# [CIG-MC] units for viscE?

Eh Tan tan2 at geodynamics.org
Thu Mar 26 12:22:49 PDT 2009

```John Armitage wrote:
> Hi,
>
> Perhaps this is a simple question, but I am struggling to understand the
>   units for the parameter viscE. This is the activation energy (?),
> which for olivine is 540 kJ/mol. This is the input value I have used for
> my old 2D version of Citcom (divided by the gas constant).

Hi John,

Citcom deals with non-dimensional units. You will need to
non-dimensionalize the activation energy in the input file.

For example, if you use "rheol=2", the formula of viscosity in the code is:
visc' = visc0' * exp{[E->viscosity.E + (1 - z) * E->viscosity.Z]
/(T' + E->viscosity.T)};

The Arrhenius formulation for viscosity (dimensional) is:
visc = visc0 * exp[(Ea+p*Va)/(R*T)]
where Ea is the activation energy, Va is the activation volume, p is the
hydrostatic pressure, T is the absolute temperature.

Applying non-dimensionalization:
T = DT * (T0' + T')
p = (1-z) * rho * g
where DT - temperature contrast (from Rayleigh number)
T' - nondimensional temperature
T0' - nondimensional surface tempereture
=>
visc = visc0 * exp{(Ea+p*Va) / [R*DT*(T0' + T')]}
= visc0 * exp{[Ea/(R*DT) + p*Va/(R*DT)] / (T0' + T')}

so:
E->viscosity.E = Ea/(R*DT);
E->viscosity.Z = Va*rho*g/(R*DT);
E->viscosity.T = T0';

Note that visc0 also needs to be non-dimensionalized. This will affect
how you define the Rayleigh number.

> The input for viscE in the new Citcom (plume-input, in the inflow
> version) is 6.9077553. Where does this number come from?

The default "rheol=0" has this formula for viscosity:
visc = visc0 * exp[E->viscosity.E * (1 - T)]

This formula is not based on Arrhenius equation, and E->viscosity.E does
not correspond to the activation energy in physics.
So, if one wish to have 1000x viscosity variation in the model, he/she
will use viscE = log(1000) = 6.9077553.

--
Eh Tan
Staff Scientist
Computational Infrastructure for Geodynamics
California Institute of Technology, 158-79