4. Oscillation system between the main island of Kyushu and Okinawa Trough

The amplification of harbor oscillation requires continuous wave energy incidence into the harbor. Figure 14 shows the water surface displacements at Point ①, off the mouth of Urauchi Bay, owing to the atmospheric-pressure wave of pattern (a), where L = 10.0 km, Pmax = 1.0 hPa, and Cp = 20.0 m/s. In the figure, the numerical result, in consideration of wave reflection at the west coasts of the main island of Kyushu, is compared with that without wave reflection at the west coasts of the main island of Kyushu, where the target domain for the latter is a restricted area between 123°E and 130°E. In the former case, an oscillation system is generated off the southern Kyushu, between the main island of Kyushu and Okinawa Trough, resulting in the continuous motion of water surface, to make heavier harbor oscillation in, for example, Urauchi Bay. Another oscillation system off the northern Kyushu may also appear between the main island of Kyushu and other islands, without the submarine trough, as suggested by Hibiya and Kajiura [3].

In order to examine the generation of an oscillation system between Okinawa Trough and the main island of Kyushu, we perform numerical experiments for a hypothetical seabed configuration. Figure 15(a) shows the actual seabed configuration along the latitude of 31.8°E, where Urauchi Bay is located as shown in Figure 5, while Figure 15(b) shows the hypothetical seabed configuration, where the trough length is extended to make the distance between wave reflection points larger. In both cases, the perfect reflection boundary condition is adopted at the west coasts of the main island of Kyushu.

In the one-dimensional computation for long waves, the nonlinear surface wave equations based on a variational principle [17] is applied to consider both the strong nonlinearity and dispersion of long waves over the shallower areas, as well as the deeper trough, where the velocity potential is assumed to show a linear distribution in the vertical direction. The water surface profile is given by η (m) = 0.2 m sin [2π(x 790.0 km)/27.7 km] (790.0 km ≤ x ≤ 817.7 km), and the velocity potential is zero everywhere, at the initial time. Figure 16 shows the water surface displacements at Points P1–P5, for the hypothetical seabed configuration illustrated in Figure 15(b), where the fundamental equations were solved using the implicit

#### Figure 14.

The numerical results for the water surface displacements at point ① indicated in Figure 5. The atmosphericpressure profile is pattern (a), where L = 10.0 km, Pmax = 1.0 hPa, and Cp = 20.0 m/s. The solid and broken lines represent the results with and without wave reflection at the west coasts of the main island of Kyushu, respectively.

scheme [18]. An oscillation system with repeated reciprocation of long waves has been built up, resulting in the periodical oscillation at Point P4, where Koshiki Islands are situated. Such continuous undulation in water surface contributes to amplify harbor oscillation in bays and harbors at the west coasts of the southern

The water surface displacements at the Points P1–P5 for the hypothetical seabed configuration illustrated in

The seabed configurations of East China Sea along the latitude of 31.8°E: The actual seabed configuration

Long-Wave Generation due to Atmospheric-Pressure Variation and Harbor Oscillation…

(a), and a hypothetical seabed configuration with an extended trough (b).

DOI: http://dx.doi.org/10.5772/intechopen.85483

Kyushu.

91

Figure 16.

Figure 15(b).

Figure 15.

Long-Wave Generation due to Atmospheric-Pressure Variation and Harbor Oscillation… DOI: http://dx.doi.org/10.5772/intechopen.85483

Figure 15.

wave height of about 0.3 m, and the wave period of the long wave with the

without the submarine trough, as suggested by Hibiya and Kajiura [3].

4. Oscillation system between the main island of Kyushu and Okinawa

The amplification of harbor oscillation requires continuous wave energy incidence into the harbor. Figure 14 shows the water surface displacements at Point ①, off the mouth of Urauchi Bay, owing to the atmospheric-pressure wave of pattern (a), where L = 10.0 km, Pmax = 1.0 hPa, and Cp = 20.0 m/s. In the figure, the numerical result, in consideration of wave reflection at the west coasts of the main island of Kyushu, is compared with that without wave reflection at the west coasts of the main island of Kyushu, where the target domain for the latter is a restricted area between 123°E and 130°E. In the former case, an oscillation system is generated off the southern Kyushu, between the main island of Kyushu and Okinawa Trough, resulting in the continuous motion of water surface, to make heavier harbor oscillation in, for example, Urauchi Bay. Another oscillation system off the northern Kyushu may also appear between the main island of Kyushu and other islands,

In order to examine the generation of an oscillation system between Okinawa Trough and the main island of Kyushu, we perform numerical experiments for a hypothetical seabed configuration. Figure 15(a) shows the actual seabed configuration along the latitude of 31.8°E, where Urauchi Bay is located as shown in Figure 5, while Figure 15(b) shows the hypothetical seabed configuration, where the trough length is extended to make the distance between wave reflection points larger. In both cases, the perfect reflection boundary condition is adopted at the

In the one-dimensional computation for long waves, the nonlinear surface wave equations based on a variational principle [17] is applied to consider both the strong nonlinearity and dispersion of long waves over the shallower areas, as well as the deeper trough, where the velocity potential is assumed to show a linear distribution in the vertical direction. The water surface profile is given by η (m) = 0.2 m sin [2π(x 790.0 km)/27.7 km] (790.0 km ≤ x ≤ 817.7 km), and the velocity potential is zero everywhere, at the initial time. Figure 16 shows the water surface displacements at Points P1–P5, for the hypothetical seabed configuration illustrated in Figure 15(b), where the fundamental equations were solved using the implicit

The numerical results for the water surface displacements at point ① indicated in Figure 5. The atmosphericpressure profile is pattern (a), where L = 10.0 km, Pmax = 1.0 hPa, and Cp = 20.0 m/s. The solid and broken lines represent the results with and without wave reflection at the west coasts of the main island of Kyushu,

maximum wave height is around 2600 s.

Natural Hazards - Risk, Exposure, Response, and Resilience

west coasts of the main island of Kyushu.

Trough

Figure 14.

respectively.

90

The seabed configurations of East China Sea along the latitude of 31.8°E: The actual seabed configuration (a), and a hypothetical seabed configuration with an extended trough (b).

Figure 16.

The water surface displacements at the Points P1–P5 for the hypothetical seabed configuration illustrated in Figure 15(b).

scheme [18]. An oscillation system with repeated reciprocation of long waves has been built up, resulting in the periodical oscillation at Point P4, where Koshiki Islands are situated. Such continuous undulation in water surface contributes to amplify harbor oscillation in bays and harbors at the west coasts of the southern Kyushu.
