6.2 Amplification in the L-type harbors

Figure 23 shows L-type harbors, as well as an I-type harbor, where the harboraxis length is 2000 m, while the bending position of the L-type harbors is different. The still water depth h is 20.0 m in the computational domains.

#### Figure 23.

The horizontal shapes of the L-type harbors with different bending positions, as well as the I-type harbor, where the harbor-axis length is 2000 m. The still water depth h is 20.0 m.

#### Figure 24.

The values of amplification factor R at the head of the L-type harbors with different bending positions LA, as well as that of the I-type harbor with the same harbor-axis length, shown in Figure 23.

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

Shown in Figure 24 is the amplification factor R at the head of the L-type harbors with different bending positions, as well as the I-type harbor, shown in Figure 23, where R is defined by the ratio between the maximum wave height at each point, and the wave height of the incident waves, that is, 0.2 m; kl is dimensionless wave number, that is, 2πl= T ffiffiffiffiffi gh � � p . Although both the values of R and kl for the first mode in all the harbors are almost the same, the value of R for the second mode increases as the distance between the bending position and the harbor head, LA, is increased. It should be noted that when LA is 1000 and 1200 m, the value of R at the head of the L-type harbors is larger than that of the I-type harbor with the same harbor-axis length.

#### 6.3 Amplification in the I-type harbors with a narrowed area

Figure 25 shows I-type harbors with a narrowed area, where the position, or the width, of the narrowed area is different. The still water depth h is 20.0 m in the computational domains.

Shown in Figure 26 is the amplification factor R at the points indicated in Figure 25 for the I-type harbors with a narrowed area, where the same symbols are used for the numerical results as that for the corresponding positions shown in Figure 25. The value of R at the head for the first mode is larger in harbor I2 than that in harbor I1, where the narrowed area is located at the harbor mouth, while the second mode shows the opposite phenomenon. The value of R at the head for the

Figure 25.

T-type, while the actual bay is Urauchi Bay. We examine numerical calculation results for the amplification factor of wave height due to oscillation in these harbors.

The computational domain for harbor oscillation in an I-type harbor. The incident waves, the wave height of

Figure 23 shows L-type harbors, as well as an I-type harbor, where the harboraxis length is 2000 m, while the bending position of the L-type harbors is different.

The horizontal shapes of the L-type harbors with different bending positions, as well as the I-type harbor, where

The values of amplification factor R at the head of the L-type harbors with different bending positions LA, as

well as that of the I-type harbor with the same harbor-axis length, shown in Figure 23.

The still water depth h is 20.0 m in the computational domains.

the harbor-axis length is 2000 m. The still water depth h is 20.0 m.

which is 0.2 m, enter the computational domain through its leftward boundary.

Natural Hazards - Risk, Exposure, Response, and Resilience

6.2 Amplification in the L-type harbors

Figure 22.

Figure 23.

Figure 24.

96

The horizontal shapes of the I-type harbors with a narrowed area, where the position, or the width, of the narrowed area is different. The harbor length is 2000 m, and the still water depth h is 20.0 m.

#### Figure 26.

The values of amplification factor R at the points indicated in Figure 25 for the I-type harbors with a narrowed area. The numerical results are represented with the same symbols as that used for the corresponding positions shown in Figure 25.

Conversely, the amplification factor R for the C-type harbor shows large values at the longitudinal centers of the I-type harbors, as well as that of the connecting channel, for the value of R depends on the phase difference between the long waves

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

Shown in Figure 29 are the seabed configurations of I-type harbors with a seabed crest or a seabed trough, where the still water depth is 10.5 or 29.5 m at the longitudinal center, respectively; except at the longitudinal center, the seabed is uniformly sloping inside the harbors. The still water depth is 20.0 m at both the head and mouth of the harbors, as well as outside the harbors in the computational domains. The length and width of the harbors are 2000 and 400 m, respectively. Figure 30 shows the amplification factor R at the head of the I-type harbors with a seabed crest or trough, shown in Figure 29, as well as that of the I-type harbor with a flat seabed, shown in Figure 23. In the I-type harbor with the seabed crest, the first and the second modes appear at lower values of kl than those with the seabed trough, respectively, for the average water depth is shallower in the former than in the latter. At the head of the I-type harbor with the seabed crest, the value of R for the first mode is larger than that for the second mode, while at the head of the

The side views of the I-type harbors with a seabed crest (the left-hand side) and a seabed trough (the right-hand side). The length and width of the harbors are 2000 and 400 m, respectively. The still water depth is 20.0 m

The values of amplification factor R at the head of the I-type harbors with the seabed crest or trough shown in

Figure 29, as well as that with a flat seabed, shown in Figure 24.

