Inner core cookbook - modifications of the manual #2075

MarineLasbleis · 2018-01-26T04:36:00Z

Update of the manual part on the inner core convection: new figures, with regime diagram, and update of the text.

Slight updates on the cookbook file associated (remove unused parts and update values for initial temperature field that was too high.)

jdannberg

That's great, thank you for contributing this! If you address the few small comments I had, we can merge this.

jdannberg · 2018-01-26T04:56:01Z

cookbooks/inner_core_convection/inner_core_traction.prm

@@ -116,7 +116,7 @@ subsection Mesh refinement

  subsection Minimum refinement function
    set Variable names = depth, phi, theta
-    set Function expression = if(depth>0.1,if(depth>0.3,5,6),7)
+    set Function expression = if(depth>0.1,if(depth>0.2,2,5),6)


This is not used, correct? With the parameters in the section above, no adaptive refinements are done (as the 'Time steps between mesh refinement' are set to 0).

The point was to keep "no refinement" for using on laptops (with this refinement, the number of points can be quite high), but to provide the function if needed by someone. (It took us a while to understand it!)

jdannberg · 2018-01-26T05:11:29Z

doc/manual/manual.tex

-linearly from the boundary to zero at the center of the inner core. 
+by discussions with John Rudge. Additional materials and comments by Mathilde Kervazo and Marine Lasbleis}
+
+This is an example of convection in the inner core of the Earth. The model is based on a spherical geometry, with a single material. Three main particularities are constitutive of this inner core dynamics modelling: it consists of a self-gravitating sphere where the gravity decreases linearly from the boundary to zero at the center of the inner core; the boundary conditions combine normal stress and normal velocity, and take into account the rate of phase change (melting/freezing) at the inner-outer core boundary; the material is temperature dependent density,  that makes the density profile unstably stratified as temperature increases towards the center of the core.


the material is temperature dependent density, that... --> the material has a temperature dependent density [no comma] that...

Also, I think it would make sense to clarify the part about the self-gravitation, saying that we do not actually compute self-gravitation, but that the gravity profile is linear, and as density variations in the inner core are very small, this means that it resembles the gravity profile of a self-gravitating sphere (otherwise all of the readers from the mantle convection community will be confused, and ask us if we can do self-gravitation).

jdannberg · 2018-01-26T05:27:06Z

doc/manual/manual.tex

@@ -7860,12 +7856,18 @@ \subsubsection{Inner core convection}
  H,
 \end{align}

-where $Ra$ is the Rayleigh number. 
+where $Ra$ is the Rayleigh number and 6 is the 'source term', originated from the time-dependence of the reference temperature (secular cooling). In spherical geometry, $H=6$. 


You probably mean: H is a source terms that originates...
Could you also add the fact that this is related to the nondimensionalization? Something like, 'Because we remove the adiabatic background temperature from the energy equation during non-dimensionalization, we have to add a source term that describes the decrease of the adiabatic temperature over time (secular cooling).

jdannberg · 2018-01-26T05:29:04Z

doc/manual/manual.tex

+
+\vspace{0.3cm}
+\textbf{Thermal evolution of the inner core.}
+Thermal evolution of the inner core implies that, owing to secular cooling, the temperature decreases with respect to the initial state. The growing inner core is however stable if formerly solidified material is colder than the current adiabatic profil attached to the liquidus temperature at the inner core boundary, as a result of diffusion. If not, it is unstable to thermal convection.  


profil --> profile

I don't really understand the part about the stable/unstable conditions, in particular the relation to the liquidus temperature. Do you mean that the adiabatic temperature always starts from the liquidus temperature at the inner core boundary? It could make sense to put that part into a separate sentence (that comes earlier).

I removed it and added a sentence before!

jdannberg · 2018-01-26T05:41:12Z

doc/manual/manual.tex

-of plumes scaling with the Rayleigh number; whereas for low values of $\mathcal{P}$, the inner core is in a 
-translation regime, where material freezes at one side and melts at the other side, so that the velocity field 
-is uniform, pointing from the freezing to the melting side. 
+Three main areas can be distinguished: the stable area, the plume convection area and the translation mode of convection area (Figure~\ref{fig:diagramme-regime}). For low Rayleigh numbers (below the critical value $Ra_c$), there is no convection and thermal diffusion dominates the heat transport. However, if the inner core is convectively unstable ($Ra$>$Ra_c$), the convection regime depends mostly on $\mathcal{P}$. For low $\mathcal{P}$ (<29), the convective translation mode dominates, where material freezes at one side and melts at the other side, so that the velocity field is uniform, pointing from the freezing to the melting side. Otherwise, at high $\mathcal{P}$ (>29), convection takes the usual form of thermal convection with shear free boundary and no phase change, that is the one-cell axisymmetric mode at the onset, and chaotic plume convection for larger Rayleigh number. In this case, melting and solidification at the ICB have only a small dynamic effect. At intermediate values of P, the first unstable mode is a linear combination of the high-P convection mode and of the small-P translation mode.


