Index
 Natural Example Model Data Physics Analysis References
Results

Movement of Set up
For all data that produced graphs of the displacement data the movement of the glacier downstream was from the bottom of the picture to the top.  The displacement vectors derived, showed that there was a dominate movement of the particles down glacier with there being only minor movement of the glacier to sides of the glacier.  The grounding line of the glacier, the level of the water, is the line in the middle of the graphs.  The end of the constraints of the tube is around the top line of the graphs, this will be where the lobe is produced by the flubber that is later cut off.  The lines of the constrains are drawn on each of the graphs.  The picture to the right is the setup that I used for analyzing the displacement vectors.

To extract data from the photos that were taken, I digitized particles at two times and calculated a displacement field which is shown in the first two pictures above.  I then used this as a proxy for the velocity field.  From the velocity field I calculate dthe components of the velocity gradient tensor seen below.

Velocity Tensor

Velocity Data
The first graph is from the fourth run of the model, where these vector analysis was produced in the program Surfer.  The two time periods that I used were 2 hours and 10 minutes and 2 hours and 15 minutes of the run.  This was the two time sets right before the first cutting off of the lobe produced by the flubber.  The second graph is from the next two time periods, from 2 hours and 20 minutes and 2 hours and 25 minutes.  The third graph is the second velocity field subtracted from the first velocity field.  The move negative the acceleration, the larger the difference between the two times, where the second time period is moving faster the first one.

The reason that I cut out the data from the below the 600 point is that when I was analyzing the data from below that area in the first time period there was a very low frequency of data points in the area.  This caused the velocity field to say that there was slowing in the area below 600 point on the y-axis and in-between the 550 and 800 point on the x-axis.  This area should have had much higher velocity.  This caused there to be a much higher acceleration in those areas.  The low frequency of data points may have caused the program Surfer to misinterpret the velocity field in the area.  So to correct this problem I decided to omit the data in the acceleration graph.

Even with the possible error, there seems to be an overall acceleration of the flubber from Time 1 to Time 2.  This can be seen by the contour graph having an overall negative movement, with some areas moving faster than others.  The fastest movement of the flubber is -13 points per square minute and an average movement of -3 to -4 points per square minute.  The reason that the flubber does not move constantly is probably due to the internal structure of the flubber.  There is an area of slowing along the right side of the graph.  This is most likely an error due to different frequencies of data points in the area.  Top
Strains Time 1
Strains Time 2


The volumetric strain rate from the graphs does not show a huge pattern other than there is an overall deficit of the volume down glacier.  This means that there is a change in the amount of flubber from one time to another.  In time 2 there seems to be slight banding of the change of volumetric strain.  There seems to be layers of positive change followed by areas of negative volumetric strain.  This is probably due to the banding of the added layers of the added flubber in the model.  This can be seen in the pictures by crevasses or slight indentations created in glacier.  This can be seen in figure at the top of the page.
Equations that were used:
equations
These equations came from Koons 1995.


The graphs also show that there was a shear strain in the system that had the flubber being strained from the center of the glacier to the sides of the glacier, with little change in the horizontal direction.  This data leads to the idea that there is a large amount of strain along the sides of the glacier.  This shear would have been produced by the friction between the flubber and the walls of the tube.  Both times show that there is a mirroring of the shear strain along the center of the system, with there seeming to be an equal amount of shear on both sides, with the right side being negative and teh left side being positively sheared.  Top