6.5 Amplification in the I-type harbors with a seabed crest or trough

I-type harbor with the seabed trough, the reverse is true.

outside the harbors in the computational domains.

coming through two mouths.

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

Figure 29.

Figure 30.

99

#### Figure 27.

The horizontal shape of the C-type harbor, where two I-type harbors are connected with a rectangular-section channel. The still water depth h is 20.0 m.

second mode is larger in harbor I3 than that in harbor I4, where the harbor width at the narrowed area is narrower than that in harbor I3.

#### 6.4 Amplification in the C-type harbor

Depicted in Figure 27 is a C-type harbor, where two I-type harbors are connected with a rectangular-section channel, such that the C-type harbor has two mouths. The still water depth h is 20.0 m in the computational domain.

Figure 28 shows the amplification factor R in the C-type harbor shown in Figure 27. At the heads of the I-type harbors, the long waves coming through two mouths are in almost opposite phase, such that the value of R becomes lower than that at the head of the corresponding I-type harbor alone, as shown in Figure 24.

#### Figure 28.

The values of amplification factor R at the longitudinal centers of the I-type harbors, the heads of the I-type harbors, and the longitudinal center of the connecting channel, for the C-type harbor shown in Figure 27.

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

Conversely, the amplification factor R for the C-type harbor shows large values at the longitudinal centers of the I-type harbors, as well as that of the connecting channel, for the value of R depends on the phase difference between the long waves coming through two mouths.

#### 6.5 Amplification in the I-type harbors with a seabed crest or trough

Shown in Figure 29 are the seabed configurations of I-type harbors with a seabed crest or a seabed trough, where the still water depth is 10.5 or 29.5 m at the longitudinal center, respectively; except at the longitudinal center, the seabed is uniformly sloping inside the harbors. The still water depth is 20.0 m at both the head and mouth of the harbors, as well as outside the harbors in the computational domains. The length and width of the harbors are 2000 and 400 m, respectively.

Figure 30 shows the amplification factor R at the head of the I-type harbors with a seabed crest or trough, shown in Figure 29, as well as that of the I-type harbor with a flat seabed, shown in Figure 23. In the I-type harbor with the seabed crest, the first and the second modes appear at lower values of kl than those with the seabed trough, respectively, for the average water depth is shallower in the former than in the latter. At the head of the I-type harbor with the seabed crest, the value of R for the first mode is larger than that for the second mode, while at the head of the I-type harbor with the seabed trough, the reverse is true.

#### Figure 29.

second mode is larger in harbor I3 than that in harbor I4, where the harbor width at

The horizontal shape of the C-type harbor, where two I-type harbors are connected with a rectangular-section

Depicted in Figure 27 is a C-type harbor, where two I-type harbors are connected with a rectangular-section channel, such that the C-type harbor has two

Figure 28 shows the amplification factor R in the C-type harbor shown in Figure 27. At the heads of the I-type harbors, the long waves coming through two mouths are in almost opposite phase, such that the value of R becomes lower than that at the head of the corresponding I-type harbor alone, as shown in Figure 24.

The values of amplification factor R at the longitudinal centers of the I-type harbors, the heads of the I-type harbors, and the longitudinal center of the connecting channel, for the C-type harbor shown in Figure 27.

mouths. The still water depth h is 20.0 m in the computational domain.

the narrowed area is narrower than that in harbor I3.

Natural Hazards - Risk, Exposure, Response, and Resilience

6.4 Amplification in the C-type harbor

channel. The still water depth h is 20.0 m.

Figure 27.

Figure 28.

98

The side views of the I-type harbors with a seabed crest (the left-hand side) and a seabed trough (the right-hand side). The length and width of the harbors are 2000 and 400 m, respectively. The still water depth is 20.0 m outside the harbors in the computational domains.

#### Figure 30.

The values of amplification factor R at the head of the I-type harbors with the seabed crest or trough shown in Figure 29, as well as that with a flat seabed, shown in Figure 24.

Figure 31.

The horizontal shapes of the T-type harbor (the left-hand side), the I-type harbor (the middle), and the L-type harbor (the right-hand side), where the T-type harbor includes both the I-type and L-type harbors. The harbor width is 600 m, and the still water depth h is 20.0 m.

#### 6.6 Amplification in the T-type harbors

A T-type harbor has two heads, as shown in Figure 31, where an I-type and Ltype harbors are also depicted for comparison. The harbor width is 600 m, and the still water depth h is 20.0 m in the computational domains.

