1. Introduction

At Urauchi Bay of Kamikoshiki Island, situated in the western offing of Kyushu Island, Japan, as shown in Figure 1, heavy harbor oscillations occurred during February 24–26, 2009, where the maximum total amplitude of water level reached 3.0 m [1], resulting in that eight fishing boats were capsized and several houses were flooded, as shown in Figures 2–4. In terms of time, Japan Standard Time (JST) is used in this chapter. According to the Grid-Point-Value (GPV) pressure data, published by Japan Meteorological Agency (JMA), atmospheric-pressure waves propagated almost eastward over East China Sea, during this term.

#### Figure 1.

The still water depth around both the main island of Kyushu, and Urauchi Bay in Kamikoshiki Island, Kagoshima Prefecture, Japan. East China Sea is spread to the west of these islands.

the long waves are called "meteotsunamis." Meteotsunamis amplified depending on the conditions of atmospheric-pressure waves [7] can become external forces to create huge oscillation, severe inundation, etc. to coastal areas. Long ocean waves supposed to be meteotsunamis have been discussed based on observed data for many coastal zones, considering local characteristics concerning both geographic features and meteorological phenomena (e.g. [8, 9]); Bailey et al. [10] reported meteotsunamis caused by storms, which attacked the east coasts of the United States, facing the continental shelf; recent meteotsunami cases around the world were summarized by Tanaka and Ito [11]. In nearshore zones, meteotsunamis are amplified through not only shoaling but also harbor oscillation in ports, harbors, and bays. Harbor oscillation, also called seiche, with the harbor paradox [12], depends on incident-wave period, harbor shape, and water depth. The oscillation in harbors of various horizontal shapes has been studied using linear theories [13],

A damaged fishing boat (the left-hand side), and the basement of a jetty, where part of armor stones have been flowed out (the right-hand side). These photos were taken by the author at Oshima Fishing Port on February

The receding flows through the seawall at 8:36 on February 25, 2009 (the left-hand side), and an inundated house fence (the right-hand side). These photos were taken by Satsumasendai City Office at and near Oshima

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

hydraulic experiments [14], nonlinear numerical models [15], etc.

Figure 3.

Figure 4.

28, 2009.

83

Fishing Port, respectively.

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

In this chapter, first, we numerically simulate long ocean waves due to atmospheric-pressure waves with different pressure-profile patterns, including the atmospheric-pressure waves that caused the large harbor oscillation in Urauchi Bay on February 25, 2009. Second, simple estimate equations concerning both the wave height and wavelength of long waves generated by atmospheric-pressure variation are proposed using atmospheric-pressure data above the ocean, for easy prediction methods are required for disaster prevention by, for example, fisheries cooperatives and local authorities, although the numerical computation is necessary to research both the mechanisms and characteristics of meteotsunamis. Third, we apply a numerical model based on the nonlinear shallow water equations, to study oscillation in harbors of various shapes, including the types of "L," "I" with a narrow region, "I" with a seabed crest or trough, "C," and "T," as well as Urauchi Bay, which has two heads like a T-type harbor. Finally, we discuss disaster measures against meteotsunamis, generated to propagate toward the west coasts of Kyushu. Several methods for the real-time prediction of meteotsunami generation are

#### Figure 2.

The refloatation operation for the fallen fishing boats around 8:00 (the left-hand side), and eight flooded cars at 8:33 (the right-hand side), on February 25, 2009. These photos were taken by Satsumasendai City Office at Oshima Fishing Port, which is located at one of two heads of Urauchi Bay, as indicated in Figure 1.

