Journal of Coastal Zone Management

There are many angles in describing what is a breakwater. Among others are, a structure constructed on coasts as part of coastal defense against both wind generated waves and longshore drift, as an offshore barrier to break the force of waves and as an enclosed structure to protect and provide calm waters inside the anchorage or basin area by reflecting and dissipating wave energy. But mostly, especially in nearshore and inshore areas, the breakwater is constructed to protect shoreline from erosion due to wave action. The breakwaters can be a permeable or solid type, either stationed below (a submerged breakwater) or above (emerged, at all time) the water surface depends on its’ intended applications. A permeable submerged breakwater, also referred to as artificial ‘reefs’ is more environmentally friendly and is becoming more preferable as a protection structures [1,2]. expressed the potential of dome-shaped artificial reefs as an environmental enhancer as well as a wave attenuator. The first installation of the submerged reef was in southern Caribbean shore of the Dominican Republic. The reef survived the Hurricane George and Hurricane Mitch (Category 5) shortly after installation and has been effectively stabilizing the beach [3].

Currently, more and more breakwaters in various type of materials have been used as a defense mechanism, either a soft or hard structures, i.e. rocks, geotube, concrete blocks and even in some cases, piles [4] gives an extensive reviews of breakwater in both submerged and emerged conditions, rigid and flexible geometry, in various types of materials, as in conventional rubble mound, and even a pipelines. Mostly, the alternative types are opted to cater for a short supply of rocks especially the boulders.

Needless to say, an extensive experimental and numerical investigations have been conducted to examine the performance of various submerged or semi-immersed structures in dispersing or dissipating waves. Most semi- or submerged structure are porous or permeable to better depress reflections, transmission waves and reducing wave energy. However, substantial findings on the performance of non-porous piles in transmitting waves could be found as early as in 1950’s [5] and further researched in later years [6-11]. The performance results from their laboratory experiments are shown in Table 1. A study between non-porous and porous pile range between 0 to 0.222 percent porosity is also thoroughly investigated by [6-11]. Their investigations found that a porous medium could introduced better water circulation in confined water body such that in marina. [12,13] completed an investigation on one-row and two-row porous cylinder under semi-emerged and submerged conditions. In their study, they found that less porous cylinder dissipates lesser wave energy as submergence depth increased. The percentage of wave energy loss increased as the number of row increased, but the reflection effects from the increased row escalated as wave frequency risen, which would likely raise an environmental issue if need to adhered to a specified water quality standard requirement.

Table 1: Various Studies on Cylindrical Structures

Nevertheless, there is still a lot of unclear understanding on the geometrical effect of a cylindrical type structures in dissipating wave energy that needs to be tackled by researchers out there. Researchers are still investigating the best way, material and ideal geographical features of a structure that could give optimal performance in reducing wave energy either through laboratory or site test. Hence, this experiment is conducted to investigate the performance of the cylindrical models in dissipating wave energy through various hydraulic parameters.

Experiment were performed in a wave flume with dimensions of 18 m (length) × 0.9 m (width) × 0.7 m (height). The test waves are generated using a programmable piston-type wave maker installed at one end of the tank was controlled using an electronic analog control panel and at the other end of the tank, a L-shaped steel bar served as a wave absorber to diminish undesired reflected waves. The wave flume is provided with see through panels on both sides of flume to facilitate observations and photography. Figure 1 depicts the schematic diagram of the experimental setup.

Figure 1: Schematic diagram of Wave Flume and dimension details of the model.

Models were located almost at the middle of the tank at 10 m away from the wave maker. Capacitance type wave probes were installed, three on the sea side (upstream) and two at the lee side (downstream) of the cylinder model. The upstream three, numbered #1, #2, and #3, were used to record the incident and reflected waves in front of the models. While probe #4 and #5 were installed downstream to record wave transmission over models.

In this study, the quantification of two records are analyzed using the following guideline [12]:

0.05<Δl/L < 0.45…………………………….(1)

where,

Δl=distance between any two wave gauges; and

L=incident wave length

Following data analysis, the reflection coefficient, K_r is expressed by,

K_r=H_r/H_i………………………………………. (2)

where,

H_r=reflected wave height;

H_i=incident wave height; and

H_t=transmission wave height the transmission coefficient can be expressed by,

K_t=H_t/H_i …………………………………………..(3)

and total energy loss, E_l is expressed by,

E_l=1 – K_t² – K_r²………………………(4)

Figure 2 shows the definition sketch and detail of the cylinder models. Each model unit is constructed from PVC pipe. Four different porous model units were manufactured, representing four different porosities varying from 0.0625 to 0.48. Porosity, P, is defined as the ratio of pores to the total surface area of the cylinder model. Two sizes of cylinder with diameter, D=0.1 m and 0.2 m of identical height, h’=0.25 m are used to form one-row of four identical model units, for each porosity size of the cylinder model, as shown in Figure 2 [15,16].

Figure 2: Cylinder model –D1 (top), D2 (middle) and D3 (bottom), left to right – porosity, P=0.0625, 0.14, 0.28 and 0.48, respectively.

