There are various ice rheology implemented in Elmer/Ice.

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 suggestion 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 (MATC function):

!! 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

Strictly speaking the homologous temperature should be used as input to the Glen function above, but if homologous temperature is not readily available then using temperature (in Celsius) is a good approximation (which deteriorates for thicker glaciers/ice sheets).

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).

An example using Glen's flow law can be found in `[ELMER_TRUNK]/elmerice/examples/Test_Glen_2D`

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The flow of **anisotropic** ice can be modelled using the General Orthotropic Flow Law (GOLF) from Gillet-Chaulet et al. (2005) implemented in the AIFlow Solver or the Continuum-mechanical Anisotropic Flow model based on an anisotropic Flow Enhancement factor (CAFFE, Seddik et al., 2008) implemented in the User Function CAFFE. The evolution of the fabric as a function of stress and velocity gradient for both anisotropic models can be computed using the Fabric Solver.

The rheology of **porous ice**, namely firn and snow, is represented using the porous law proposed by Gagliardini and Meyssonnier (1997). This law is implemented in Elmer/Ice in the Porous Solver. Density evolution can be computed from the mass conservation equation.