*5.1. Wave Field*

The formation of shoreline undulations including sand spits along the east coast of Lingayen Gulf may occur due to high-angle wave instability [1] because of oblique wave incidence with a large angle to the shoreline. Thus, the wave field in Lingayen Gulf was calculated using the energy balance equation [9], given the seabed contours of the gulf, as shown in Figure 2. The direction of incident waves was assumed to be N, corresponding to the direction of the most frequent energy mean waves, as shown in Table 1, referring to the Global Wave Statistics [8], with a wave height of 2.81 m and a wave period of 6.2 s. The directional spreading parameter (*S*max) was selected to be 25 for waves with a large steepness and 75 for ocean waves.

Figure 26 shows the results of the calculation when *S*max is given as 75. The wave height in the vicinity of the Balili River mouth near the bay mouth is 1.2 m, and the wave height reduces toward the bottom of the gulf, resulting in *H* = 0.9 m near the sand spit at Santo Tomas. The wave direction is shown in Figure 26b, where a positive angle is the value measured counterclockwise with respect to the -*Y* direction.

**Figure 26.** Predicted wave height and wave direction in Lingayen Gulf (*S*max = 75), (**a**) wave height, (**b**) waive direction.

The wave angle relative to the direction normal to the coastline is over 45◦ at any point, taking the direction of the coastline into account. Similar results when *S*max is 25 are shown in Figure 27. The reduction of the wave height from the entrance of the gulf toward the bottom of the gulf is the same as that when *S*max is 75, with *H* = 1.37 m around the Balili River and *H* = 1.1 m near the sand spit at Santo Tomas. Comparing the two results highlights that the wave height along the coastline is greater when *S*max is 75 than that when *S*max is 25 because of the concentration of wave propagation. The wave angle relative to the direction normal to the coastline is greater than or close to 45◦ at any point. When the angle between the direction normal to the shoreline and the wave direction exceeds 45◦ at a point along the shoreline, the shoreline protrusion occurs at such a point owing to high-angle wave instability [1,2,12]. Thus, shoreline undulations or sand spits are capable of forming along the east coastline in Lingayen Gulf.

**Figure 27.** Predicted wave height and wave direction in Lingayen Gulf (*S*max = 25) (**a**) wave height, (**b**) waive direction.
