INTRODUCTION

 

AREA OF CONCERN

Wave refraction and wave breaking emanating from Lake Mendota into the Yahara River outlet will be examined.  Lake Mendota is located in Madison, Wisconsin (shown on the left).  The Yahara River originates in Columbia County and eventually empties into Lake Mendota.  The outlet region is illustrated in the figure on the right.

                

                                   http://www.greeningearthsociety.org/                                                  http://limnology.wisc.edu/lake_information/mendota/mendota.html

REASON FOR CONCERN

Lake Mendota is the largest water body in Dane County and is the most heavily used in southern Wisconsin.  Recreational boaters of the lake spend an estimated $3 million per year in the local economy (DNR, 2003).  The Yahara River outlet is an important channel for boats traveling in and out of Lake Mendota.  The outlet is very shallow and needs to be dredged to provide clearance for boats. In 1994, a large dredging project was conducted with the assumption that another dredging project would not be required for another 40 years.  However, sediment has accumulated at a rapid rate which has necessitated additional maintenance dredging.  The shoreline erosion and new sediment accumulation in the outlet is illustrated below.  The phenomena that enhances shoreline erosion and creates rapid sediment accumulation in particular regions must be identified.   Only then, can decisions regarding long term projects be made for the channel. 

                                                        Source:  Dane County Department of Public Works

 

WAVE REFRACTION

Wave refraction is the process by which intermediate of shallow water waves have their direction changed because the bottom contour is not parallel to the wave crest.  Refraction typically occurs in transitional to shallow water depths because the wave celerity decreases with decreasing depth.  As a result, the portion of the wave crest that is in the more shallow water will progress forward at a slower speed compared to the crest portion that is in deeper water.  This results in “bending” of the wave crests to become increasingly parallel to the shoreline.  The bending also generates increases/decreases in the wave energy and wave height.  Wave refraction may also be generated from wind or currents.

 

 

 

 

 

 

 

                                                                                                                       

                                                                                                                        Source: www.rocks.gg.utk.edu 

WAVE BREAKING                                                                                                     

In shallow water, the maximum wave height is limited to:

        OR                             Miche (1944)

If the ratio of the wave height to water depth is greater than 0.9 in shallow water, the wave will break.

 

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