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

The beach changes continued up to 6×103

the tombolo behind the breakwater. After 1.5×104

steps. After 3×104

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

shown in Fig. 15(d). After 8×103

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After 1×104

breakwater by 2×104

longshore sand transport.

steps and the volume of sand deposited behind the

steps, the sand spit extended from the right end of the

steps, a continuous sand bar developed from

steps, a large tombolo was formed by the trapping of sand.

breakwater increased along with the shoreline recession downcoast of the breakwater, as

the left end to the breakwater. Then, a small sand spit started to emerge at 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

steps, another sand spit, which elongated from the left end, extended to connect

When waves were obliquely incident with an angle of ±60° to the direction normal to the shoreline with the probability of 0.5:0.5, cuspate forelands have developed by 3×104 steps, as 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. Results are shown in Fig. 17(b) - 17(h).

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 18 shows the wave field after approximately 5×103 steps when waves are incident from the 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 forelands.

Furthermore, in Fig. 17(b), cuspate foreland A protruded more than that under the initial condition. The same changes continued until 1×104 steps with rapid elongation of the sand spit 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 leftward development of the sand spit at the tip of the cuspate foreland.

After 1.5×104 steps, the sand spit elongated from the tip of cuspate foreland B connected to 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 2×104 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 breakwater.

**Figure 17.** Deformation of cuspate forelands formed under the condition of oblique wave incidence from ±60° with probabilities of 0.5:0.5 after construction of a breakwater offshore of apex of cuspate foreland A.

### *4.2.4. Effect of breakwater placed offshore of bay of cuspate forelands*

To investigate the topographic changes caused by the difference in the wave-sheltering effect which was produced by the change in location of the breakwater, the location of the breakwater was altered from offshore of the apex in the former case to offshore of the bay of the cuspate forelands. The same bathymetry shown in Fig. 17(a) with four cuspate forelands was selected as the initial bathymetry (Fig.19(a)), and an impermeable breakwater of a 1000 m length was placed offshore of a bay between the cuspate forelands A and B. Beach changes until 4×104 steps were predicted under the condition that waves were incident with an angle of ±60° to the direction normal to the shoreline with probabilities of 0.5:0.5. Figures 19(b) - 19(h) show the results.

elongated toward the lee of the breakwater from the tip of the cuspate forelands until 5×103 steps, while enclosing a lagoon inside (Figs. 19(b) and 19(c)). The same changes continued after

to the breakwater, and no beach changes occurred along the lagoon shore. With time, the double tombolo developed, resulting in increase in the size. Finally, the initial shape of the cuspate forelands with rhythmic shapes shown in Fig. 19(a) entirely disappeared. Comparing

lagoons enclosed inside the barrier was different; two in Fig. 17(h) and one in Fig. 19(h),

about to connect to the breakwater. After 1.5×104

**Figure 18.** Wave field around a breakwater after 5.1×103 and 5×103 steps.

breakwater, forming a double tombolo. After 2×104

although double tombolo developed in both cases.

the beach topographies after 4×104

steps and the sand spits extended from the tip of the cuspate forelands A and B were

steps, both sand spits connected to the

steps, the double tombolo fully attached

steps, as shown in Figs. 17(h) and 19(h), the number of

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1×104

In this case, almost half of the cuspate forelands A and B were included in the wave-shelter zone of the breakwater. Because of the symmetry of the location of cuspate forelands A and B relative to the breakwater, the wave field also showed symmetry, so that a pair of sand spits

**Figure 18.** Wave field around a breakwater after 5.1×103 and 5×103 steps.

*4.2.4. Effect of breakwater placed offshore of bay of cuspate forelands*

probabilities of 0.5:0.5 after construction of a breakwater offshore of apex of cuspate foreland A.

the results.

