**4. Effects of anthropogenic factors on development of sand spits and cuspate forelands**

### **4.1. General conditions**

The formation of sand spits and cuspate forelands with rhythmic shapes has already predicted in Chapter 3. Here, we investigated the effects of the construction of a groin and a breakwater to the topographic changes in the field where sand spits and cuspate forelands with rhythmic shapes fully developed. All the calculation conditions were the same as those in Chapter 3 except the structural conditions. Five calculations were carried out with the installation of a groin of 800 m length or an offshore breakwater of 600 m or 1000 m length.

In Cases 1 and 2, a groin or a breakwater was placed at the center of the calculation domain, respectively, after the development of sand spits under the condition that waves were obliquely incident from the left with an angle of 60°, as shown in Fig. 2. In Cases 3 and 4, in which waves are incident with an angle of ±60° with probabilities of 0.5:0.5, as shown in Fig. 7, a breakwater was placed offshore of the apex or the bay of the cuspate forelands, respectively. In Case 5, a breakwater was installed under the condition that waves are incident with an angle of ±60° with probabilities of 0.65:0.35, as shown in Fig. 10. The wave direction was randomly determined on the basis of the probability distribution at every step of the calculation of the wave field. The lengths of the groin and breakwater were determined, taking both the scale of sand spits and cuspate forelands and the wave diffraction effect of the structures into account. The calculation with no structures was carried out up to 3×104 steps, and then the beach changes up to an additional 3×104 steps were predicted after the installation of the structures.

### **4.2. Calculation results**

probabilities. The shape of the sand spit A is very similar to that of the sand spit second from the right end in Fig. 10(c) calculated with probabilities of 0.65:0.35, and that of the sand spit C is similar to that located at right end in Fig. 11(b) calculated with probabilities of 0.70:0.30. On the north shore of the Azov Sea, easterly wind is considered to be predominant, and the sand spit D located at the west end could receive sufficiently large wave energy from the east because of long fetch, whereas wave action from the west is weak because of shorter fetch. As a result, wave action from the east became stronger and sand spit with a narrow, slender neck was considered to be formed. In contrast, in the sand spit A, the fetch from the east was short so that the wave action from the east was weakened, whereas wave action from the west was strengthened because of a long fetch. In addition, the increase in the fetch of the easterly wind was considered to cause the increase in scale of the sand spit. Zenkovich qualitatively ex‐ plained these features using a schematic diagram [1], but in this study these features observed

Falqués et al. [6] predicted the development of sand waves caused by high-angle wave instability using equations similar to that of our model. Their sand transport equation had the same stability mechanism as that in our model. However, because the calculation domain of the wave field was restricted between the offshore zone and the breaking point, they only predicted the development of sand waves but not the development of sand spits protruding offshore. In this study, wave decay in the breaker zone and the wave-sheltering effect by the sand spit themselves were evaluated, taking the local change in topography in the surf zone

in the field were successfully explained using the BG model.

**cuspate forelands**

436 Computational and Numerical Simulations

**4.1. General conditions**

into account and using the energy balance equation for irregular waves.

groin of 800 m length or an offshore breakwater of 600 m or 1000 m length.

**4. Effects of anthropogenic factors on development of sand spits and**

The formation of sand spits and cuspate forelands with rhythmic shapes has already predicted in Chapter 3. Here, we investigated the effects of the construction of a groin and a breakwater to the topographic changes in the field where sand spits and cuspate forelands with rhythmic shapes fully developed. All the calculation conditions were the same as those in Chapter 3 except the structural conditions. Five calculations were carried out with the installation of a

In Cases 1 and 2, a groin or a breakwater was placed at the center of the calculation domain, respectively, after the development of sand spits under the condition that waves were obliquely incident from the left with an angle of 60°, as shown in Fig. 2. In Cases 3 and 4, in which waves are incident with an angle of ±60° with probabilities of 0.5:0.5, as shown in Fig. 7, a breakwater was placed offshore of the apex or the bay of the cuspate forelands, respectively. In Case 5, a breakwater was installed under the condition that waves are incident with an angle of ±60° with probabilities of 0.65:0.35, as shown in Fig. 10. The wave direction was randomly determined on the basis of the probability distribution at every step of the calculation of the

### *4.2.1. Effect of groin on formation of sand spits*

The beach changes until 3×104 steps were calculated under the conditions that waves are obliquely incident from the direction of 60° and then a groin of 800 m length and 4 m point depth was installed across the central sand spit after the sand spits have fully developed owing to the shoreline instability (Fig. 14(a)). These sand spits have developed while moving rightward, and the sand spit that moved out of the right boundary enters again from the left boundary as it is because of the periodic boundary condition at both ends. Figures 14(b)-14(j) show the results.