Can you add: material freezes at one side of the inner core and melts at the other side

jdannberg · 2018-01-26T05:45:20Z

doc/manual/manual.tex

+
+\begin{figure}[h]
+\begin{center}
+\includegraphics[height=0.57\textwidth]{cookbooks/inner_core_convection/Diagstab.pdf}


That figure is really cool! Can you add a sentence that each dot and triangle is one model run done with ASPECT, and the following text will provide more details on how to modify the input file to do those model runs?

jdannberg · 2018-01-26T05:51:02Z

doc/manual/manual.tex

+    \includegraphics[width=0.25\linewidth]{cookbooks/inner_core_convection/Ra1e2P-1rescalemodif.png}
+    \includegraphics[width=0.25\linewidth]{cookbooks/inner_core_convection/Ra1e5P4rescalemodif.png}
+    \caption{Convection regimes in the inner core for different values of $Ra$ and $\mathcal{P}$. From left to right: no convection, translation, plume convection; the 2D slices of the top are with the default temperature scale while at the bottom an adaptative scale is used.}
+    \label{fig:inner-core-regimes}


Nice! Would it be too much effort to also add velocity vectors somehow? I just think that would make a lot of sense, because then one would really see that one model is convecting, one translating, and one basically does not move at all.

I guess we would need to go back to your initial figure for that... Or I can try to find the run somewhere on the harddrive. Let's see that Tuesday?

jdannberg · 2018-01-26T05:51:28Z

doc/manual/manual.tex

+    \label{fig:inner-core-regimes}
+       \end{center}
+\end{figure}
+:w


I think this should be an empty line.

jdannberg · 2018-01-26T05:57:30Z

doc/manual/manual.tex

+:w
+\vspace{0.3cm}
+\textbf{Mesh refinement.}
+The temperature is set at 1 et the boundary, and for the translation case, a large temperature gradient can be imposed at the boundary layer, especially for the translation regime. For this, a specific refinement can be set for defining correctly the boundary layer at the inner core boundary. 


Maybe it would make more sense to formulate that in a different way:
The temperature is set to 0 at the outer boundary, and a large temperature gradient can develop in the boundary layer, especially for the translation regime. The adaptive mesh refinement allows it to resolve this layer at the inner core boundary.

jdannberg · 2018-01-26T05:58:07Z

doc/manual/manual.tex

+\textbf{Mesh refinement.}
+The temperature is set at 1 et the boundary, and for the translation case, a large temperature gradient can be imposed at the boundary layer, especially for the translation regime. For this, a specific refinement can be set for defining correctly the boundary layer at the inner core boundary. 
+
+In order to have a mesh that is much finer at the outer boundary than in the center of the domain, this expression for the mesh refinement subsection can be used in the input file :


Please remove the space between file and the colon

jdannberg · 2018-01-26T06:01:51Z

/run-tests

bangerth · 2018-01-26T13:54:43Z

A new contributor -- most excellent! Welcome aboard, @MarineLasbleis !

jdannberg · 2018-01-30T05:54:29Z

Okay, looks good, thank you!
I'll do the update to the figure in a separate pull request.

MarineLasbleis added 5 commits January 24, 2018 16:33

precisions on inner core dynamics

d09350e

new figures for cookbook inner core

196b8e2

remove unused values for output

07b5c78

equations valid if no growth

7776f6c

cookbook inner core

dd947f2

jdannberg reviewed Jan 26, 2018

View reviewed changes

MarineLasbleis added 2 commits January 28, 2018 15:35

update of manual for inner core

2f121f4

remark on 'self gravitation'

a4dddd3

jdannberg merged commit 41be1dc into geodynamics:master Jan 30, 2018

jdannberg mentioned this pull request Jan 30, 2018

Merge old and new inner core figures and add Marine as a contributor #2077

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Inner core cookbook - modifications of the manual #2075

Inner core cookbook - modifications of the manual #2075

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jdannberg commented Jan 30, 2018

Inner core cookbook - modifications of the manual #2075

Inner core cookbook - modifications of the manual #2075

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jdannberg commented Jan 26, 2018 • edited

bangerth commented Jan 26, 2018

jdannberg commented Jan 30, 2018

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edited