How to calculate the Rayleigh number in if I use the Steinberger Model?

Dear users

I’ve finally been able to setup my Steinberger’s simulation using two compositional fields and two tables generated by Perplex.

I’d like to have more control over my simulation and I’d like to choose the correct Rayleigh number to reproduce some results from the literature. In ASPECT i cannot choose it like in CITCOM, but it has to be calculated.

I searched in the user manual and it’s possible to calculate it in different occasions and with different formulas.

The point is that i didn’t find a concrete formula in the manual referred to the Steinberger’s model. The only one that i found where the Steinberger’s paper is cited is this (page 137 of the manual):

Can I use this formula to calculate the Rayleigh number?

Thank you for the availability

Hi Francesco,

The problem with the Rayleigh number is that as soon as your material properties change within your model, there is no longer a single Rayleigh number. You can define a local Rayleigh number based on the material properties at a given point, or you can compute some sort of average over your model or pick representative values.

So you can definitely use the equation you have above, but rho varies with depth, alpha varies with depth, the viscosity varies with depth, your thermal conductivity might vary with depth, and even g might vary with depth. What “reference” values you pick to put into the equation to compute Ra is somewhat arbitrary. You somehow have to pick values for all these properties that are representative for the convective system you want to describe with the Rayleigh number, and then, yes of course you can use this equation to compute it.


This is what i thought…
I did a python script to plot the Rayleigh number according to my tabulated files and the values of my simulation. Does that make sense? Values of the Rayleigh number of 5 x 10 ^7 is in agreement for what i found in the literature, the drops vary with the values of alpha (so of the temperature of the material). Can this be accepted in a scientific pubblication? Also is it correct if I say that the Rayleigh number of my simulation is 5 x 10^7 for this graph?
Thank you for the availability!

I am actually a bit surprised by your plot. I would expect Ra to decrease with depth (lower alpha, higher viscosity, higher conductivity).

But for a scientific publication, as long as you provide all material properties, you do not need to say what your Rayleigh number is. If you give a Rayleigh number, you need to say how you computed the Rayleigh number. So no, based on your graph, I would not say that the Rayleigh number is 5e7. But you can define reference values for all material properties and choose them in a way that your result is 5e7. Some people also give a surface Rayleigh number with the values of the material properties at the surface.

thank you for the clarifications! The rayleigh number increase because in the graph i’m assuming constant viscosity, which is not true.

Also, i wanted to ask, where can i take the thermal diffusivity of my PerpleX material? Because it’s not present on my table and so i cannot calculate my surface Rayleigh if i want to take a reference.
Still thank you for the help!