Figure 32 shows the amplification factor R<sup>m</sup> at the heads of the T-, I-, and L-type harbors shown in Figure 31, where R<sup>m</sup> is defined by the ratio between the maximum wave height at each point and that at the harbor mouth. The second mode, specific to T-type harbors, appears when the wave period of the incident waves,T, is about 640 s, where the oscillation shows antinodes at two heads of the T-type harbor.

facing Urauchi Bay, where the amplification factor R<sup>m</sup> is defined by the ratio between the maximum wave height at each point and that at the bay mouth. It should be noted that Oshima Fishing Port is located at one of the bay heads, while Kuwanoura Fishing Port is at another bay branch, but not at its head. Although the oscillation period T for the first mode is 1580 s at both Oshima and Kuwanoura Fishing Ports, the period T for the second mode is 720 s at Oshima Fishing Port, while 600 s at Kuwanoura Fishing Port. The values of R<sup>m</sup> for both the first and second modes at Oshima Fishing Port, where eight fishing boats capsized owing to the heavy harbor oscillation during February 24–26, 2009, as mentioned above, are

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

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

The values of amplification factor Rm at Oshima and Kuwanoura Fishing Ports facing Urauchi Bay, as shown in Figure 1, where the former is located at a bay head, while the latter in another branch is not at another bay

The time variations of the water surface displacements at Oshima and Kuwanoura Fishing Ports are shown in Figure 34, where those for T = 800 s, near the second modes, show large phase difference between these two branches, for

The time variations of water surface displacements at Oshima and Kuwanoura Fishing Ports facing Urauchi

Bay, where T is the wave period of the incident waves. (a) T = 1600 s; (b) T = 800 s.

larger than those at Kuwanoura Fishing Port, respectively.

Figure 33.

Figure 34.

101

head.

6.7.2 Water surface displacements at the ports of Urauchi Bay

#### 6.7 Harbor oscillation in Urauchi Bay

#### 6.7.1 Amplification in Urauchi Bay

Urauchi Bay has two bay heads, as shown in Figure 1, such that the bay has a shape similar to that of a T-type harbor. Figure 33 shows the amplification factor R<sup>m</sup> at two fishing ports, that is, Oshima Fishing Port and Kuwanoura Fishing Port,

#### Figure 32.

The values of amplification factor Rm at points A and B, which are located at the heads of the T-, I-, and L-type harbors shown in Figure 31, where Rm is defined by the ratio between the maximum wave height at each point and that at the harbor mouth.

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

#### Figure 33.

6.6 Amplification in the T-type harbors

width is 600 m, and the still water depth h is 20.0 m.

Natural Hazards - Risk, Exposure, Response, and Resilience

6.7 Harbor oscillation in Urauchi Bay

6.7.1 Amplification in Urauchi Bay

harbor.

Figure 32.

100

and that at the harbor mouth.

Figure 31.

still water depth h is 20.0 m in the computational domains.

A T-type harbor has two heads, as shown in Figure 31, where an I-type and Ltype harbors are also depicted for comparison. The harbor width is 600 m, and the

The horizontal shapes of the T-type harbor (the left-hand side), the I-type harbor (the middle), and the L-type harbor (the right-hand side), where the T-type harbor includes both the I-type and L-type harbors. The harbor

Figure 32 shows the amplification factor R<sup>m</sup> at the heads of the T-, I-, and L-type harbors shown in Figure 31, where R<sup>m</sup> is defined by the ratio between the maximum wave height at each point and that at the harbor mouth. The second mode, specific to T-type harbors, appears when the wave period of the incident waves,T, is about 640 s, where the oscillation shows antinodes at two heads of the T-type

Urauchi Bay has two bay heads, as shown in Figure 1, such that the bay has a shape similar to that of a T-type harbor. Figure 33 shows the amplification factor R<sup>m</sup> at two fishing ports, that is, Oshima Fishing Port and Kuwanoura Fishing Port,

The values of amplification factor Rm at points A and B, which are located at the heads of the T-, I-, and L-type harbors shown in Figure 31, where Rm is defined by the ratio between the maximum wave height at each point

The values of amplification factor Rm at Oshima and Kuwanoura Fishing Ports facing Urauchi Bay, as shown in Figure 1, where the former is located at a bay head, while the latter in another branch is not at another bay head.

facing Urauchi Bay, where the amplification factor R<sup>m</sup> is defined by the ratio between the maximum wave height at each point and that at the bay mouth. It should be noted that Oshima Fishing Port is located at one of the bay heads, while Kuwanoura Fishing Port is at another bay branch, but not at its head. Although the oscillation period T for the first mode is 1580 s at both Oshima and Kuwanoura Fishing Ports, the period T for the second mode is 720 s at Oshima Fishing Port, while 600 s at Kuwanoura Fishing Port. The values of R<sup>m</sup> for both the first and second modes at Oshima Fishing Port, where eight fishing boats capsized owing to the heavy harbor oscillation during February 24–26, 2009, as mentioned above, are larger than those at Kuwanoura Fishing Port, respectively.

