*5.1.4. Changes in longitudinal profiles*

Figures 15(a)-15(d) show the experimental and predicted changes in longitudinal profiles along transect *X* = 0 m located at the right boundary, and transects *X* = 9, 12 and 14 m crossing the flat shallow seabed, respectively. Along transect *X* = 0 m, although the experimental and predicted results, which indicated that the depth of closure was -12 cm, are in agreement, as shown in Fig. 15(a), the eroded volume in the calculation was overestimated in the nearshore zone, where there was less scarp erosion. However, the sand budget in the cross section was approximately maintained and the parallel recession of the cross section while maintaining a constant slope was accurately predicted in the calculation. Along transect *X* = 9 m, the development of a berm of 5 cm height after 1 hr, as shown in Fig. 15(b), was observed in both the experiment and simulation, but the location of the berm was slightly seaward in the simulation. After 8 hr, however, the berm location had moved landward and a stable barrier island had formed. These experimental and calculated changes are in good agreement. Furthermore, no beach changes occurred on the flat shallow seabed because the elongation of the sand spit was too rapid to permit wave intrusion into the flat seabed. Along transect *X* = 12 m, the elongation of the sand spit was limited until 1 hr, as shown in Fig. 15(c), and there was little development of the berm. However, a substantial berm had developed after 8 hr. The experimental and calculated results are in good agreement regarding these points. Along transect *X* = 14 m near the left boundary, although a sand bar did not develop until 1 hr, a large amount of sand had been deposited after 8 hr, forming a barrier island with a 1.2 m width, as shown in Fig. 15(d). In this case, the seabed slope gradually steepened because of the continuous deposition of sand along the offshore steep slope, resulting in the deposition of sand up to a depth of -23 cm, which is approximately two fold larger than the depth of closure of -12 cm.

## **5.2. Formation of cuspate foreland on steep coast**

## *5.2.1. Bathymetric changes*

Figures 16(a)-16(f) show the results for the calculation of the development of a cuspate foreland on a steep coast *t* = 0, 0.5, 1, 2, 4, and 8 hr after the start of wave generation given the same conditions as those in the experiment. The contour lines that extended parallel to

BG Model Based on Bagnold's Concept and

Its Application to Analysis of Elongation of Sand Spit and Shore – Normal Sand Bar 357

**Figure 14.** Sand transport flux (Case 1: flat shallow seabed).

**Figure 13.** Changes in wave height (Case 1: flat shallow seabed).

**Figure 14.** Sand transport flux (Case 1: flat shallow seabed).

**Figure 13.** Changes in wave height (Case 1: flat shallow seabed).

BG Model Based on Bagnold's Concept and

Its Application to Analysis of Elongation of Sand Spit and Shore – Normal Sand Bar 359

each other at the initial stage around the location with an abrupt change in the coastline orientation rapidly changed over time, causing sand deposition in the deep zone and the formation of a cuspate foreland after 0.5 hr. After 1 hr, the shoreline protruded further and a neck in the contour had formed downcoast of the sand deposition zone of the cuspate foreland. The size of this neck increased with time, and a sand spit that enclosed a shallow sea inside the neck had formed after 2 hr. This morphology is very similar to that of Miho Peninsula, formed by the extension of a sand spit, and Miho Bay in Shizuoka Prefecture (Uda & Yamamoto, 1994). Because of the continuous sand supply from upcoast, the sand spit elongated and the tip became connected to the downcoast shoreline. As a result, the shallow sea located inside the neck had formed a pond after 4 hr. After 8 hr, a steep slope had formed along the shoreline of the cuspate foreland owing to the continuous sand deposition in the deeper zone, whereas a wave base with a gentle slope had formed on the

Figures 17(a)-17(f) show bird's-eye view of the development of a cuspate foreland on a steep coast. Although sand transported from upcoast was deposited on the steep seabed, the deposition of sand started near the location with an abrupt change in the coastline orientation, forming a neck in the contours, as shown in Figs. 17(a) and 17(b). This neck moved landward with time, and finally a sandy beach with a flat surface and a steep slope

Figures 18(a)-18(c) show the distributions of the calculated wave height after wave generation for 0, 1 and 8 hr. At the initial stage, the longshore change in the wave height is large near the location with an abrupt change in the coastline orientation. Although a semicircular cuspate foreland developed until 1 hr, a marked decay in the wave height occurred over the short distance along the protruding shoreline, because the wave height was extremely low behind the protruded shoreline. The change in longshore sand transport due to this decay in wave height was successfully taken into account by the additional term given by Ozasa & Brampton (1980). The spatial change in longshore sand transport is large in this area because of the abrupt decrease in wave height, meaning that sand was rapidly deposited. However, after 8 hr, the area where the wave height abruptly decreased had

Figure 19 shows the sand transport flux after wave generation for 0, 1 and 8 hr. Although the sand transport flux was initially large to the right of *X* = 8 m, which is the sand supply area, as in Case 1, after 1 hr the area with a large sand transport flux had moved leftward with the elongation of the sand spit. Moreover, the sand transport flux was reduced because the angle between the direction normal to the contour lines and the direction of incident waves decreased near the right boundary. After 8 hr, the sand spit had reached the left boundary, and the absolute value of sand transport flux decreased because the angle

disappeared and the wave height was smoothly distributed alongshore.

coast from which sand was supplied.

*5.2.2. Changes in wave field*

*5.2.3. Sand transport flux*

offshore of the shoreline had formed after 8 hr.

**Figure 15.** Changes in longitudinal profiles (Case 1: flat shallow seabed).

each other at the initial stage around the location with an abrupt change in the coastline orientation rapidly changed over time, causing sand deposition in the deep zone and the formation of a cuspate foreland after 0.5 hr. After 1 hr, the shoreline protruded further and a neck in the contour had formed downcoast of the sand deposition zone of the cuspate foreland. The size of this neck increased with time, and a sand spit that enclosed a shallow sea inside the neck had formed after 2 hr. This morphology is very similar to that of Miho Peninsula, formed by the extension of a sand spit, and Miho Bay in Shizuoka Prefecture (Uda & Yamamoto, 1994). Because of the continuous sand supply from upcoast, the sand spit elongated and the tip became connected to the downcoast shoreline. As a result, the shallow sea located inside the neck had formed a pond after 4 hr. After 8 hr, a steep slope had formed along the shoreline of the cuspate foreland owing to the continuous sand deposition in the deeper zone, whereas a wave base with a gentle slope had formed on the coast from which sand was supplied.

Figures 17(a)-17(f) show bird's-eye view of the development of a cuspate foreland on a steep coast. Although sand transported from upcoast was deposited on the steep seabed, the deposition of sand started near the location with an abrupt change in the coastline orientation, forming a neck in the contours, as shown in Figs. 17(a) and 17(b). This neck moved landward with time, and finally a sandy beach with a flat surface and a steep slope offshore of the shoreline had formed after 8 hr.
