Homework #8 ESP Humphrey 2015
This will be our last
investigation of numerical landscape modelling of Geomorphic
processes. This exercise is designed to
show you that it is possible to answer relevant questions by combining some
ideas of how our world erodes with simple modelling. As in previous questions, these questions can
be addressed in Excell or MATLAB or the program of
your choice. Come talk to me if you get stuck.
Questions:
0. However, the first
thing I want to see is a couple of sentences describing the geomorphic
feature which you want to study for your project. Tell me where it is, and what you think it
is.
Ok, now for our last effort with modeling. Hopefully you have got your model working and this shouldn’t be too hard. The first 2 questions should be quick and easy. Question 3 is just to get Reynolds numbers in your mind. Question 4 is only for those of you that are not struggling with the modeling, even though it is a lot of work I will only give 1 mark for the entire 4th question.
1. The above figure is a
cross-section of two gulleys in the Laramie Basin,
separated by a remnant pile of erodable material
about 5m high, with dimensions in the figure, with a 1 meter grid. Model the
behavior of the interfluve, under the process of just rainsplash.
Assume the erosion rate, C, is as in previous problems. And assume points A and
B don't move up or down. (hint: this just requires
rewriting the initial topography in the previous homework). Run your model until the hillcrest is lower
than point A. At
what time does this occur? (Hint:
this problem is very similar to the previous homework, but the time is much
longer. You may run out of room in your
spreadsheet! You might need to write
this so that every 10,000 years or whatever, you start over again, by moving
the final elevations back to column A, and starting again. Also note you only need to model the region
between A and B)
2. Now assume points A and B
are the locations of small streams. Point B is eroding downward at 1m per
5000years, but A is not eroding. What happens to the interfluve and streams
over time? Specifically, when will the stream at B capture
the stream at A? Hint, what you need to do is change the
Boundary Condition [BC] at the location of B.
The way to do this is to move the elevation of B down the appropriate
amount with each time step. Other than
that, the problem is again similar to the previous problem. You can assume that B will capture stream A
when it is downhill all the way from A to B.
3. Estimate Reynolds numbers, and use them to
describe the state of turbulence in the region of:
a) ·
the Laramie River,
b) ·
a grain of 1mm sand falling at 5cm/sec in the Laramie River, (the trick is to
decide what length scale to use)
c) ·
a grain of 1mm sand on the bed of the Laramie River, (the trick is to figure
out which velocity to use)
d) ·
the weather (atmosphere) above Laramie, (the trick is to figure out the D,
distance to use)
e) ·
a cup of coffee as you add cream,
f) ·
water in a squirt gun nozzle,
g) ·
a swimming amoeba.
4. (this
weeks geomorph puzzle)
Model the figure above for sheetwash and rainsplash. Use a Dsheetwash
as in previous problems. Model the
evolution for 20,000yrs. (Hints, you
need to move the x origin to the top of the bump. With the origin x=0 at the hill crest your
model should work for the right hand slope down to B, but you may have problems with the left
hand slope because the x distances are negative. You can solve this two ways: one is to just
make all the x values be positive in the leftward direction, this should work
and is the easy method. The more elegant
method is to be very careful with the signs, in particular remember that Dx is negative. If you are careful, this approach will also
work.) The answer to this question is a
plot of the profile.
Good luck, ask your friends, and then ask me, if you have trouble. Question 4 is fairly advanced stuff.