442 Computational and Numerical Simulations

To investigate the topographic changes caused by the difference in the wave-sheltering effect which was produced by the change in location of the breakwater, the location of the breakwater was altered from offshore of the apex in the former case to offshore of the bay of the cuspate forelands. The same bathymetry shown in Fig. 17(a) with four cuspate forelands was selected as the initial bathymetry (Fig.19(a)), and an impermeable breakwater of a 1000 m length was placed offshore of a bay between the cuspate forelands A and B. Beach changes until 4×104 steps were predicted under the condition that waves were incident with an angle of ±60° to the direction normal to the shoreline with probabilities of 0.5:0.5. Figures 19(b) - 19(h) show

**Figure 17.** Deformation of cuspate forelands formed under the condition of oblique wave incidence from ±60° with

In this case, almost half of the cuspate forelands A and B were included in the wave-shelter zone of the breakwater. Because of the symmetry of the location of cuspate forelands A and B relative to the breakwater, the wave field also showed symmetry, so that a pair of sand spits elongated toward the lee of the breakwater from the tip of the cuspate forelands until 5×103 steps, while enclosing a lagoon inside (Figs. 19(b) and 19(c)). The same changes continued after 1×104 steps and the sand spits extended from the tip of the cuspate forelands A and B were about to connect to the breakwater. After 1.5×104 steps, both sand spits connected to the breakwater, forming a double tombolo. After 2×104 steps, the double tombolo fully attached to the breakwater, and no beach changes occurred along the lagoon shore. With time, the double tombolo developed, resulting in increase in the size. Finally, the initial shape of the cuspate forelands with rhythmic shapes shown in Fig. 19(a) entirely disappeared. Comparing the beach topographies after 4×104 steps, as shown in Figs. 17(h) and 19(h), the number of lagoons enclosed inside the barrier was different; two in Fig. 17(h) and one in Fig. 19(h), although double tombolo developed in both cases.

**Figure 19.** Deformation of cuspate forelands formed under the condition of oblique wave incidence from ±60° with probabilities of 0.5:0.5 after construction of a breakwater offshore of bay of cuspate forelands.

**Figure 20.** Deformation of sand spits formed under oblique wave incidence from ±60° with probabilities of 0.65:0.35

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Owing to these reasons, the tip of the sand spit A rapidly extended to connect the breakwater until 5×103 steps, as shown in Fig. 20(b), and this elongation of the sand spit caused the waves incident from the left to be sheltered in the area right of the breakwater, as shown in Fig. 21(b), resulting in the reversal of the direction of longshore sand transport from rightward to leftward. Thus, the direction of the elongation of sand spit B was reversed and extended toward the lee of the breakwater. Sand spit C also rapidly extended rightward because waves incident from the left were sheltered. The construction of the breakwater further affected the beach changes of sand spit D far from the breakwater, and rightward development ceased and a

After 1×104 steps, sand spit B rapidly extended to the lee of the breakwater, and after 1.5×104 steps, sand spits B and C markedly elongated to connect to sand spit A, leaving two lagoons

steps, sand spit B reduced to a tombolo along with the

steps, a double tombolo developed, leaving

after construction of breakwater.

rounded shoreline was formed.

behind the breakwater. After 2×104

connection of sand spit C with A. After 2.5×104

### *4.2.5. Effect of breakwater on formation of asymmetric sand spits*

In this case, sand spits with asymmetric shapes were formed first under the condition that waves were obliquely incident from the direction of ±60° normal to the shoreline with probabilities of 0.65:0.35, as shown in Fig. 10. Then, an offshore breakwater of a 600 m length (the same condition as that shown in Fig. 15) was constructed in a zone offshore of sand spits A and B, and beach changes were calculated until 4×104 steps. The calculation results are shown in Figs. 20(a)-20(h).

Figure 21 shows the wave field after approximately 5×103 steps when waves were obliquely incident from the right and left. Because not only the probability of each wave direction was not equal as 0.65:0.35 but also sand spit B was located closer to the breakwater than sand spit C, an extremely asymmetric wave field was formed. Sand spit C was barely subjected to the wave-sheltering effect by the breakwater, whereas sand spit B effectively entered into the wave-shelter zone of the breakwater under the wave incidence from the left. Moreover, sand spit A was subjected to receive a strong wave-sheltering effect by the breakwater because of its proximity to the breakwater.

**Figure 20.** Deformation of sand spits formed under oblique wave incidence from ±60° with probabilities of 0.65:0.35 after construction of breakwater.