After 2×103 steps, the sand spit located left of the groin connected to the groin with a lagoon inside, whereas erosion started right of the groin because rightward longshore sand transport was obstructed by the groin. After 4×103 steps, part of the sand blocked by the groin started to be transported to the right while turning around the tip of the groin. The same situation continued after 6×103 steps, and a sand spit was formed owing to the deposition of sand turning around the tip of the groin up to 8×103 steps. Furthermore, as a result of sand discharge to the area right of the groin between 4×103 and 8×103 steps, the volume of sand left of the groin decreased, and the location of the starting point P of sand bar approached the groin with time, resulting in the decrease in the scale of the lagoon behind the sand bar.

Until 1×104 steps, the sand spit formed at the tip of the groin elongated rightward along with the reduction in the scale of the sand bar left of the groin. After 1.5×104 steps, the sand spit extending from the tip of the groin became a flying spit [20, 21] because of the reduction in sand supply by longshore sand transport. Because the flying spit is an unstable topography, it rapidly disappeared until 2×104 steps. Then, because of the increased sand supply owing to the connection of another sand spit to the groin, a sand spit elongated obliquely from the tip of the groin until 3×104 steps. It was realized from the comparison of Figs. 14(a) and 14(j) that sand was deposited, forming a steep slope along the shoreline on the exposed side, but the water depth generally decreased in the offshore zone owing to the sweeping motion of the sand spit, causing offshore sand movement. In contrast, sandy beach with a gentle slope was formed in the lee of the sand spits and six branches were formed behind the sand spit. The longshore sand transport was pushed seaward by the construction of a groin.

### *4.2.2. Effect of breakwater on formation of sand spits*

The beach changes until 3×104 steps were calculated under the conditions that waves were obliquely incident from the direction with an angle of 60° to the direction normal to the shoreline, and then a breakwater of 600 m length was installed offshore of sand spit A after

shown in Fig. 16(a). The same situation continued after 4×103

sand spit A was obliquely transported landward, and sand spit A disappeared while leaving the outline of the sand spit. During the period, sand spit B further extended to the lee of the breakwater. The change in wave field corresponding to this stage is shown in Fig. 16(b). Although the tip of sand spit B is subjected to strong impact of waves diffracted from the left end of the breakwater, wave height is significantly reduced between the tip of sand spit B and the breakwater, thus the tip of sand spit B extended so as to approach the breakwater.

Development of Sand Spits and Cuspate Forelands with Rhythmic Shapes and Their…

**Figure 15.** Deformation of sand spits formed under oblique wave incidence from 60° after construction of a breakwa‐

ter.

steps and the rest of the sand of

http://dx.doi.org/10.5772/57043

439

**Figure 14.** Deformation of sand spits formed under oblique wave incidence from 60° after extension of a groin.

the full development of sand spits owing to the high-angle wave instability (Fig. 15(a)). The beach changes were further calculated until 3×104 steps, as shown in Figs. 15(b) - 15(j).

After 2×103 steps, sand spit A behind the breakwater was eroded, because it was fully included in the wave-shelter zone of the breakwater, as shown in Fig. 16(a), and the wave height was significantly reduced with the change in wave direction, resulting in the reduction in rightward longshore sand transport. In contrast, sand spit B elongating left of the lee of the breakwater rapidly extended to the lee of the breakwater because of large longshore sand transport, as shown in Fig. 16(a). The same situation continued after 4×103 steps and the rest of the sand of sand spit A was obliquely transported landward, and sand spit A disappeared while leaving the outline of the sand spit. During the period, sand spit B further extended to the lee of the breakwater. The change in wave field corresponding to this stage is shown in Fig. 16(b). Although the tip of sand spit B is subjected to strong impact of waves diffracted from the left end of the breakwater, wave height is significantly reduced between the tip of sand spit B and the breakwater, thus the tip of sand spit B extended so as to approach the breakwater.