Each of the models were tested using three water levels, 0.27 m, 0.30 m and 0.35 m under uniform wave conditions and various frequencies. Incident wave frequencies were selected from 24 to 47 Hz for each water level. The 47 Hz is the peak frequency that can be used at the lowest water level due to the limitations of the flap-type wave paddle to generate waves without breaking before it reaches the tested cylinder. In this study the tested cylinder height was kept constant. Each test started with a quiescent surface and the models were fixed firmly in the flume bed to prevent unwanted vibration or ripples. Table 2 summarize the experimental runs for the cylindrical models.

Table 2: summarize the experimental runs for the cylindrical models.

Three models with four different porosities (12 cases) were examined to elucidate the effects of the porosity of submerged models on wave transmissions under various water levels. First, D1, D2, and D3 model in various porosities were tested in different water level conditions and wave steepness, H_i/L, which resulted in variations of transmission, reflection and energy loss coefficients. Second, the effect of cylinder size or model diameter in breaking the surface wave were tested with respect to wave number, kh.

Figure 3 shows the correlation between wave transmission and reflection coefficients and the variation of H_i/L at water level 0.27 m. Three sub-graphs, (a) to (d), show the results of K_t, and K_r values obtained using model D1, D2, and D3 with porosities of 0.0625, 0.14, 0.28, and 0.48, respectively. The K_t, and K_r values were plotted on the left and right of each sub-graph, respectively. Four symbols in each graphs represent the experimental results obtained using four types of porosities. The graphs indicate the effect of cylinder’s perforations on wave reflection and transmission at a given model porosity.

Figure 3: Effect of perforations on K_t (left) and K_r (right) for D1, D2 and D3 cylinder at h=0.27 m. Sub-graphs (a) to (d) show results for cylinders with porosity, P=0.0625, 0.14, 0.28 and 0.48 respectively

As shown in Figure 3, the geometrical effect of the model becomes apparent as the porosity declines. The decreased in K_t value is more significant in D1 model as compared with model D2 and D3 especially when the porosity is 0.0625. The K_t is higher when H_i/L is less than 0.013, since longer incident waves are likely to pass through the model and less energy is dissipated. The value of K_t is minimum at H_i/L between 0.02 to 0.03. When the porosity increase from 0.0625 to 0.48, the maximum decrease in K_t value for model D1 is around 0.14. While in model D2 and D3, the maximum decrease in K_t value are 0.28 and 0.31, respectively. No obvious effects of model’s type on K_t were observed especially when the porosity is above 0.14. As for wave reflection, K_r, the effect of porosity in all model tested is insignificant at all H_i/L parameter. As shown in the right graph of Figure 3, the experimental results display minimal variance in K_r value when H_i/L is less than 0.013. Almost all the K_r values are in the range of 0.25–0.55 at H_i/L=0.006 – 0.013 and K_r<0.35 at H_i/L=0.02–0.03, irrespective of model type. Therefore, Figure 3 elucidates the effect of porosity on wave transmission and reflection.

Figure 4 shows the results of wave energy loss, E_l. Four sub-graphs, (a) to (d), present the experimental results of model D1, D2, and D3 for cases of porosities 0.0625, 0.14, 0.28, and 0.48, respectively. The Figure shows that the effect of the type of model is unclear when porosity increased above 0.0625. The maximum variations of E_l, for model D1, D2, and D3 is almost similar with E_l do not exceed 0.6 (at porosity 0.28 and 0.48) in all H_i/L. Nonetheless, this phenomenon is different when the porosity is small with all models show a distinct variance in E_l. The effect of smaller porosity is most significant in dual cylinder model D3 as compared with model D1 and D2, with the maximum variance in E_l value is lowest at all H_i/L values. Higher frequency produced higher wave energy and shorter wave length. Thus, indicated that the dual cylinder setup for model D3 is effective in dissipating more wave energy at higher H_i/L values as compared to single cylinder model setup in all porosity tested.

Figure 4: Effect of perforations.

P, on El for D1, D2 and D3 cylinder at h=0.27 m. Sub-graphs (a) to (d) show results for cylinders with porosity, P=0.0625, 0.14, 0.28 and 0.48 respectively. Figure 5 displays the experimental results of K_t and K_r. three sub-graphs, (a) to (c), present the test results for cases of model D1, D2, and D3 at porosity 0.0625, respectively. The effect of water level increment on K_t is more pronounced for model D2 and D3, a bigger diameter cylinder, than smaller diameter cylinder, model D1. In Figure 5b and 5c, K_t decreased when water level decreased. From water level, h=0.27 m to 0.30 m, the variance in K_t for D2 and D3 is almost similar, the increment does not exceed 0.12 for H_i/L lower than 0.02. The increased in K_t is more than 0.1 for D2 and less than 0.1 for D3 at H_i/L>0.02, respectively. K_t grows to more than 0.8 as Hi/L approaches 0.011 when h=0.35 m, and declines as H_i/L approaches 0.022 for model D2. K_t remains between 0.66–0.92 when H_i/L is less than 0.02 and decreases below 0.66 when H_i/L starts to increase at h=0.35 m for model D3.