*4.2.5. Effect of breakwater on formation of asymmetric sand spits*

probabilities of 0.5:0.5 after construction of a breakwater offshore of bay of cuspate forelands.

A and B, and beach changes were calculated until 4×104

in Figs. 20(a)-20(h).

444 Computational and Numerical Simulations

its proximity to the breakwater.

In this case, sand spits with asymmetric shapes were formed first under the condition that waves were obliquely incident from the direction of ±60° normal to the shoreline with probabilities of 0.65:0.35, as shown in Fig. 10. Then, an offshore breakwater of a 600 m length (the same condition as that shown in Fig. 15) was constructed in a zone offshore of sand spits

**Figure 19.** Deformation of cuspate forelands formed under the condition of oblique wave incidence from ±60° with

Figure 21 shows the wave field after approximately 5×103 steps when waves were obliquely incident from the right and left. Because not only the probability of each wave direction was not equal as 0.65:0.35 but also sand spit B was located closer to the breakwater than sand spit C, an extremely asymmetric wave field was formed. Sand spit C was barely subjected to the wave-sheltering effect by the breakwater, whereas sand spit B effectively entered into the wave-shelter zone of the breakwater under the wave incidence from the left. Moreover, sand spit A was subjected to receive a strong wave-sheltering effect by the breakwater because of

steps. The calculation results are shown

Owing to these reasons, the tip of the sand spit A rapidly extended to connect the breakwater until 5×103 steps, as shown in Fig. 20(b), and this elongation of the sand spit caused the waves incident from the left to be sheltered in the area right of the breakwater, as shown in Fig. 21(b), resulting in the reversal of the direction of longshore sand transport from rightward to leftward. Thus, the direction of the elongation of sand spit B was reversed and extended toward the lee of the breakwater. Sand spit C also rapidly extended rightward because waves incident from the left were sheltered. The construction of the breakwater further affected the beach changes of sand spit D far from the breakwater, and rightward development ceased and a rounded shoreline was formed.

After 1×104 steps, sand spit B rapidly extended to the lee of the breakwater, and after 1.5×104 steps, sand spits B and C markedly elongated to connect to sand spit A, leaving two lagoons behind the breakwater. After 2×104 steps, sand spit B reduced to a tombolo along with the connection of sand spit C with A. After 2.5×104 steps, a double tombolo developed, leaving two lagoons behind. After 3×104 steps, sand was deposited offshore of the breakwater to form a sandy beach, and after 4×104 steps, a new sand spit started to extend from the right end of the breakwater because of the net rightward sand transport.

figure. The extension of many ridges left of sand bar A shows that waves are incident from the direction normal to shoreline (a). A slender sand bar B also extends with protrusions formed by breaching inside the lagoon on the other side. This indicates that sand bar B was formed by the action of waves incident from the direction normal to shoreline (b). Furthermore, at the tip of sand bar A, a small sand spit C extends rightward. Since the white seabed in Fig. 23(a) is assumed to show a shallow seabed covered with sand, a very shallow seabed extends offshore of sand spit C, and on the right side of sand spit C, the seabed depth suddenly increases, implying that sand spit C developed at the corner of the abruptly changed shoreline. This also agrees with the results given in [9]. The fact that the tip of sand spit C extended rightward

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Thus, the sand bars were formed when waves were incident to the coast from two directions in a shallow sea with an offshore shoal. Although the wave-sheltering effect was produced by a shoal in Fig. 23(a), the same results were obtained in this study, when a breakwater was constructed. Figure 23(b) is the same results as shown in Fig. 20(h). The calculation results are in good agreement with the example of the formation of the sand bars with two lagoons inside

In Figs. 14 and 15, which show the results on a coast with predominant longshore sand transport, a sand spit elongated at the tip of the structure owing to the successive sand supply from the upcoast. This elongation of a sand spit well explains the results observed at Santa

shows the wave action from direction (b).

Barbara in California [22].

**Figure 22.** Location of study area near Azov Sea.

and the formation of small sand spit C in Fig. 23(a).

