Written and prepared by Jered Hansen
University of Wisconsin-Madison
Department of Civil and Environmental Engineering

Sky rocketing water front real-estate prices along with an increasing amount of Jet-Ski owners has lead to speculation and concern on the effect of Jet-Ski generated waves on shoreline erosion.  This erosion not only causes a loss of land but also causes habitat destruction, sediment resuspension, and the release of nutrients (phosphorous and nitrogen) which promote algae blooms.  Boats are know to cause a slight increase in shoreline erosion, but the effects of Jet-Ski generated waves have yet to be determined.  The continuous crashing of waves on the shoreline naturally causes it to erode and wash away, but are Jet-Ski's inflicting a significant impact on the waves that bombard the shore?  This project will reveal if Jet-Ski generated waves are a legitimate cause for concern along precious waterfront property.

Whitewater Lake

Lake Characteristics:

Whitewater Lake covers 640 square acres and is located 50 miles south east of Madison.  The Lake has a mean depth of 11 feet and a max depth of 38 feet.  The surrounding shoreline of Whitewater Lake is primarily taken up by residential housing and restaurants.  The majority of houses surrounding the lake are used for weekend vacation homes.  Activities such as boating, swimming, and fishing are enjoyed here.  The increase in residential housing has resulted in much more traffic on Whitewater Lake.  Making up a large portion of this increased traffic are Jet-Skiers which flock to the Lake in an attempt to unleash their wild side.

Objective:

My intentions for this project are to compare boat generated waves with jet-ski generated waves.  These sources of waves will be analyzed and compared by means of wave kinematics (sediment resuspension) and wave dynamics (wave energy density and wave power).

Motivation:

Whitewater Lake was chosen for my research project because a good friend of mine, along with his family, owns a house on the lake.  I often come here during the summer months to boat and Jet-Ski.  With shoreline property on this Lake doubling nearly every ten years, the concept of shoreline erosion is a primary concern for many lake front property owners.  Sediment resuspension is another negative effect that induced waves can cause on lakes.  It is directly related to the bottom water velocity which is increased by waves.  Out of curiosity, I want to assure myself that the recreation I so often seek on this lake is not causing an increased effect on shoreline erosion or the endangerment of the lake.  Below, you will find an aerial photo Whitewater Lake.

Data Collection

The data was collected by choosing three locations on a dock in which the water depth was known and considered to be deep, intermediate, and shallow.  (see image below)  At each of these locations I had my partner drive the Jet-Ski by at velocities of 15 MPH, 30 MPH, and 45 MPH.  Wave characteristics, such as wave period, wave height, and wave length, were collected for the generated waves of the three different velocities.  The wave characteristics of each velocity at each location was were measured several times to assure the accuracy the the recorded value. 

Calculations

Characteristics of waves generated by a Jet-Ski:

Energy Density

Wave Power

The power generated by a wave is also a direct indicator of the erosion impact it will cause on the shoreline.  Wave power can be calculated by using the following equation:

                                                                                    Equation 2

where c=L/T, n=0.5 for deep water, 1 for shallow water, and can be calculated by the equation 3 for intermediate water.  Since the wave power should essentially be the same at deep, intermediate, and shallow water, the average wave power for each velocity will be calculated and used in the analysis.  The wave power has been calculated for the different velocities at each location and placed in Table 1.

Sediment Resuspension

Fine sediments carry most of the contaminants that are introduced into lakes.  When these sediments are resuspended the contaminants associated with them are reintroduced into the water.  Also, when sediments are resuspended, they can be further eroded or transported throughout the lake.  For this reason it is critical to limit the amount of sediment resuspension caused by human induced waves.  Sediment resuspension is directly related to the lakes bottom water velocity.  This bottom velocity (See Table 1) can be calculated using the wave calculator or the following equation from the course notes:

Table 1:  Collected and collected data from Jet-Ski generated waves

Characteristics of waves generated by a boat:

Energy Density

The characteristics of boat generated waves will be calculated using theoretical formulas and ultimately compared to the characteristics of Jet-Ski waves.  Before calculating the energy density, the wave height must first be obtained using the following equation which was created by Bhomik et.al. in 1991.

 Equation 5

Wave Power

The wave power can be computed through implementation of the wave calculator.  The requirements of the wave calculator are to input the deep water wave height, deep water wave period, and local depth.  The wave calculator will then compute the corresponding wave length which is required to calculate the wave power.  I will assume that the deep water wave height is 93.3% of the max wave height which is the case for the recorded data from Jet-Ski waves.  I will also make the assumption that the deep water wave periods are roughly the same for boat and Jet-Ski waves.  The resulting computations for wave energy density and wave power can be seen in Table 2 below. 

Sediment Resuspension

The calculated wave characteristics of boat generated waves can be plugged into the wave calculator or equation 4 to obtained the bottom water velocity.  The results can be seen in Table 2. 

Table 2:  Calculated data for boat generated waves

Results

Wave Energy Density Comparison

Wave Power Comparison

The energy density for boat waves was larger then Jet-Ski waves at all water depths.  This is due to the slightly larger wave heights that a boat emits.  It is evident that the energy density emitted by both vessels in intermediate water is about half that of the energy density in shallow water.  The deep water values consistently lie in between the two.  Through research, it was also brought to my attention that vessel generated waves cause significantly more damage to the shoreline in narrow water ways then they do wide open water.  Both of these are reasons why "No Wake" signs are placed at shallow and narrow locations of a body of water.  This statement holds true for Whitewater Lake.  If you look at the aerial photo of Whitewater Lake you will notice that it becomes narrow at two different locations in the middle in the middle of the Lake.  Both of these locations have floating "No Wake" signs.  These signs have been strategically placed in locations where Jet-Ski and Boat waves can produce relatively large energy densities.  It is also apparent, from the graph, that the energy density from going 15 MPH is about twice the magnitude of the energy density from going 45 MPH.  This indicates that if an individual driving a boat/jet-ski while passing a "No Wake" zone simply slows down to a speed considered to be acceptable (around 15 MPH) then they will be inducing more harm on the shoreline then if they were going full speed. 

The wave power graph provides similar characteristics to those just discussed.  The wave power generated from boat is slightly more then the power generated from a Jet-Ski at all velocities.  Also, a higher wave power results from a slower velocity which signifies more potential for shoreline erosion.  The wave power created from a vessel traveling 15 MPH is three times the wave power created when traveling 45 MPH.  This may seem counterintuitive to many but it was a common thing observed throughout the project. 

The bottom velocity of the water was nearly identical for boat and Jet-Ski generated waves at all vessel velocities and locations.  The velocity at the bottom also increases with a decrease in depth.  This goes along with what we were taught in the course notes.  It came as a surprise that the bottom velocity more then doubled from intermediate to shallow water.  This is a large jump when considering that the difference in location of the two recorded data sets was less then one meter apart. 

Causes for Error:

While this project was carefully carried out, there were clearly assumptions made along that way that could have affected the quality of the results.  This research project was not meant to product results that are 100% accurate, but merely to provide a rough analysis of wave characteristics for boat and Jet-Ski waves.