Abstract:

The goal of my project was to observe the water circulation in Lake Mendota using a physical model.  The model I used was made by a student for her coastal engineering project a year ago.  Thank you Erin Hubbard.  The model is made out of plaster and plywood.  My first goal was to make sure the model was waterproof.  My first attempt to do this failed.  I used a two-part epoxy but this did not seal the thousands of tiny holes.  I was then forced to line the bottom of the model in a thin sheet of plastic.  This worked but was not ideal.

There are several reasons to use a physical model.  These are outlined below.

Physical goals of a physical model include

• Physical models seek qualitative insight into a phenomenon not yet described or understood. 
• They are used to obtain measurements to verify or disprove a theoretical result.
They are also used to obtain measurements for phenomenon that are so complicated that they have not been analyzed using a theoretical approach.

Nature is integrated into the equations which govern the phenomenon (no simplifying assumptions are used and no unknowns are omitted as with numerical modeling)

The size of the model is much smaller than the prototype so data can be obtained much easier.

Scale effects are introduced which may affect various forces such as surface tension. 

The model is generally more simplistic than the prototype.

My objective was to determine the effects of wind on the water circulation in Lake Mendota.  The circulation patterns can help explain sediment deposits and areas where erosion is an issue.  I decided to focus on the northern region of the lake where the Yahara River enters the lake.  I narrowed my study to determining the affects of both wind direction and speed.  I hypothesized that both the wind and winds' direction would play a major role in the water circulation.  I guessed that no wind at all and the wind from the South would inhibit water circulation, while the wind from the North would evenly distribute the waters from the Yahara River.  I also thought that the winds from the East and West would concentrate the waters from the Yahara River at the opposite end.  (See the Conclusion section for what really happened!)
 
 

Coastal Environment of Targeted Area:

I chose to focus on the North side of Lake Mendota where the Yahara River enters Lake Mendota.  Notice how this area is relatively flat like a "shelf" and then there is a steep drop off to form a "ridge."  (Note that this map is in meters.)

The Model

For a model to replicate the prototype, geometric and dynamic similarity must be met.  In other words the model and prototype have to look the same and the forces in each have to have the same relative magnitude.  This model is a distorted model meaning that the length scale and vertical scale are not equal.  Also, because this model is a free surface model, surface tension and viscous forces are less important than gravitational or inertial forces.  For this reason, Froude's Number is dominant.  The following is a table showing the scale of the model to the prototype.
 
 

Characteristic	Dimension	Model to Prototype Scale Relation, r
Length	L	Lr = 1:9600
Height	L	Lh = 1:120
Area	L2	Ar = Lr2 = 1:92160000
Volume	L3	Vr = Lr2Lh = 1:110, 592,000,000
Time	T	Tr = Lr1/2 = 97.98
Velocity	L / T	Vr = Lr / Lr1/2 = 97.98

 

Approach to the Issues

In order to test my hypotheses, I used pink dye to trace the circulation patterns.  In order to introduce the dye I used a pump and introduced the dye as if it were the Yahara River.  I then used an industrial sized lab fan and a transformer to control the wind speed.  I recorded the patterns at intervals using a digital camera.  I ran five tests with the intentions of running at least ten.  Time became a factor and I was not able to test the effects of wind speed, only direction.  While keeping the wind speed and the inflow from the Yahara River constant, I tested the effects of the wind; my tests included no wind at all as well as wind from the North, South, West, and East.

Results and Discussion:

Test No.1:  No Wind

This test ran for a total of 70 minutes.  After 30 minutes the dye was circulating counter clockwise as it passed over the steep ridge.  And after 70 minutes the dye began to build up and form "fingers."  These fingers may have been due to either the ridge itself or may have been attributed to the water equilibrating to the temperature of the room (the water I was using for the lake water and the dye was from a hose and was rather cold).
 
 

Test No. 2:  North Wind

The arrows in the picture on the left show the direction the dye was moving after only three minutes.  After 20 minutes the dye was concentrated in the west bay, as outlined in the picture on the left.
 
 

Test No.3:  South Wind

The arrows on the picture on the left show the direction of the flow after 3 minutes.  After 20 minutes the dye was almost completely mixed throughout the lake and was beginning to concentrate near the Yahara River.
 
 

Test No.4: West Wind

Again, the arrows in the picture on the left show the direction of the flow.  This case seemed to result in the most even distribution.
 
 

Test No.5: East Wind

The arrows should be self explanatory by this time.  This case was the most interesting.  After 10 minutes the dye started to circulate clockwise on the shelf near the Yahara River. There is a closer view of this below.  The water seemed to just pass over the ridge and then would get caught by the wind from the East and forced back onto the shelf.

After 20 minutes the dye became concentrated towards the west side of the lake.
 
 

Conclusion:
The results from my project are qualitative because of the limitations of a physical model.  I have proven that the wind direction has a definite impact on circulation.  The winds from the East and South (as well as no wind at all) impede circulation from the Yahara River into Lake Mendota.  Winds from the West and North help to circulate the water from the Yahara River into Lake Mendota.  As far as wind speed is concerned, I did not have time to evaluate this realm of circulation.
 
 

References:

Kamphius, J.W. (1985), Physical Modeling in Coastal Engineering, (R.A. Dalrymple, Editor), A.A. Balkema, Rotterdam

Erin Hubbard, (1999), Physical Model of Lake Mendota, http://www.cae.wisc.edu/~chinwu/CEE514_Coastal_Engineering/2000_Students_Web/Erin_Hubbard/Modeling_lake_Mendota.htm

Kamphius, J.W. (2000), Introduction to Coastal Engineering and Management, World Scientific Publishing

Wisconsin Department of Natural Resources, Nonpoint Source Control Plan
for the Lake Mendota Priority Watershed Project, (May 1997), http://www.dnr.state.wi.us/org/water/wm/nps/plans/mensum/mendota.htm

Center for Limnology, UW-Madison,http://scifun.chem.wisc.edu/chemweek/lakelore/lakelore.html

Beletsky, D. (1999) Journal of Great Lakes Research Volume 25, Great Lakes Environmental Research Laboratory http://www.glerl.noaa.gov/data/char/circ/mean/mean-circ.html