**Figure 21.** Wave field around a breakwater after 5.1×103 and 5×103 steps.

### **4.3. Discussion**

The beach changes observed when a breakwater was constructed, as shown in Fig. 19, can be observed in Taman located in southwestern Russia bounded by the Azov Sea and the Black Sea (Fig. 22). Figure 23(a) shows an example of sand bars with two lagoons inside in a shallow water body due to the wave-sheltering effect of a shoal [1]. Sand bars with two lagoons inside have been formed by the wave-sheltering effect by the shoal shown in the lower part of the figure. The extension of many ridges left of sand bar A shows that waves are incident from the direction normal to shoreline (a). A slender sand bar B also extends with protrusions formed by breaching inside the lagoon on the other side. This indicates that sand bar B was formed by the action of waves incident from the direction normal to shoreline (b). Furthermore, at the tip of sand bar A, a small sand spit C extends rightward. Since the white seabed in Fig. 23(a) is assumed to show a shallow seabed covered with sand, a very shallow seabed extends offshore of sand spit C, and on the right side of sand spit C, the seabed depth suddenly increases, implying that sand spit C developed at the corner of the abruptly changed shoreline. This also agrees with the results given in [9]. The fact that the tip of sand spit C extended rightward shows the wave action from direction (b).

Thus, the sand bars were formed when waves were incident to the coast from two directions in a shallow sea with an offshore shoal. Although the wave-sheltering effect was produced by a shoal in Fig. 23(a), the same results were obtained in this study, when a breakwater was constructed. Figure 23(b) is the same results as shown in Fig. 20(h). The calculation results are in good agreement with the example of the formation of the sand bars with two lagoons inside and the formation of small sand spit C in Fig. 23(a).

In Figs. 14 and 15, which show the results on a coast with predominant longshore sand transport, a sand spit elongated at the tip of the structure owing to the successive sand supply from the upcoast. This elongation of a sand spit well explains the results observed at Santa Barbara in California [22].

**Figure 22.** Location of study area near Azov Sea.

two lagoons behind. After 3×104 steps, sand was deposited offshore of the breakwater to form

steps, a new sand spit started to extend from the right end of

a sandy beach, and after 4×104

446 Computational and Numerical Simulations

the breakwater because of the net rightward sand transport.

**Figure 21.** Wave field around a breakwater after 5.1×103 and 5×103 steps.

The beach changes observed when a breakwater was constructed, as shown in Fig. 19, can be observed in Taman located in southwestern Russia bounded by the Azov Sea and the Black Sea (Fig. 22). Figure 23(a) shows an example of sand bars with two lagoons inside in a shallow water body due to the wave-sheltering effect of a shoal [1]. Sand bars with two lagoons inside have been formed by the wave-sheltering effect by the shoal shown in the lower part of the

**4.3. Discussion**

(a) Example of sand bars with two lagoons inside a shallow water body [1]

changes was predicted. It was concluded that the construction of a groin had a marked impact on the sandy beach; the alteration from the field with the development of the sand spits to that with the elongation of a single sand spit, as well as the acceleration of offshore sand transport

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and Shiho Miyahara2

[1] Zenkovich, V. P. (1967). Processes of Coastal Development, Interscience Publishers,

[2] Ashton, A., Murray, A. B., Arnault, O. (2001). Formation of coastline features by large-scale instabilities induced by high angle waves, Nature, Vol. 414, pp. 296-300.

[3] Ashton, A., Murray, A. B. (2006). High-angle wave instability and emergent shoreline shapes: 1. Modeling of sand waves, flying spits, and capes: Jour. Geophys. Res., Vol.

[4] Littlewood, R., Murray, A. B., Ashton, A. D. (2007). An alternative explanation for the

[5] Serizawa, M., Uda, T., Miyahara, S. (2012). Prediction of development of sand spits and cuspate forelands with rhythmic shapes caused by shoreline instability using BG

[6] Falqués, A., van den Berg, N., Calvete, D. (2008). The role of cross-shore profile dy‐ namics on shoreline instability due to high-angle waves, Proc. 31st ICCE, pp.