#### 6.7.2 Water surface displacements at the ports of Urauchi Bay

The time variations of the water surface displacements at Oshima and Kuwanoura Fishing Ports are shown in Figure 34, where those for T = 800 s, near the second modes, show large phase difference between these two branches, for

#### Figure 34.

The time variations of water surface displacements at Oshima and Kuwanoura Fishing Ports facing Urauchi Bay, where T is the wave period of the incident waves. (a) T = 1600 s; (b) T = 800 s.

Urauchi Bay shows the oscillation resemble to a T-type harbor, with antinodes at two heads and a node at near the bifurcation.

the width, as well as the still water depth, of the actual bay is not uniform; the shape

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

We discuss disaster measures against meteotsunamis, generated to propagate toward the west coasts of Kyushu. In order to predict the generation and propagation of meteotsunamis in real time, it is necessary to obtain atmospheric-pressure variation far from Kyushu. If we know the sites, concerning the generation of meteotsunamis through atmospheric-pressure variation, the valuable information on atmospheric

a.We give some atmospheric-pressure variation at a site, to generate numerical simulation for atmosphere in a huge area including the Asian Continent, the Indian Ocean, and East China Sea, with a typical atmospheric condition for

b. If an atmospheric-pressure wave appears over East China Sea, we give the atmospheric-pressure wave at the sea surface as an external force, to obtain the amplitude distribution of long waves along the west coasts, as well as the islands, of Kyushu, by applying the numerical model based on Eqs. (1)–(3).

c. We repeat the abovementioned calculation process for various conditions on atmospheric pressure, with atmospheric-pressure variation at different sites.

(NOWPHAS) conducted by the Ministry of Land, Infrastructure, Transport and Tourism, at the coasts of Kyushu, with the corresponding atmosphericpressure conditions, to identify the sites in the Asian Continent and the Indian Ocean, which concerns the generation of meteotsunamis in East China Sea,

According to the real-time variation in atmospheric pressure at the important sites, we can pick up bays and ports, which involve the risk of meteotsunami attack,

Conversely, we can also utilize a pattern recognition system for atmosphericpressure distributions, instead of the inverse analysis, to exemplify dangerous

7.1.2 Prediction for the amplitude of long waves using atmospheric pressure above East

We can predict approximate values for meteotsunami parameters, including long-wave amplitude, based on real-time variation in atmospheric pressure at several sites in East China Sea. If we obtain atmospheric-pressure data from barometers at plural islands, such as Danjyo Islands and Uji islands, shown in Figure 5, far from

d.Using the results, we analyze inverse problems, where we give the distributions of long-wave amplitude, observed by, for example, the nationwide ocean wave information network for ports and harbors

to make adequate preparations for the meteotsunamis over a few days.

through atmospheric-pressure variation.

atmospheric-pressure patterns.

China Sea

103

pressure is restricted, such that the following inverse analysis is available:

of the actual bay is curving at some angle.

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

7.1.1 The application of an inverse analysis

each season.

7. Countermeasures against meteotsunamis

7.1 The real-time prediction of meteotsunami generation

#### 6.7.3 The damping processes of oscillations in the T-type harbor and Urauchi Bay

In order to study the damping process of oscillation in the T-type harbor shown in Figure 31, we continuously give incident waves to obtain a quasi-steady state of harbor oscillation, after which the incidence of waves is stopped when t = 0.0 s. Figure 35 shows the time variations of the maximum water level at point A indicated in Figure 31, during the damping of harbor oscillation for the first, second, and third modes after t = 0.0 s. The wave period of the incident waves,T, for the first, the second, and the third modes are 1150, 650, and 300 s, respectively, based on Figure 32. The damping of the oscillation for the second mode is slower than that for both the first and the third modes, because part of wave energy is trapped in the second-mode oscillation between two harbor heads.

Conversely, Figure 36 shows the time variations of the maximum water level at Oshima and Kuwanoura Fishing Ports facing Urauchi Bay shown in Figure 1. The wave period of the incident waves,T, is 1600 s for near the first mode, and 720 s for the second mode, based on Figure 33. The first-mode oscillation remains longer than the second-mode oscillation, which is not applicable to the T-type harbor mentioned above. Although future work is required to make this reason clear, we can tell the following difference between an actual bay and a typical T-type harbor:

Figure 35.

The time variations of the maximum water level at point A in the T-type harbor shown in Figure 31, for the harbor oscillation of the first, the second, and the third modes.

#### Figure 36.

The time variations of the maximum water level at Oshima and Kuwanoura Fishing Ports facing Urauchi Bay shown in Figure 1. The wave period of the incident waves,T, is 1600 s for near the first mode, and 720 s for the second mode, based on Figure 33.

the width, as well as the still water depth, of the actual bay is not uniform; the shape of the actual bay is curving at some angle.
