One of the mysteries of geophysics is how heat is transported from the Earth’s core, through the mantle and into the crust. A controversial aspect of this process is the idea that massive plumes of hot material from deep in the mantle well up towards the surface, causing volcano hotspots such as Iceland and Hawaii. Now, two physicists in the US have shown that — at least in theory — such mantle plumes could exist for long enough to cause hotspots.

The mantle is a region of dense rock that extends 50–3000 km below the surface of the Earth. Although the mantle is solid, geophysicists believe that it can also flow in response to the extreme temperatures and pressures generated by the Earth’s core. As a result, convective processes — such as mantle plumes — are likely to play an important role in how heat is transported through the mantle.

Laboratory experiments

The theory of mantle plumes got a boost in 1999 when Anne Davaille at the University of Paris 7 simulated them in a small tank containing two unmixed liquids of slightly different densities. Two liquids were used to mimic one of the many boundaries between rock layers that are believed to exist in the mantle.

When the denser liquid at the bottom of the tank was heated, Davaille observed several different types of behaviour ranging from violent mixing to the emergence of thin tendrils of denser liquid that extended up into the less dense fluid.

The tendrils formed on the boundary between the two fluids where the lower fluid pushed into the upper fluid to create a cone-shaped intrusion with a wide base and narrow top from which the tendril emerged. While the tendrils persisted for long periods of time, it wasn’t clear from the experiment whether the tendrils would occur on the density, time and length scales relevant to the Earth’s mantle.

Mathematical model

Now, Laura Schmidt and Wendy Zhang at the University of Chicago have come up with a new mathematical model of how tendrils form in Davaille’s experiments (Phys Rev Lett 100 044502). The researchers believe that their model can be scaled up to explain how mantle plumes many kilometres across could arise.

Schmidt and Zhang began with equations that described the shape and flow of the tendrils, which they solved using a combination of analytical and numerical techniques. Their calculations suggest that the cones occur at “stagnation points” which endure for long periods of time and anchor the tendrils. Such stagnation points have also been observed in a similar experiment done by Schmidt at the University of Chicago.

Schmidt told that the tendrils remain stable for long periods of time because they remain isolated from larger-scale convective flow in the tank. This enduring quality of the tendrils is important, because mantle plumes responsible for hotspots would have to endure for more that 100 million years.

Possible mechanism

According to Schmidt, the calculations suggest that the tendrils “are a generic feature of convecting multi-layer liquids, and would be present in a layered mantle”. She describes the tendrils as “a possible mechanism behind hotspot persistence”.

Schmidt and Zhang now plan to do a more rigorous check of their theory against experiment by seeing if their model can predict the rate of flow through tendrils of different sizes. They are also doing a more detailed study of what factors affect the stability of the tendrils.