**Author details**

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

B

steps (Fig. 20(h))

A

**a**

C

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 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

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

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

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

(b) Calculation results after 4 × 10<sup>4</sup>

**b**

**5. Conclusions** 

448 Computational and Numerical Simulations

**5. Conclusions**

transport.

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

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

conventional 3-D model for predicting beach changes for various applications.

3-D model for predicting beach changes for various applications.

Takaaki Uda1 , Masumi Serizawa2 and Shiho Miyahara2