Figure 5: Effect of water level, h, on Kt and K_r at cylinder perforation, P=0.0625. Sub-graphs (a) to (c) show results for cylinders D1, D2 and D3 respectively.

At intermediate water level, h=0.30 m, as H_i/L increases to 0.015, the Kt is decreases from 0.79 to 0.72 and further declines as H_i/L approaches 0.022 for model D2. As for model D3, when H_i/L increase from 0.08 to 0.015, K_t decreases from 0.69 to 0.58 and further decrease to less than 0.55 as H_i/L exceed 0.024, respectively. K_r decreases as wave steepness H_i/L decreases. The effect of water level increment on K_r is not that significant, where, at H_i/L between 0.007 to 0.035, the decline trends are similar in both model D2 and D3.

Figure 6 show the primary wave energy loss due to submergence depth of cylinder. The Figure formats are the same as used in Figure 5. For low submergence depth, z/h=0.074 (water level, h=0.27 m), the effect of cylinder type is noticeable. As H_i/L>0.022, the data show a loss of more than 0.35 of the energy of the incident wave. At higher frequency waves (i.e. the wave steepness H_i/L<0.02), the variations in energy losses due to changes in water level becomes larger as the water level increases. The maximum E_l is about 0.59 at h=0.27 m and 0.30 m, and 0.50 at 0.35 m water level, in model D1. Whilst in model D2 and D3, at each respective water level, h=0.27 m, 0.30 m, and 0.35 m, the maximum E_l is about 0.70, 0.65, and 0.43 for D2; and 0.79, 0.70, and 0.57, for D3, respectively. In general, E_l decreases as water level rises, irrespective of cylinder type, but bigger diameter cylinders shown higher energy loss.

Figure 6: Effect of water level, h, on El at cylinder perforation, ε=0.0625. Sub-graphs (a) to (c) show results for cylinders D1, D2 and D3 respectively

Figure 7 plots the effect of model type on wave transmission at different kh. Four sub-graphs, (a) and (b), show the results of tested models with cylinder porosity, 0.0625 and 0.14 at water level, h=0.27 m, and sub-graphs (c) and (d) with cylinder porosity, 0.0625 and 0.14 at water level, h=0.30 m, respectively. In Figure 7, all three models show high variance in K_t values at kh between 0.65 to 1.08, with the changes are more pronounced in model with porosity 0.0625 at water level at 0.27 m. The effect of cylinder type on wave transmission is evident in all kh values irrespective of porosity and water level change, especially between model D1 and D3. The significant variance of K_t between D1 and D3 model is due to the presence of double cylinder in model D3 which provides high turbulence effect on the model’s crest, thus dampened the wave energy, hence, less wave is transmitted. Even though model D1 and D2 are constructed from a single cylinder but differ in diameter, the effect of cylinder geometry on K_t values is unclear especially at kh between 0.65 and 1.08, but the difference in K_t between the model is significant as kh>1.08 (higher wave frequency or shorter wave length). A longer wave length generated by low frequency waves, hence, lower kh, produced low wave energy and turbulence effect, thus the difference in diameter has likely less significant effect in dampening the wave at the lee of the model. In general, model D3 gives the best performance in attenuating waves with the least waves transmitted especially at higher wave frequency (kh>1.08) and model D1 is the least effective porous cylinder to attenuate wave energy.

Figure 7: Influence of type of cylinder on K_t with ε =0.0625 (left) and 0.14 (right). Sub-graphs (a) to (c) show results for tests under water level, h=0.27 m, and 0.30 m respectively

Experimental results have shown that the incident wave conditions and the submerged breakwater geometry influence the wave fields. The porosity of the breakwater also plays an important role in dissipating wave energy. When the measurements were being made, strong turbulence were observed after waves passed bigger diameter cylinder unit, less porous, and low submerged model, indicating that the primary wave energy is thus reduced significantly, as shown in the results presented herein.

This study address how variation of porosity, water level and cylinder type, affect non-breaking wave transformations. The important findings of the laboratory test shown that when the percentage of porosity decreased, more wave energy was dissipated, this resulted in the decrease in transmitted wave heights. It was also found that lower water level (h=0.27 m) has a significant influence on the loss coefficient at bigger model size as compared to higher water level at 0.35 m for similar porosity. Overall, the bigger diameter model (single or double cylinder) with lower porosity (P=6.25% and 14%) showed promising performance in reducing wave height at the lee of the model, having high percentage of wave energy loss, and smaller model was relatively to be the least effective model in dissipating wave energy against longer waves (that is, lower kh values) to the same environments among all three models. The low reflection and high energy loss showed by all models in shallow water depth and high wave steepness reflects the effectiveness of the cylindrical model to perform as a potential wave barrier for offshore berthing especially in regions where environment friendly is required and tidal fluctuations are large.