Dear professors,
Hello. This is a two-dimensional model of a quarter circle that I set for Callisto. The result of the model is a bit strange. I think it’s a problem with my setting of the model.
I simply set up the model in two layers, the upper layer of ice and the lower layer of mantle. However, the results of the model’s operation show that the heat from the lower mantle accumulates at the bottom of the ice shell, and the rising heat from the bottom does not have an impact on the upper part.
May I ask where the problem lies with this model of mine?
Best wishes,
36.prm (3.1 KB)
Lu
@ddarkerlu Others may be able to address specific points, but I do want to point out the following: If you have an incompressible model, you should expect hot material to rise up and stay hot, and cold material to well down and stay cold. As a consequence, the picture of the lower layer in your model seems entirely appropriate to me. You may ask, then, why if the core-mantle boundary of Earth is ~5000K, why the plumes that rise close to the surface of earth are not also ~5000K hot. That’s because the earth is not incompressible, and material that rises up expands as it rises because the pressure decreases, and the adiabatic expansion cools the material. Similarly, slabs that descend into the deep earth are compressed by the ambient pressure and consequently increase in temperature.
As for why the lower layer seems to have little impact on the upper layer: This all depends on the viscosities and thermal conductivities of the two layers. If your density difference is so large that no material can cross the interface, then you need a high enough thermal conductivity for energy to cross the interface. And you need a low enough viscosity for material to distribute the energy that crosses the interface.
Best
W.
I don’t have much to add to Wolfgang’s message – my comments below just clarify how your model’s behaviour follows from the assumptions you’ve made.
Your initial conditions include a linear radius-temperature profile. This profile results in density decreasing with increasing depth in both the mantle and ice layers. This density decrease is gravitationally unstable and leads to convective overturn.
After the initial overturn, the bulk of the model is gravitationally stable. Thermal conduction across the inner, mantle-ice and outer interfaces then leads to local upwellings and downwellings initiating at those boundaries.
To summarise, your model seems to be behaving correctly. The question you need to answer is whether your initial and boundary conditions are appropriate for the problem you are trying to solve. For example, you may want to revisit whether the initial temperature profile reflects a realistic thermal state for the system you’re modeling, or consider including a “burn-in” period — a phase of early model evolution run without analysis — to allow transient artifacts from the initial conditions to relax before “time zero”.
Best wishes,
Bob
Thank you very much for answering my question. It has been very inspiring to me. I’m going to change my parameters according to your opinion.
Best
Lu
Thank you very much for providing a new idea for my model construction. I will learn more about some basic Settings of ASPECT.
Best
Lu