Such atmospheric-pressure waves propagating over the sea surface have often generated significant long ocean waves, through an amplification mechanism, that is, the Proudman resonance [2], especially when the phase velocity of the atmospheric-pressure wave is close to that of the long ocean waves, as examined by, for example, Hibiya and Kajiura [3] and Vilibic et al. [4], where they numerically reproduced the large harbor oscillation in Nagasaki Bay, Kyushu, Japan, and that in Ciudadella Harbor, Balearic Islands, Spain, respectively. Once long ocean waves are generated by meteorological disturbance due to the instability of a wintry weather system, as well as a storm, and reach a nearshore zone, the wave height of the secondary undulation increases owing to the decrease of water depth, like a tsunami caused by a submarine earthquake (e.g., [5]), a land slide (e.g., [6]), etc., such that

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

#### Figure 3.

The receding flows through the seawall at 8:36 on February 25, 2009 (the left-hand side), and an inundated house fence (the right-hand side). These photos were taken by Satsumasendai City Office at and near Oshima Fishing Port, respectively.

#### Figure 4.

A damaged fishing boat (the left-hand side), and the basement of a jetty, where part of armor stones have been flowed out (the right-hand side). These photos were taken by the author at Oshima Fishing Port on February 28, 2009.

the long waves are called "meteotsunamis." Meteotsunamis amplified depending on the conditions of atmospheric-pressure waves [7] can become external forces to create huge oscillation, severe inundation, etc. to coastal areas. Long ocean waves supposed to be meteotsunamis have been discussed based on observed data for many coastal zones, considering local characteristics concerning both geographic features and meteorological phenomena (e.g. [8, 9]); Bailey et al. [10] reported meteotsunamis caused by storms, which attacked the east coasts of the United States, facing the continental shelf; recent meteotsunami cases around the world were summarized by Tanaka and Ito [11]. In nearshore zones, meteotsunamis are amplified through not only shoaling but also harbor oscillation in ports, harbors, and bays. Harbor oscillation, also called seiche, with the harbor paradox [12], depends on incident-wave period, harbor shape, and water depth. The oscillation in harbors of various horizontal shapes has been studied using linear theories [13], hydraulic experiments [14], nonlinear numerical models [15], etc.

In this chapter, first, we numerically simulate long ocean waves due to atmospheric-pressure waves with different pressure-profile patterns, including the atmospheric-pressure waves that caused the large harbor oscillation in Urauchi Bay on February 25, 2009. Second, simple estimate equations concerning both the wave height and wavelength of long waves generated by atmospheric-pressure variation are proposed using atmospheric-pressure data above the ocean, for easy prediction methods are required for disaster prevention by, for example, fisheries cooperatives and local authorities, although the numerical computation is necessary to research both the mechanisms and characteristics of meteotsunamis. Third, we apply a numerical model based on the nonlinear shallow water equations, to study oscillation in harbors of various shapes, including the types of "L," "I" with a narrow region, "I" with a seabed crest or trough, "C," and "T," as well as Urauchi Bay, which has two heads like a T-type harbor. Finally, we discuss disaster measures against meteotsunamis, generated to propagate toward the west coasts of Kyushu. Several methods for the real-time prediction of meteotsunami generation are

Such atmospheric-pressure waves propagating over the sea surface have often generated significant long ocean waves, through an amplification mechanism, that

The refloatation operation for the fallen fishing boats around 8:00 (the left-hand side), and eight flooded cars at 8:33 (the right-hand side), on February 25, 2009. These photos were taken by Satsumasendai City Office at Oshima Fishing Port, which is located at one of two heads of Urauchi Bay, as indicated in Figure 1.

atmospheric-pressure wave is close to that of the long ocean waves, as examined by, for example, Hibiya and Kajiura [3] and Vilibic et al. [4], where they numerically reproduced the large harbor oscillation in Nagasaki Bay, Kyushu, Japan, and that in Ciudadella Harbor, Balearic Islands, Spain, respectively. Once long ocean waves are generated by meteorological disturbance due to the instability of a wintry weather system, as well as a storm, and reach a nearshore zone, the wave height of the secondary undulation increases owing to the decrease of water depth, like a tsunami caused by a submarine earthquake (e.g., [5]), a land slide (e.g., [6]), etc., such that

is, the Proudman resonance [2], especially when the phase velocity of the

The still water depth around both the main island of Kyushu, and Urauchi Bay in Kamikoshiki Island,

Kagoshima Prefecture, Japan. East China Sea is spread to the west of these islands.

