that the heating is transferred upwards to the fluid, but has not reached the top plate. At approximately t = 8000 s, Tb achieves its maximum, 57 °C, and Tt begins to increase gradually, which implies that the bottom heating reaches the top plate. From then on, the whole tank is completely full of DC staircase structures. Then the bottom-plate temperature begins to decrease and the top-plate temperature continues to increase. At approximately t = 14800 s, both Tb and Tt change abruptly, which corresponds to the disappearance of the last interface within the tank. Subsequently, both Tb and Tt approach constant values, where the whole steady flow state belongs to Rayleigh–Bénard convection26.
Figure 3a shows an instantaneous shadowgraph image taken at t = 3375 s. There are three interfaces and three convecting layers in the tank. In the convecting layer, the fluid density is homogeneous, while in the interface, large density (or index of refraction) gradient exists, which produces strong light intensity fluctuation. Figure 3b shows the intensity fluctuation profile , where the positions of peaks are corresponding to those of the interfaces. Figure 3c shows the intensity fluctuation profile of shadowgraph image as a function of time . It exhibits the temporal evolution of the DC staircase in the experiment, accompanied with dynamic processes, i.e. the layer generation, development, and disappearance. Once the system is heated, a convecting layer forms and thickens gradually from the bottom of system. A sharp interface lies between the convecting layer and the above static fluid. When the bottom convecting layer reaches a certain thickness, a new convecting layer forms above the interface. Meanwhile, the convecting layers and interfaces migrate upward. A similar process continues until a new convecting layer forms above the uppermost interface. In the evolution process, two adjacent layers may merge, or one layer is eroded by another one. At about t = 8000 s, the whole tank is occupied by seven convecting layers. Henceforth, the layer merging is the only process and the number of layers gradually reduces. At about t = 14800 s, only a single convecting roll exists in the entire tank after the last interface disappears, and the convective flow state approach a stable Rayleigh–Bénard convection. As shown in Figure 2 and Figure 3c, the temperature variances of the top and bottom plates are corresponding to the dynamic changes of the staircases. The recorded temperature and salinity profiles are shown in Figure 4. Note that the temperature and salinity profiles are continuously shifted by 1.5 °C, and 3.0 g/kg, respectively, for better clarify. The time interval between two neighbor profiles is 404 s. In this figure, these profiles clearly exhibit the dynamics changes of the staircase structures. The patterns of the staircases are corresponding with layers and interfaces recorded in the shadowgraph measurements (Figure 3c).
Figure 1. Schematic of the experimental setup (a) Main component parts of the experimental setup. (b) Setup of the working tank. Please click here to view a larger version of this figure.
Figure 2. Temperature changes at the bottom (red curve) and top (black curve) plates during the experiment. The gray curve denotes the environment temperature. Please click here to view a larger version of this figure.
Figure 3. Instantaneous shadowgraph image and post-processing (a) Shadowgraph image at t=3375 s, (b) Intensity fluctuation along z direction, , of the image intensity in Figure 3a, (c) Temporal evolution of DC pattern with color shading showing . The white dashed line corresponds to profile shown in Figure 3b. Please click here to view a larger version of this figure.
Figure 4. Successive DC evolution profiles. Top: Temperature profiles, Bottom: Salinity profiles. Increments of temperature by 1.5 °C, and salinity by 3.0g/kg between the neighboring profiles are applied. The time interval between two neighbor profiles is 404 s. Please click here to view a larger version of this figure.
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 and salinity are recorded by a high-accuracy probe. With these measurements, one can not only qualitatively observe the changes of staircase, but also quantitatively analyze the changes of temperature, salinity, and density. Furthermore, the variances of layer thickness and heat flux can be parameterized for in situ oceanic applications26,27. Some representative experimental results are shown and discussed with the figures.
In step 3.2, the Tank A, Tank B and the working tank are connected during the establishment of the initial linear density stratification for the working tank. By the law of the connected vessels, the fluid in the tank A automatically flows into the tank B, and the flow rate from the tank B into the work tank is precisely twice that from the tank A into the tank B, which can result in a vertically linear density gradient of the working fluid29. In step 5.1, the position of each interface could be identified based on the local maximum intensity fluctuation of the profile ; this is because there are strong light intensity fluctuations at the positions of the DC interfaces.
Compared with previous DC experiments in the literature, the present setup and method can measure the temperature and salinity profiles and record the fluid-pattern images synchronously. The temporal and spatial resolutions are high enough to capture the thin interfaces as well as other fine turbulent structures. The main limitation of this method is that the heat exchange between the inside and outside of the working tank has not been recorded, which will be further improved if the accurate vertical heat flux need to be measured.
It is worth to point out that in this experiment the initial density stratification and boundary conditions can readily be controlled as required for different purposes. Some complex working conditions can also be achieved with slightly adjustment, for example the nonlinear stratification can be constructed by modulating the ratio of flow rates from tank A to tank B and that from tank B to the working tank in the two-tank methods29. Therefore, it is expected that the present experimental setup and method could be applied to simulate some other oceanic phenomena, such as the oceanic horizontal convection, deep-sea hydrothermal eruptions, surface mixed layer deepening, and effect of submarine geothermal on ocean circulation, and so on.
The authors have nothing to disclose.
This work was supported by the Chinese NSF grants (41706033, 91752108 and 41476167), Grangdong NSF grants (2017A030313242 and 2016A030311042) and LTO grant (LTOZZ1801).
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 |