## User Function USF_LateralFriction

### General Informations

• USF Fortran File: `USF_LateralFriction.f90`
• USF Name: `LateralFriction_x` and `LateralFriction_y`
• Required Input Variable(s): A `Flow solution` in `FlowSolverName`

### General Description

This user function return the modified gravity force -g + K * |u|^(m-1) u
where K is the a `lateral friction coefficient` and m the `lateral friction exponent`, as in Gagliardini et al. (2010). When m=0, this is equivalent to the shape factor (no dependency to the velocity). How to evaluate the `lateral friction coefficient` K as a function of the glacier width W is given in the supplementary material of Gagliardini et al. (2010). Noting that K as defined here is equal to K/rho_i in the paper, it comes K = (n+1)^(1/n) / [rho_i W^(1+1/n) (2A)^(1/n)] and m=1/n (A and n are Glen's law parameter and exponent, respectively).

This solver works only in 2D (no sense in 3D). It works for non-structured mesh.

### SIF contents

The required keywords in the SIF file for these user functions are:

```\$yearinsec = 365.25*24*60*60
\$rhoi = 900.0/(1.0e6*yearinsec^2)
\$gravity = 9.81*yearinsec^2
\$Afactor = 80.0
\$n = 3.0
\$etai = 1.0/(2*Afactor)^(1.0/n)
\$W = 10.0e3
\$Kspring = etai* (n+1)^(1/n) / (rhoi * W^(1+(1/n)))

Body Force 1
Flow BodyForce 1 = Variable Coordinate 1
Real Procedure "ElmerIceUSF" "LateralFriction_x"
Flow BodyForce 2 = Variable Coordinate 1
Real Procedure "ElmerIceUSF" "LateralFriction_y"

Lateral Friction Gravity 1 = Real 0.0
Lateral Friction Gravity 2 = Real \$-gravity
Lateral Friction Coefficient = Real \$Kspring
Lateral Friction Exponent = Real \$1.0/n
Flow Solver Name = String Flow Solution
End
```

### Examples

An example using the user function USF_LateralFriction can be found in `[ELMER_TRUNK]/elmerice/Tests/LateralFriction`.

### Reference

When used this solver can be cited using the following references:
Gagliardini O., G. Durand, T. Zwinger, R. Hindmarsh and E. Le Meur, 2010. Coupling of ice-shelf melting and buttressing is a key process in ice-sheets dynamics, Geophys. Res. Lett., 37, L14501, doi:10.1029/2010GL043334. 