Natural Hazards - Risk, Exposure, Response, and Resilience

Figure 1.

Figure 2.

82

proposed, using an inverse analysis, as well as the proposed simple prediction equations, after which both the structural and the nonstructural preparations for meteotsunamis are summarized.

## 2. Numerical model and calculation conditions

A set of nonlinear shallow water equations, in consideration of atmosphericpressure gradient at the sea surface, is solved in the horizontal two dimensions by applying a finite difference method. The fundamental equations are

$$\frac{\partial \eta}{\partial t} + \frac{\partial}{\partial \mathbf{x}} \{ (\eta + h) \, U \} + \frac{\partial}{\partial \mathbf{y}} \{ (\eta + h) \, V \} = \mathbf{0},\tag{1}$$

$$\frac{\partial U}{\partial t} + \frac{\partial U^2}{\partial \mathbf{x}} + \frac{\partial (UV)}{\partial \mathbf{y}} = f\mathbf{V} - \mathbf{g}\frac{\partial \eta}{\partial \mathbf{x}} - \frac{1}{\rho}\frac{\partial P}{\partial \mathbf{x}} + A\_h \left(\frac{\partial^2 U}{\partial \mathbf{x}^2} + \frac{\partial^2 U}{\partial \mathbf{y}^2}\right) - \frac{KU\sqrt{U^2 + V^2}}{\eta + h}, \tag{2}$$

$$\frac{\partial V}{\partial t} + \frac{\partial (UV)}{\partial \mathbf{x}} + \frac{\partial V^2}{\partial \mathbf{y}} = -f\mathbf{U} - \mathbf{g}\frac{\partial \eta}{\partial \mathbf{y}} - \frac{1}{\rho}\frac{\partial P}{\partial \mathbf{y}} + A\_h \left(\frac{\partial^2 V}{\partial \mathbf{x}^2} + \frac{\partial^2 V}{\partial \mathbf{y}^2}\right) - \frac{KV\sqrt{U^2 + V^2}}{\eta + h}, \tag{3}$$

where U and V are horizontal velocities in the x and y directions, respectively; η, h, and P are water surface displacement, still water depth, and atmospheric pressure at the water surface, respectively; f and Ah are the Coriolis coefficient and horizontal eddy viscosity coefficient, respectively. In the present study, gravitational acceleration g = 9.8 m/s<sup>2</sup> , seabed friction coefficient <sup>K</sup> = 2.6 � <sup>10</sup>�<sup>3</sup> , and seawater density ρ = 1035.0 kg/m<sup>3</sup> . The Sommerfeld radiation condition is adopted at the boundaries of the computational domain, while the boundaries between land and sea are assumed to be vertical walls with the perfect reflection of waves.

#### 3. Long-wave generation due to atmospheric-pressure waves

#### 3.1 The relationship between the parameters of atmospheric-pressure waves and long-wave generation

In the large area along the west coasts of Kyushu, as well as Yamaguchi Prefecture nearby Kyushu, secondary undulation, supposed to be caused by atmosphericpressure disturbance above East China Sea, often increases from February to April, sometimes leading to disasters as mentioned above. In this section, we discuss the relationship between the parameters of atmospheric-pressure waves and long-wave generation in the ocean. The computational domain is part of East China Sea, where the longitude is from 123.0 to 131.0°E, and the latitude is from 30.0 to 32.5°N, with the actual seabed configuration. The still water depth in East China Sea near the main island of Kyushu is shown in Figure 5, where it is around 800 m at the deepest site in Okinawa Trough. The grid widths Δx and Δy are 790.0 and 925.0 m, respectively, while the time step Δt is 2.0 s. In this section, the Coriolis coefficient f and horizontal eddy viscosity coefficient Ah in Eqs. (2) and (3) are 7.3 � <sup>10</sup>�<sup>5</sup> <sup>s</sup> �<sup>1</sup> and 100.0 m<sup>2</sup> /s, respectively.

pressure data, where the atmospheric pressure P is a deviation from the value of pressure for an average atmospheric-pressure condition. It should be noted that an atmospheric-pressure wave is not a pressure wave in fluids, including a sound wave

Typical four patterns for the high-pressure profiles of atmospheric-pressure waves, propagating rightward. Pmax is the maximum value of pressure, while P0 is a stable value of pressure, where P0 = 0 in (a), P0 = Pmax in (b),

The still water depth in East China Sea near the main island of Kyushu. The point indicated with ① is located off the mouth of Urauchi Bay, where the huge harbor oscillation of 3.0 m in total amplitude was observed. The

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

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

still water depth is around 800 m at the deepest site in Okinawa Trough.

