Adiabaticity , compressibility, weird result

Hi ASPECT,

Probably a basic question (I’m pretty new to ASPECT), but I’m looking at some unintuitive results that I think could be clarified quite quickly…

So I’ve run a simple isoviscous calculation with fixed T BCs in a 2D annulus to 1 billion years. At the end, I’m just wondering why, within the convective cells, the temperature is hot in the top half of the mantle and cold in the bottom half… rather than nearly isothermal (or, increasing, adiabatically with depth).

I’ve attached a screenshot (at 1 Gy). IThe parameters I’ve provided in the prm file (pasted below) include compressibility and expansion (so figured that the simulation would be adiabatic?).

I guess I have two basic Qs: is my weird result due to the calculation not being compressible?

And also, how would I adapt my parameter file to include it. I recently found the following input options: “Subsection”: Adiabatic conditions model: Parameter: “compute profile”.

Any help appreciated!

Thanks,

Harriet

PARAM file:

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TEMPLATE FOR MULTIPLE RUNS WHERE WE SWITCH INPUT PARAMTERS

DEPENDING ON MANAR’S RUNS.

Options to be switched out will be labeled “SWITCH”

in comment line above

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GLOBAL INPUTS:

set Dimension = 2
set Use years in output instead of seconds = true
set End time = 1e9

SWITCH

set Output directory = /oscar/data/hclau/hclau/out_0.0-1e23

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GRID OPTIONS:

subsection Geometry model
set Model name = spherical shell
subsection Spherical shell
set Inner radius = 3480000
set Outer radius = 6371000
set Opening angle = 360
end
end
subsection Mesh refinement
set Initial global refinement = 6
set Initial adaptive refinement = 0
set Time steps between mesh refinement = 0
end

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MODEL PARAMETERS:

subsection Gravity model
set Model name = radial constant
subsection Radial constant
set Magnitude = 9.81
end
end

SWITCH

subsection Material model
set Model name = depth dependent
subsection Depth dependent model
set Base model = simple
set Depth dependence method = File
set Data directory = /users/hclau/TPW/viscosity/
set Viscosity depth file = visc_0.0-1e23.dat
set Reference viscosity = 1e23
end
subsection Simple model
set Reference density = 4500
set Thermal expansion coefficient = 2.5e-5
set Viscosity = 1e23
set Reference specific heat = 1000
set Thermal conductivity = 4
end
end

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remove rotation

subsection Nullspace removal
set Remove nullspace = net rotation
end

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INITIAL CONDITIONS

SWITCH

ATTEMPt 1:

#subsection Initial temperature model

set Model name = function

subsection Function

set Coordinate system = spherical

set Variable names = r,phi

set Function constants = A=100, B=75, C=50, D=25, pi=3.1415926536, Ri=3480e3, Ro=6371e3, Ti=5500, To=1700

set Function expression = (r-Ri)/(Ro-Ri)(To-Ti)+Ti + Asin(7phi) + Bsin(13phi) + Ccos(0.123phi+pi/3) + Dcos(0.456*phi+pi/6)

end

#end

ATTEMPT 2:

subsection Initial temperature model
set Model name = spherical gaussian perturbation
subsection Spherical gaussian perturbation
set Amplitude = 0.01
set Angle = 0.8
set Non-dimensional depth = 0.2
set Sigma = 0.2
set Sign = 1
end
end

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BOUNDARY CONDITIONS

subsection Boundary velocity model
set Zero velocity boundary indicators =
set Tangential velocity boundary indicators = top, bottom
end

SWITCH ,

subsection Boundary temperature model
set Fixed temperature boundary indicators = top,bottom
set List of model names = spherical constant
subsection Spherical constant
set Inner temperature = 5000
set Outer temperature = 1600
end
end

SWITCH

#subsection Heating model

set List of model names = constant heating

subsection Constant heating

set Radiogenic heating rate = 1.95e-11

end

#end

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OUTPUT

subsection Postprocess
set List of postprocessors = velocity statistics, temperature statistics, heat flux statistics, visualization, particles, basic statistics
subsection Visualization
set Time between graphical output = 1e6
set Output format = vtu
set List of output variables = material properties
end
end

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Hi Harriet,

From what I can see, the only heating model you specify is constant heating (radiogenic heat production). Since you do not have adiabatic heating in the list of model names, your model would not have adiabatic heating (and you probably want to add shear heating as well).

The adiabatic conditions model only specifies how the adiabatic profile will be computed (and “compute profile” simply uses the material properties from the material model and integrates downwards, which is probably what you want to do here).

However, that’s separate from the model being/not being compressible. The “simple” material model you use for the equation of state is an incompressible material model, so if you wanted the model to be compressible in addition to including adiabatic heating, you would have to use a different base model for the depth-dependent model (like “simple compressible”).

But even for an incompressible model, your temperature profile is not really what I would expect, and it’s not quite obvious to me what causes this behavior.

Juliane

PS: For the future, when posting the content of parameter files, you can put the content between
```
content
```
Otherwise markdown will interpret all the hashtags signs as headings and make it hard to read.

Hi Juliane,

Super super helpful and glad I’m not the only one that thinks the output looks funky. OK - I’ll make those adjustments and see how the field changes.

Really appreciate this! (And the tip on the parameter file!)

Best,

Harriet

@harrietlau :
When you don’t include “adiabatic heating”, you also don’t have adiabatic cooling. That means that any hot blob rising to the surface remains hot, and not just compared to the material at the same depth but indeed compared to the material everywhere. As a consequence, hot stuff accumulates at the top of the domain, and cold stuff accumulates at the bottom of the domain (excluding the boundary layers where conductive heating/cooling dominates). This explains the overall picture you see.

Best
W.

Hi Wolfgang,

Thanks - makes things clear. This is how we (my student and I) figured what was going on.
Appreciate your comment!

Best to you.

Harriet