[7] Inman, D. L., Bagnold, R. A. (1963). Littoral processes, In The Sea, Hill, M. N., Vol. 3,

[8] Bagnold, R. A. (1963). Mechanics of marine sedimentation, In The Sea, Hill, M. N.,

[9] Serizawa, M., Uda, T. (2011). Prediction of formation of sand spit on coast with sud‐ den change using improved BG model, Coastal Sediments '11, pp. 1907-1919.

shape of 'Log-Spiral' Bays, Coastal Sediments '07, pp. 341-350.

because of the blockage of longshore sand transport.

, Masumi Serizawa2

1 Public Works Research Center, Tokyo, Japan

2 Coastal Engineering Laboratory Co., Ltd., Tokyo, Japan

111, F04011, doi: 10.1029/2005JF000422.

model, Proc. 33rd ICCE, sediment.35, pp. 1-11.

**Author details**

Takaaki Uda1

**References**

New York, p. 751.

1826-1838.

Wiley, New York, pp. 529-533.

Vol. 3, Wiley, New York, pp. 507-528.

Fig. 23. Comparison of measured and calculated double and looped spits. **Figure 23.** Comparison of measured and calculated double and looped spits.

#### Regarding the development of multiple sand spits and cuspate forelands with rhythmic shapes observed along the shore of the Azov Sea [1], the BG model was used to simulate the shoreline **5. Conclusions**

**5. Conclusions** 

evolution caused by high-angle wave instability. The wave direction was assumed to be obliquely incident from 60°, 50° and 40° counterclockwise or from the directions of ±60° with probabilities of 0.5:0.5 and 0.60:0.40, 0.65:0.35, 0.70:0.30, 0.75:0.25 and 0.80:0.20, while determining the direction from the probability distribution at each step. As a result, the 3-D development of multiple sand spits and cuspate forelands with rhythmic shapes was successfully explained by the present model and the results of the previous study in [2] were reconfirmed and reinforced. Because the wave field was predicted using the energy balance equation for irregular waves in this study, the wave field including wave refraction, wave breaking and the wave-sheltering effect can be systematically predicted. In addition, because 2-D sand transport equations were employed in our model, in contrast to the model in [2] in which the longshore sand transport formula was used, this model has the advantages of the conventional 3-D model for predicting beach changes for various applications. In addition to the prediction of the development of sand spits and cuspate forelands with rhythmic shapes owing to the high-angle wave instability under natural conditions, the impact of anthropogenic factors, such as the construction of a groin or a breakwater, on the beach changes was predicted. It was concluded that the construction of a groin had a marked impact on the sandy beach; the alteration from the field with the development of the sand spits to that with the elongation of a single sand spit, Regarding the development of multiple sand spits and cuspate forelands with rhythmic shapes observed along the shore of the Azov Sea [1], the BG model was used to simulate the shoreline evolution caused by high-angle wave instability. The wave direction was assumed to be obliquely incident from 60°, 50° and 40° counterclockwise or from the directions of ±60° with probabilities of 0.5:0.5 and 0.60:0.40, 0.65:0.35, 0.70:0.30, 0.75:0.25 and 0.80:0.20, while deter‐ mining the direction from the probability distribution at each step. As a result, the 3-D development of multiple sand spits and cuspate forelands with rhythmic shapes was success‐ fully explained by the present model and the results of the previous study in [2] were recon‐ firmed and reinforced. Because the wave field was predicted using the energy balance equation for irregular waves in this study, the wave field including wave refraction, wave breaking and the wave-sheltering effect can be systematically predicted. In addition, because 2-D sand transport equations were employed in our model, in contrast to the model in [2] in which the longshore sand transport formula was used, this model has the advantages of the conventional 3-D model for predicting beach changes for various applications.

transport. In addition to the prediction of the development of sand spits and cuspate forelands with rhythmic shapes owing to the high-angle wave instability under natural conditions, the impact of anthropogenic factors, such as the construction of a groin or a breakwater, on the beach

as well as the acceleration of offshore sand transport because of the blockage of longshore sand

changes was predicted. It was concluded that the construction of a groin had a marked impact on the sandy beach; the alteration from the field with the development of the sand spits to that with the elongation of a single sand spit, as well as the acceleration of offshore sand transport because of the blockage of longshore sand transport.
