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laboratory simulations on continental dynamics
(click on an image for a larger view)
In 1966, Wilson asked an intriguing question: "Did the Atlantic close and then re-open?" [Nature 211, 676, 1966]. There has been considerable evidence that the Atlantic Ocean has closed and re-opened about 4-5 times in the past two and a half billion years, with a period of about 300-500 million years. This period is now referred to as the "Wilson cycle".

Our table-top experiment demonstrates that in a turbulent state, Ra ~ 108, a semi-regular oscillatory state develops through a thermal feedback mechanism. The floating model-continents behave like "thermal blankets" (they reduce local heat losses due to their composition and higher viscosity), inducing dramatic changes in the convection pattern underneath. The modified flow pattern in turn moves the continents to new positions. This two-way feedback mechanism is the key to the unforced free oscillation.

This experiment was originally carried out in collaboration with Prof. Albert Libchaber. Further studies are continued in our laboratories at New York University. [ "Periodic boundary motion in thermal turbulence," by Jun Zhang and A. Libchaber, Physical Review Letters, 84, 4361, (2000) and "Thermal convection with a freely moving top boundary" by J.-Q. Zhong and Jun Zhang, Physics of Fluids, 17, 115105, (2005). We (Zhong and Zhang) plan to submit another three papers on our recent results in the spring of 2006].

Our experiments are the first successful attempt that simulates the continental dynamics. Different from other existing experiments, our experiments involve no any external force. The instabilities and rich dynamics are intrinsically embedded in the system. Our long-term goal is to explore the fundamental interaction between continents and the convective mantle using prototype table-top experiments. Indeed, in our experiments, we can readyly match with the actual Earth on its Rayleigh number, aspect ratio, heat loss contrast between what passes through the continents and what passes through the oceanic plates. We also actively seek ways to investigate the high Prandtl number effects for the Earth, which is difficult to be realized in a laboratory setting. This effort would require a combine study from both experimentation and numerical simulation. Please check our Publication list for our most recent works in this field.]
In this experiment, a Rayleigh-Bénard convection cell is cooled in a laminar hood. The free-moving floater is introduced at the free surface, which covers only part of the open fluid surface. A nearly parallel light beam is used to form a shadowgraph of the cell, which visualizes the convective flow pattern and also shows the position of the model-continent (click on the picture to have a larger view).
Four snapshots (shadowgraphs) of the continent oscillation in the convection cell, at Ra ~ 108, Pr ~ 6, Re ~ 50: (1) About 10 minutes after the floater came to the left side of the cell, a hot raising structure is visible under the floater. The system now has two large turbulent eddies, with a large scale flow pattern on the right that tends to move the floater to the right. (2) Right after the floater arrives at the right side of the cell, the flow pattern is little changed and the system is temporally stable. (3) 5 minutes after (2), a new hot (upwelling) structure is induced by the floater and the flow pattern starts to reorganize and eventually replace the old one. (4) The old flow pattern is taken over by the new structure. The large-scale eddy on the left drags the floater to the left. From (1) to (4), the system goes through half period of the oscillation. The observed time scales are largely determined by the thermal boundary thickness and the turnover time around the finite convection cell.
Liquid-crystal beads show the temperature field as well as the local velocity field of the convection cell. The blue region indicates a hot, raising flow structure. As the temperature decreases, the color changes from blue to green, yellow, red and finally the beads scatter no light (dark).
This time-series shows the movement of the free floater in a thermal turbulence: semi-regular motion is recovered from thermal turbulence. It is clear the that the thermal feedback mechanism is strong enough to override stochasticity present in the turbulent convection at high Rayleigh numbers. In this experiment, the Rayleigh number is on the order of 108. The aspect ratio is 3.3 and the floater covers 36% of the free surface of the convection cell.
As one changes the size of the model-continent, there appears to be a "phase transition" in the dynamics of the system. The motion of the continent transitions from a semi-regular oscillation to a confined motion (localization) when the continent size is increased from 0.2L to 0.8L, where L is the length of convection cell (left panel). Between the two states, an intermittency is observed. This transition can be explained in an one-dimensional phenomenological model (right panel). The grey bands in both graphs indicate the available spaces for the model-continent to move around. Our work on this particular transition is submitted for publication in the sping of 2006.
We are currently (year 2006) constructing a thermal convection system that has an annular geometry. A freely moving top boundary (model-continent) will be introduced at the free surface. Both the convective fluid and the free boundary would experience periodic boundary conditions. We have observed some very interesting dynamics. Among them is the unidirectional "hopping" of the model-continent between convergent flows at the surface (downwellings of cold flows). The rich dynamics revealed from this coupled system is the subject of our on-going effort to understand the continental dynamics.

Alfred Wegener (the originator of the idea of continental drift) once said: "Scientists still do not appear to understand sufficiently that all earth sciences must contribute evidence toward unveiling the state of our planet in earlier times, and that the truth of the matter can only be reached by combing all this evidence... It is only by combing the information furnished by all the earth sciences that we can hope to determine 'truth' here, that is to say, to find the picture that sets out all the known facts in the best arrangement and that therefore has the highest degree of probability. Further, we have to be prepared always for the possibility that each new discovery, no matter what science furnishes it, may modify the conclusions we draw."

--[The Origins of Continents and Oceans (4th edition)]

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