Weertman.md

User Function Weertman Friction Law

General Information

• USF Fortran File: USF_Sliding.f90

• USF Name: Sliding_Weertman

• Required Input Variable(s): A Flow Solution in Flow Solution Name, Normal Vector

General Description

The file USF_Sliding.f90 contains user functions to apply non-linear friction at the base of glacier.

The first user function (Sliding_Weertman) is a non-linear Weertman-type friction law and is described in this page. The second user function (Friction_Coulomb) is a non-linear water-pressure-dependent friction law, as proposed by Schoof (2005) and Gagliardini et al. (2007), and is presented here. The third user function (Sliding_Budd) is described here and is from Budd et al 1984 (Annals of Glaciology 5, page 29-36).

The friction law in Weertman_Sliding is of the form: tau_b = C.{u_b}^{m - 1} . u_b The Slip Coefficient in Elmer is then given as C.{u_b}^{m - 1} When u_b < u_{t0}, u_b in the previous equation is replaced by u_{t0} (linearisation for small velocity).

The parameters to be given are:

• Weertman Friction Coefficient → C

• Weertman Exponent → m

• Weertman Linear Velocity → u_{t0}

SIF contents

The required keywords in the SIF file for this user function are:

!!! Bedrock Boundary Condition 
Boundary Condition 1
  Target Boundaries = 1

  Normal-Tangential Velocity = Logical True
  Flow Force BC = Logical True

  Velocity 1 = Real 0.0
  
  Slip Coefficient 2 =  Variable Coordinate 1
    Real Procedure "ElmerIceUSF" "Sliding_Weertman"
  Slip Coefficient 3 =  Variable Coordinate 1
    Real Procedure "ElmerIceUSF" "Sliding_Weertman"
    
  Weertman Friction Coefficient = Real 2.412579e-2        
  Weertman Exponent = Real $1.0/3.0
  Weertman Linear Velocity = Real 0.00001

End

Examples

The Weertman friction law is used in the tests [ELMER_TRUNK]/elmerice/Tests/GL_MISMIP and [ELMER_TRUNK]/elmerice/Tests/Contact and especially tested in [ELMER_TRUNK]/elmerice/Tests/Friction_Weertman.