Hello,

I have been trying to use the AIFlow solver and I've run into a wall about understanding how the fabric inputs relate to the output velocity. In the papers (e.g., Ma et al., 2010, p. 807) and the Elmer/Ice documentation, it seems that the fabric factors a11, a22, a33 describe the orientation of the c-axes. Therefore, for a tight single pole fabric at e.g., the bottom of an ice core, we would expect something like a11=a22<<a33= approx 0.9. However, this doesn't seem to agree with the velocity patterns returned by the AIFlow solver. I have tried multiple geometries, but I'll explain one here. Take a simple vertical cylinder filled with ice (z defines the axis of the cylinder), which will exhibit Poiseuille flow in the negative vertical direction. One would expect that if the c-axes are vertical, the velocity would be lower than if the c-axes are horizontal. However, using the AIFlow solver with

Fabric 1 = Real 0.0

Fabric 2 = Real 0.0

in the sif file results in z velocities two orders of magnitude higher than with

Fabric 1 = Real 0.0

Fabric 2 = Real 1.0

or

Fabric 1 = Real 1.0

Fabric 2 = Real 0.0

in the sif file. (The latter two yield similar velocity magnitudes.) All models produce the expected flow pattern, but with the reverse of the expected velocity relationship (i.e., when c-axes are horizontal, flow is slower than when c-axes are vertical). This suggests that the Fabric factor is defining an ease-of-slip direction rather than the normal to the ease-of-slip plane (=c-axes). I do not incorporate any fabric evolution in this test case, so the prescribed Fabric factors are constant. I have tried several different viscosity models, with the most recent being 010010010.Va. Any suggestions as to what I am missing? Happy to provide the sif and geometry if it would be useful.

Thanks,

Chris

## AIFlow fabric directionality

### Re: AIFlow fabric directionality

Hello,

I have commited a fix for the computation of the euler angles for the fabric orientation in 3D.

But I think, as I understand you cylinder set-up, that your results are correct, i.e. vertical one maximum fabrics are more favorable than horizontal 1 max fabrics.

For perfectly aligned fabrics (i.e. a3=1;a1=a2=0), the orthotropic law degenerate to the single crystal transversely isotropic law with the c-axes along direction 3. In this case the most favorable deformation mode is shear 13 or 23, it is 100 times easier than shear 12 (100=1/beta, see nomenclature of the viscosity file).

Not easy to guess what exactly will be the strain-rate and stress fields in your cylinder set-up; but I assume that shear parallel to the cylinder wall will dominate. If the c-axes is vertical all the vertical planes are as easy to shear (i.e. it correspond to shear 13 or 23). We always have the image of a desk of cards to represent the deformation of the ice-crystals, because of the symetry of the stress and strain-rate tensors, shearing a plane containing the c-axis in the direction of the c-axis is as easy as shearing the basal plane.

On the contrary, If the c-axis is horizontal, along direction x for example, shear xz is easy (shear 13 for the crystal) but shear xy (shear 12 for the crystal) is 100 times harder. I think this can maybe explain your 2 order of magnitudes difference in the velocity field, with the most favorable case when the c-axes is vertical.

hope that helps.

cheers

fabien

I have commited a fix for the computation of the euler angles for the fabric orientation in 3D.

But I think, as I understand you cylinder set-up, that your results are correct, i.e. vertical one maximum fabrics are more favorable than horizontal 1 max fabrics.

For perfectly aligned fabrics (i.e. a3=1;a1=a2=0), the orthotropic law degenerate to the single crystal transversely isotropic law with the c-axes along direction 3. In this case the most favorable deformation mode is shear 13 or 23, it is 100 times easier than shear 12 (100=1/beta, see nomenclature of the viscosity file).

Not easy to guess what exactly will be the strain-rate and stress fields in your cylinder set-up; but I assume that shear parallel to the cylinder wall will dominate. If the c-axes is vertical all the vertical planes are as easy to shear (i.e. it correspond to shear 13 or 23). We always have the image of a desk of cards to represent the deformation of the ice-crystals, because of the symetry of the stress and strain-rate tensors, shearing a plane containing the c-axis in the direction of the c-axis is as easy as shearing the basal plane.

On the contrary, If the c-axis is horizontal, along direction x for example, shear xz is easy (shear 13 for the crystal) but shear xy (shear 12 for the crystal) is 100 times harder. I think this can maybe explain your 2 order of magnitudes difference in the velocity field, with the most favorable case when the c-axes is vertical.

hope that helps.

cheers

fabien

### Re: AIFlow fabric directionality

Thanks for the explanation Fabian. I will take some time to make sure I follow everything you said and post another reply if I have further questions.

Chris

Chris