**Figure 15.** Deformation of sand spits formed under oblique wave incidence from 60° after construction of a breakwa‐ ter.

the full development of sand spits owing to the high-angle wave instability (Fig. 15(a)). The

**Figure 14.** Deformation of sand spits formed under oblique wave incidence from 60° after extension of a groin.

in the wave-shelter zone of the breakwater, as shown in Fig. 16(a), and the wave height was significantly reduced with the change in wave direction, resulting in the reduction in rightward longshore sand transport. In contrast, sand spit B elongating left of the lee of the breakwater rapidly extended to the lee of the breakwater because of large longshore sand transport, as

steps, sand spit A behind the breakwater was eroded, because it was fully included

steps, as shown in Figs. 15(b) - 15(j).

beach changes were further calculated until 3×104

After 2×103

438 Computational and Numerical Simulations

The beach changes continued up to 6×103 steps and the volume of sand deposited behind the breakwater increased along with the shoreline recession downcoast of the breakwater, as shown in Fig. 15(d). After 8×103 steps, a large tombolo was formed by the trapping of sand. After 1×104 steps, another sand spit, which elongated from the left end, extended to connect the tombolo behind the breakwater. After 1.5×104 steps, a continuous sand bar developed from the left end to the breakwater. Then, a small sand spit started to emerge at the right end of the breakwater by 2×104 steps. After 3×104 steps, the sand spit extended from the right end of the breakwater further elongated, even though the volume of sand deposited behind the break‐ water did not change. Thus, the construction of the breakwater had a significant impact on the beach; otherwise, sand spits developed with the self-organization mechanism, as shown in Fig. 2. It is realized that once a tombolo is formed behind the breakwater, offshore sand movement is enhanced owing to the presence of the breakwater and the tombolo, which blocks longshore sand transport.

*4.2.3. Effect of breakwater placed offshore of apex of cuspate forelands*

Results are shown in Fig. 17(b) - 17(h).

forelands.

After 1.5×104

breakwater.

2×104

18 shows the wave field after approximately 5×103

condition. The same changes continued until 1×104

When waves were obliquely incident with an angle of ±60° to the direction normal to the

Development of Sand Spits and Cuspate Forelands with Rhythmic Shapes and Their…

shown in Fig. 7. This bathymetry was selected as the initial topography, as shown in Fig. 17 (a). Here, the cuspate foreland formed at the center is designated as A along with cuspate forelands B and C on the left and right, respectively. Then, a breakwater of a 1000 m length was placed offshore of cuspate foreland A, and the calculation was made until 4×104 steps.

Under these conditions, approximately symmetric wave-shelter zone was formed on both sides of the breakwater. The slender sand spits started to extend toward the lee of the break‐ water near the tip of cuspate forelands B and C after 5×103 steps, as shown in Fig. 17(b). These sand spits were asymmetric with the sand spit being larger size at cuspate foreland B. Figure

right and left, for example. Because the breakwater is placed offshore of cuspate foreland A and the distance between cuspate forelands A and B is shorter than that between cuspate forelands A and C, cuspate foreland B is subjected to an intensive wave-sheltering effect by the breakwater and cuspate foreland A under the condition that waves are incident from the right, whereas cuspate foreland C is located outside the wave-shelter zone by the breakwater and cuspate foreland A under the conditions that waves are obliquely incident from the left. Thus, the intensive wave-sheltering effects by the breakwater appeared at cuspate foreland B, resulting in the increase in the formative velocity of the sand spit near the tip of the cuspate

Furthermore, in Fig. 17(b), cuspate foreland A protruded more than that under the initial

at the tip of cuspate foreland B to the lee of the breakwater and it almost connected to cuspate foreland A. On the other hand, cuspate foreland C was started to be eroded because of the

cuspate foreland A and a barrier was formed with a lagoon inside. The scale of the sand spit formed at the tip of cuspate foreland C also increased, and the shoreline curvature increased downcoast of the sand spit C because of the wave-sheltering effect of the sand spit itself. After

 steps, cuspate foreland B was entirely eroded, leaving a barrier island with a straight shoreline and a tombolo was formed behind the breakwater. No beach changes occurred inside the lagoon since then. On the right side of the breakwater, a sand spit elongated leftward with many branches to cuspate foreland A. After 2.5×104 steps, the tombolo behind the breakwater further developed and the beach width was widened up to 240 m behind the breakwater. Furthermore, the sand spit extended leftward from the tip of the cuspate foreland C connected to the cuspate foreland A and a lagoon was formed behind the barrier. Finally, after 4×104 steps, a large tombolo was formed with two water bodies inside the sandy beach behind the breakwater, the cuspate forelands with rhythmic shapes, as shown in Fig. 17(a), markedly deformed, and marked beach changes were induced by the wave-sheltering effect of the

steps, the sand spit elongated from the tip of cuspate foreland B connected to

leftward development of the sand spit at the tip of the cuspate foreland.

steps, as

441

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steps when waves are incident from the

steps with rapid elongation of the sand spit

shoreline with the probability of 0.5:0.5, cuspate forelands have developed by 3×104

**Figure 16.** Wave field around a breakwater after 2×103 and 4×103 steps.
