Glen's flow law

From Elmer Wiki

This is a SIF entry for Glen's flow law (after: Paterson, W. S. B. 1994. The Physics of Glaciers. Pergamon Press, Oxford etc., 3rd edt.):

!! Glen's flow law
!-----------------
$ function glen(Th) {\
   EF = 1.0;\
   AF = getArrheniusFactor(Th);\
   _glen = (2.0*EF*AF)^(-1.0/3.0);\
}

!! Arrhenius factor needed by glen
!! (in SI units)
!---------------------------------
$ function getArrheniusFactor(Th){ \
    if (Th<-10) {_getArrheniusFactor=3.985E-13 * exp( -60.0E03/(8.314 * (273.15 + Th)));}\
    else {\
       if (Th>0) _getArrheniusFactor=1.916E03 * exp( -139.0E03/(8.314 *  (273.15)));\
            else _getArrheniusFactor=1.916E03 * exp( -139.0E03/(8.314 *  (273.15 + Th)));}\
}

Its call within the Material section looks as follows:

!! call in SI units
Viscosity = Variable Temperature
  Real MATC "glen(tx)"
Critical Shear Rate = 1.0E-03

!! call in scaled units (m-MPa-years)
Viscosity = Variable Temperature
       Real MATC "glen(tx)*31556926.0^(-1.0/3.0)*1.0E-06"
Critical Shear Rate = $1.0E-03/31556926.0

!! this holds for both unit systems
Viscosity Model = String "power law"
Viscosity Exponent = $1.0/3.0

Be very careful in choosing the correct value of the critical shear rate. A too high value leads to a way too soft ice at low shear rates, a too low value can have consequences on the numerical stability (singularity of shear thinning fluid at zero shear).