# Glen's flow law

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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.) using the built-in Elmer viscosity law (recommended, as it is evaluated at Gauss-points):

!! Glen's flow law (using Glen)
!-----------------

! viscosity stuff
!----------------

Viscosity Model = String "Glen"
! Viscosity has to be set to a dummy value
! to avoid warning output from Elmer
Viscosity = Real 1.0
Glen Exponent = Real 3.0
Critical Shear Rate = Real 1.0e-10
! Rate factors (Paterson value in MPa^-3a^-1)
Rate Factor 1 = Real 1.258e13
Rate Factor 2 = Real 6.046e28
! these are in SI units - no problem, as long as
! the gas constant also is
Activation Energy 1 = Real 60e3
Activation Energy 2 = Real 139e3
Glen Enhancement Factor = Real 1.0
! the variable taken to evaluate the Arrhenius law
! in general this should be the temperature relative
! to pressure melting point. The suggestino below plugs
! in the correct value obtained with TemperateIceSolver
Temperature Field Variable = String "Temp Homologous"
! the temperature to switch between the
! two regimes in the flow law
Limit Temperature = Real -10.0
! In case there is no temperature variable
!Constant Temperature = Real -10.0

With the values of the activation energies above, the gas constant has to be given in SI units, i.e., 8.314 J/(mol K). If you do not provide the following section

Constants
Gas Constant = Real 8.314 !Joule/mol x  K
End

the suggested SI default value is used automatically.

This Material section gives the law with a fixed rate factor:

!! Glen's flow law (using Glen)
!-----------------
! viscosity stuff
!----------------
Viscosity Model = String "Glen"
Viscosity = Real 1.0 ! To avoid warning output
Glen Exponent = Real 3.0
Critical Shear Rate = Real 1.0e-10
! gives a fixed value in MPa^-3a^-1
Set Arrhenius Factor = Logical True
Arrhenius Factor = Real \$1.0E-16 * 1.0E18
Glen Enhancement Factor = Real 1.0

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.) using the old power law:

!! Glen's flow law (using power 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-09

!! 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-09 * 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).