Physical Model of Lake Mendota
 
 
 
 

The contour lines in this sketch are at 2 meter intervals

  1. Introduction
Lake Mendota in Madison Wisconsin is one of the most studied lakes in the world, biologically.However, little research has been undertaken to understand the hydrology or sediment transport regimes of the lake.Recently this has become a problem in that an area required for navigation is filling in with sediment of an unknown origin.
  1. Objectives
    The physical bed model is intended to consider possible source locations and determine which is most likely.
  1. Background
 Sediment accumulation near the Yahara River inlet (see contour map) has impeded boat traffic in the area.  Area residents have supported a dredging project for the past couple of years.  However, the rate of sediment accumulation and cost of dredging make this project one that might best be remedied some other way.
  1. Project Design
The main issues with this design were, what to build the model with and how to make it.A four-foot by four-foot model seemed reasonable and results in a nice even scale relationship of one inch on the model being equal to eight hundred horizontal feet of the lake (1:9600).The vertical scale is different to reduce the effects of evaporation and surface tension.It sets one inch of the model equal to ten feet of lake depth (1:120).

 Froude number modeling will be used to relate the model to the prototype since gravitational forces are assumed to be more important that viscous ones.The equation for the Froude number is as follows:

Where u = velocity

g = gravity constant (9.81 m/s2)

L = length of any pertinent portion, usually the depth of the lake

 To keep the Froude number the same in the model and prototype the following relationships will also be required.
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

    5. Model Construction

Using these dimensions, the model can then be constructed easily of plywood and plaster.The contours are  being developed using the Madison Area Lakes map distributed by the Geological and Natural History Survey.   Once drawn on a plywood base, they will be built up to the contours using drywall plaster with nails rising to the   correct height as guides.Two different layers of this system will be required since the maximum nail height is   4 inches and the model will be roughly 8 inches high.
  1. Transport Modeling
 Water will be the fluid used in the model since it is inexpensive and easily available.

 The sediment used to model that presently on the bottom of the lake will be selected in accordance with the Noda Model Law, which has been used successfully by the US Army Corp of Engineers in several model applications.

 The sediment will be placed in a thin veneer on the model surface so that both scouring and filling can be examined.

 Water cycling through the lake will be accomplished using a pump, which distributes water at the mouth of the Yahara and retrieves it at the Yahara Locks.

 Wave action will be reproduces using motorized paddles and wind will be simulated with small, mechanized fans blowing from the prevailing wind direction.

 As of this time, no mechanism will be used to model motorboat traffic since it is not considered a major sediment source.

  1. Results
This section is not yet finished, since the model has not yet been constructed or run.The same true for the section titled“Discussion”.
  1. Discussion
  2. References
       Hoopes, J.A.(2000) Correspondence, University of Wisconsin-Madison.

 Grace, P. J. (1989), Investigation of Breakwater Stability at Presque Isle Peninsula Erie, Pennsylvania, Technical Report CERC-89-3, Department of the Army, Buffalo, New York, pp 9-10.

 Kamphius, J.W. (1985), “On Understanding Scale Effects in Coastal Mobile Bed Models,”Physical Modeling in Castal Engineering, (R.A. Dalrymple, Editor), A.A. Balkema, Rotterdam, pp. 141-162.

Murphy, G. (1950),  Similitude in Engineering, The Ronald Press Company, New York, pp. 167-169.

 Seabergh, W.C. (1983), Design for Prevention of Beach Erosion at Presque Isle Beaches, Erie, Pennsylvania, Technical Report HL-83-15, Department of the Army, Buffalo, New York, pp 9-20.

 Wu, C.H. (2000), Correspondence, University of Wisconsin-Madison.