ON THE WAVE RUN-UP AFTER BREAKING ON THE BEACH RT HIRATSUKA, KANAGAWA PREFECTURE

Abstract

The previous paper (Terada, 1972) has discussed the daily changes of the longitudinal profile of the beach. This paper describes the relationship between the wave run-up after breaking and deep water waves. Symbols used in this paper and their definitions are given in Fig. 1. Table 1 shows the results of measurments of deep water waves and the wave run-up during the survey period. Figure 2 illustrates the relationship between the relative run-up height R/H0 and the deep water wave steepness H0/L0. In this figure it is noticed that R/H0 decreases with increasing H0/L0. The equation obtained for the beach at Hiratsuka is given as follows: R/H0=0, 118(H0/L0)-0.5. (1) Hunt (1959) expressed the laboratory relationship between R/H0 and H0/L0 by the fol-lowing equation: R/H0=1, 01tan α(H0/L0)-0.5φ; (2) where tan a is beach slope, and φ is the reduction factor which decreases with increasing sand grain size. Accordingly, in case where tan a and H0/L0 are constant, R/H0 varies with the value of φ. Namely, the relative run-up height decreases with increasing sand grain size. Applying Eq. (2) to Hiratsuka and substituting tan α=0.102 and φ=0.82 (dm s≈1.0mm) into the equation, we obtain the following equation: R/H0=0, 083(H0/L0)-0.5. (3) Comparing Eq. (1) with Eq. (3), the actual value of R/H0 is about 40% larger than the estimated value by Eq. (2) for the same value of H0/L0. This discord may probably be caused by the difference between the irregular wave in the present field and the regular wave in the wave tank experiment. Figure 4 shows the relationship between the wave run-up length Rx and the breaker height Hb, Rx tending to increase with increasing Hb. The relationship between Rx and Hb takes the form: Rx=17.6Hb. (4) In the investigation of the wave run-up on the beach at Santa Rosa Island, U. S. A. Waddell (1973) formulated the relationship between Rx and Hb in the following equation: Rx=57.8 Hb. (5) Comparing Eq. (4) with Eq. (5), the value of Rx on Santa Rosa Island is about 3 times larger than that on Hiratsuka for the same value of Hb. Some study on the notable dif-ference in Rx at both locations will be attempted in the following. Table 2 shows the conditions of topographic feature, beach sand and breaker height on Hiratsuka and on Santa Rosa Island. Except the beach slope which is approximately equal at both locations, great differences between the both locations are present in the foreshore width, backshore width and sand grain size. These factors on Hiratsuka are about 2 to 4 times larger than those on Santa Rosa Island, and further, the specific gravity of minerals consituting th beach sand is slightly larger in the case of Hiratsuka. The breaker height on Hiratsuka is about 3 times larger than that on Santa Rosa Island. H0/L0 is theoretically represented Hunt's equation (2), from which R is derived as follows: R=1, 01 tan α H0 (H0/L0)-0.5φ. (6) Also, as it is obvious in Fig. 1, Ry can be written in the form: Ry=Rx•tan α. (7) The value of R in Eq. (6) is not equal to the value of Ry in Eq. (7). However, as both are equivalent to each other in their physical phenomena, Eq. (6) is expressed by the fol-lowing equation, which is obtained by substituting Eq. (7) into R in Eq. (6):