Modeling Energy Loss with Reef Balls

Wave Transmission

Looking at my experimental results, the wave heights measured before and after can be compared to see if wave attenuation was effective. In order to do this, the equations found in the technical background will be used to compare the expected results with the actual.

Water Depth	Experiment	Wave Height Reef Balls, Before, Hc (in.)	Expected Wave Height After Reef Ball (in.)	Actual Wave Height After Reef Balls, Ht (in.)	% Wave Height Reduction
5.25 ''	A	1.75	1. 45	1.25	28.6
5.25 ''	B	1.25	1.04	.75	40.0
4.25''	C	2.75	2.08	1.75	36.4
4.25''	D	1.75	1.32	1.25	28.6

Table 1: Comparing two different water depths and their ability to attenuate waves, the wave heights

before and after the reef ball are shown, along with the expected results and percent wave height reduction

In every case, as shown in table 1, the actual wave height was less than the expected wave height. Overall, the actual wave heights are less than the expected wave heights. This means that the reef balls did a better job at attenuating the wave, than the equations predicted using the minimum Kt value. However, it is important to consider that too much of a decrease in wave height can force the wave to have not enough energy. This may allow the sediments to drop out of suspension too soon and sediments will accumulate just past the lee of the structure. Instead, the sand needs to stay in suspension long enough to reach the shoreline and then drop out to result in accretion. Unfortunately, the percent wave height reductions did not meet the 60% wave height reduction requirements of the Freibel and Harris method. This may be due to many different factors. First, my assumptions may not have held true throughout the experiment and could have altered the wave heights. Second, this experiment was performed at an elementary level to provide a basic conceptual understanding of how reef balls, acting as submerged breakwaters, can attenuate wave energy. Therefore, data recording may not have been the most accurate. In addition, the length of the wave tank used for the experiment was not long enough to ignore the impact reflected waves could have on the wave height after passing the reef balls. Reflected wave heights, when passing the wave propagating past the reef balls will create an amplified wave height, which could have caused the wave measurement to be higher than it would be in reality.

Taking a look at how the difference is water depth affected the wave transmission coefficient, Kt, can be seen in table 2. Using equation 2 from the technical background section and values that would give Kt the minimum amount of wave reduction to still be effective, Kt should not be any larger than .892.

Wave Depth	Experiment	Experimental Wave transmission coefficient, Kt
5.25''	A	0.714
5.25''	B	0.600
4.25''	C	0.640
4.25''	D	0.714

Table 2: A comparison of how Kt varies with the wave depth. The experimental Kt correlates

to the corresponding experiment.

Energy Density

Using equation 4 from the technical background, the wave energy density can be calculated using the wave heights measured from the experiment as shown in table 3. These energy densities then can be analyzed to find the percent wave energy loss resulting from the artificial reef (Table 4).

Wave Depth	Experiment	Energy Density Before (N-m)	Energy Density After (N-m)
5.25''	A	2.42	1.66
5.25''	B	1.24	.856
4.25''	C	5.98	3.42
4.25''	D	2.42	1.32

Table 3: Measurements of the energy density before the reef balls and after the wave has passed the reef balls

Experiment	% Energy Loss
A	31.4
B	31.0
C	42.8
D	45.5

                                              Table 4: The percent of wave energy density lost after the
                                            wave travels over the reef balls

             The results show that a significant amount of energy is lost as the waves propagate over the reef balls. Although these percent energy losses may not reflect the necessary amount to ensure sediment deposition along the shoreline, conceptually what can be seen is that reef balls can be placed in strategic locations off the shoreline to manipulate wave properties, such as energy density. With the proper design, wave heights can be effectively decreased, potentially resulting in shoreline stabilization.

        Even though this experiment demonstrates the concept of wave attenuation with reef balls, looking at a case study will help exemplify the effectiveness in using reef balls to attenuate wave energy.

Case Study:
Gran Dominicus Resort, Dominican Republic

    Around 450 reef ball units were deployed into the water at the Gran Dominicus Beach Resort, along the southern coast of the Dominican Republic, to maintain their shoreline. Both the stability and the results of implementing the reef balls will be discussed.

Figure 2: On the left is a picture of the shoreline before the reef balls were installed in the Summer of 1998. The picture on the right shows the gain in shoreline after the reef balls were implemented in April 2001. (Harris, 2001)

Reef balls provide a long term solution because their material and stability offer resistance to brute forces. In order to ensure stability, strong rebar reinforcement was drilled into the ground to help the reef balls stay in place. Shortly after the reef balls were installed, a hurricane hit the island; however, an inspection was performed afterwards and none of the reef balls had moved. However, as water levels increased during the hurricane, the wave heights surpassed the wave height limit that reef balls can effectively attenuate wave energy. Therefore, if water levels do become significantly high enough, during events like El Nino, which can cause severe storms, increased storm waves will not be affected by the reef balls and can continue to erode the shoreline.

Figure 3: A profile view of the West Breakwater Gap Beach monitoring shoreline growth from

February 1999 to April 2001 (Harris, 2001)

At Gran Dominicus Resort, implementing reef balls has been very successful, and shoreline accretion has resulted as can be seen in figure 2. Furthermore, no adjacent shoreline effects have been noted; in fact, adjacent shorelines have also experienced accretion (but not as significant as the shoreline directly impacted by the reef balls) (Harris, 2001). Figure 3 depicts a ten meter gain in shoreline as a result from implementing these reef balls. Although this solution seem beneficial, drawbacks can result from a successful project like this. For instance, reef balls are not placed very far off of the shore to begin with. As shown in figure 3, only about 15 meters, about 45 feet, of swimming area is permitted after the shoreline has widened . Possible solutions could be to reduce the gain in shoreline by removing some sand through beach nourishment processes. Removing a small amount of accreted sand can provide a larger area for swimmers and it can also be stored in reserve in case a hurricane or big storm does come along and washes out the shoreline (Harris, 2001). This additional sand then can be added back to the shoreline in a very cost effective manner.

Discussion
Overall, my project has demonstrated how reef balls act as submerged breakwaters to decrease the wave height as it passes over the structure. This decrease in wave height may allow sediments to drop out of suspension. The smaller the distance between the top of the structure and the air-water interface, the greater the potential for attenuating wave energy. It is important to consider that if reef balls are placed at a water depth too deep, a very little amount, if any, of wave transmission will occur. This happens because the top of the structure is too deep for the wave to be impacted by it. In deep water, wave movement is essentially zero, deep below the water surface; thus, the wave will not even be impacted by the structure. Although the results of my experiment did not provide an adequate decrease in wave height, additional rows could be added to help attenuate the waves. This is often implemented in many real life scenarios, such as the Gran Dominicus case study. Well, I hope you had fun and learned something throughout my experiment!