## User Function Weertman Friction Law

### General Informations

• 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 dependant 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:

The Slip Coefficient in Elmer is then given as

When , in the previous equation is replaced by (linearisation for small velocity).

The parameters to be given are:

• Weertman Friction Coefficient
• Weertman Exponent
• Weertman Linear Velocity

### 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.