著者

高橋 龍太郎 羽鳥 徳太郎

出版者

東京大学地震研究所

雑誌

東京大学地震研究所彙報 (ISSN:00408972)

巻号頁・発行日

vol.40, no.4, pp.873-883, 1963-03-10

---

1. There are many theoretical studies on the generation of gravity waves due to an initial surface elevation or to a surface impulse. As to model experiments, however, very few studies have been made on this subject. Recent investigations of after-shocks and the propagation of tsunami waves have revealed that most of the generating area of a tsunami seems to be strongly elliptical in shape. The present experiment has been undertaken to clarify experimentally the characteristics of waves generated by a sudden dislocation of the bottom of elliptic shape. The experiment was carried out in a model basin (25m×40m×0.6m), in Chiba Prefecture, belonging to the Earthquake Research Institute. (Fig. 19). 2. The wave generator is an iron box, 94 cm × 56 cm × 4 cm in size, placed at the bottom level of the basin. It has an elliptic opening on the top covered with a rubber membrane, 2 mm thick, 90 cm × 30 cm (Fig. 20). This elliptic rubber membrane is made to swell out suddenly by compressed air as shown in Figs. 1 and 21. The wave-height gauge is of the parallel-wire type, consisting of 2 stainless steel triangular plates (Fig. 2). The sensitivity of the recorder is such that a deflection of 10mm on the record corresponds to 5.0mm in the water level change. No remarkable effect of capillarity exists in the records. The wave-heights were recorded by a 12-channel portable optical oscillograph. Eleven wave-height gauges were used, the remaining channel of the oscillograph being reserved for recording the motion of the center of the rubber membrane. The oscillograph chart was driven at a speed of either 10 or 30 mm/sec. 3. Records of waves due to the upheaval of the membrane were obtained at every foot from the center of the origin up to 4m and for a water depth of 5.0 cm and 17.3 cm. Details of experimental runs are shown in Table 1 and Fig. 5. A record in Fig. 6 shows the displacement of the center of the rubber membrane when the paper speed is 100 mm/sec. The time of the displacement was fixed at about 1/40 sec for all runs in the experiments. Figs. 7 and 8 show the final forms of the rubber membrane when expanded under certain pressures. Forms may be considered to be nearly a part of a paraboloid. 4. Figs. 22 and 23 are wave-height records for the water depths of 5.0 cm and 17.3 cm respectively. In these records, Nos. 1, 2 and 7 show wave-heights, respectively, just above the center of the origin and at the ends of the short and long axes of the elliptic rubber membrane. No. 12 is a record of the displacement of the centre of the origin. The front of a wave train is propagated roughly with the velocity √gh, except in the immediate neighbourhood of the origin, where a considerably larger velocity is observed. (Fig. 9) Wave trains have a dispersive character as shown in Fig. 11. 5. The initial surface elevation of water above the origin is about half of the displacement of the bottom itself. (Fig. 12). The ratio of the wave-heights at the ends of the long and short axes of the origin area is one-third, but for the positions distant from the origin, this ratio decreases. This result is interesting because the height ratio coincides with the length ratio of the elliptical axes (Fig. 13). The amplitude of an initial crest seems to decrease as r-0.5 and r-0.74 when the depths are 5.0cm and 17.3cm respectively (Fig. 14). Energy of the long-wave can be expressed as follows: E∝rη2L r: distance, η: wave-height, L: length of wave. Then we have EB/EA=(ηB/ηA)2 LB/LA EA, ηA and LA are energy, wave-height and wave length respectively along the long axis. EB, ηB and LB are corresponding quantities along the short axis. At the elliptic margin of the origin we have ηb/ηa = 3, Lb/La = 0.42, therefore Eb/Ea = 3.8, in the case of a water depth of 5 cm. For the distances 1m ≧ r ≧ 4m ηB/ηA = 1.8, LB/LA = 0.40, EB/EA = 1.3 Fig. 16 shows the azimuthal distribution of energy obtained by Run 8. The relation between the wave-length of the waves emitted into a certain direction and the radius of the ellipse in that direction seems to indicate that these two lengths are roughly proportional in the case of shallow water. (Fig. 17).