An atmospheric-pressure wave of pattern (a), for example, has three parameters, that is, wavelength L, the maximum value of pressure, Pmax, and phase velocity Cp, where these values are kept constant before the wave stops in the numerical calculation. The pressure profile for an atmospheric-pressure wave of pattern (a) is

<sup>L</sup> ð Þ <sup>x</sup> � xc

where the initial position of the pressure peak, xc, is at the longitude of 124°E.

0 x � xc ð Þ j j>L=2 ,

� � � � <sup>x</sup> � xc ð Þ j j≤L=<sup>2</sup> ,

(4)

and a shock wave, but the propagation of an atmospheric-pressure profile.

2π

described as

85

Figure 6.

Figure 5.

P xð Þ¼ ; t<sup>0</sup>

and P0 < Pmax in (c) and (d).

pmax 2

8 < :

1 þ cos

In the computation, it is assumed that the atmospheric pressure is uniform from north to south, and atmospheric-pressure waves travel eastward at a constant phase velocity over East China Sea. The distribution of atmospheric pressure along the latitude lines is classified into four patterns shown in Figure 6, based on the GPV

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

#### Figure 5.

proposed, using an inverse analysis, as well as the proposed simple prediction equations, after which both the structural and the nonstructural preparations for

A set of nonlinear shallow water equations, in consideration of atmosphericpressure gradient at the sea surface, is solved in the horizontal two dimensions by

> ∂ ∂y

where U and V are horizontal velocities in the x and y directions, respectively; η, h, and P are water surface displacement, still water depth, and atmospheric pressure at the water surface, respectively; f and Ah are the Coriolis coefficient and horizontal eddy viscosity coefficient, respectively. In the present study, gravita-

adopted at the boundaries of the computational domain, while the boundaries between land and sea are assumed to be vertical walls with the perfect reflection

3.1 The relationship between the parameters of atmospheric-pressure waves

In the large area along the west coasts of Kyushu, as well as Yamaguchi Prefecture nearby Kyushu, secondary undulation, supposed to be caused by atmosphericpressure disturbance above East China Sea, often increases from February to April, sometimes leading to disasters as mentioned above. In this section, we discuss the relationship between the parameters of atmospheric-pressure waves and long-wave generation in the ocean. The computational domain is part of East China Sea, where the longitude is from 123.0 to 131.0°E, and the latitude is from 30.0 to 32.5°N, with the actual seabed configuration. The still water depth in East China Sea near the main island of Kyushu is shown in Figure 5, where it is around 800 m at the deepest site in Okinawa Trough. The grid widths Δx and Δy are 790.0 and 925.0 m, respectively, while the time step Δt is 2.0 s. In this section, the Coriolis coefficient f and horizontal eddy viscosity coefficient Ah in Eqs. (2) and (3) are 7.3 � <sup>10</sup>�<sup>5</sup> <sup>s</sup>

In the computation, it is assumed that the atmospheric pressure is uniform from north to south, and atmospheric-pressure waves travel eastward at a constant phase velocity over East China Sea. The distribution of atmospheric pressure along the latitude lines is classified into four patterns shown in Figure 6, based on the GPV

3. Long-wave generation due to atmospheric-pressure waves

∂2 U ∂x<sup>2</sup> þ

∂2 U ∂y<sup>2</sup> � �

> ∂2 V ∂y<sup>2</sup> � �

∂2 V ∂x<sup>2</sup> þ

, seabed friction coefficient <sup>K</sup> = 2.6 � <sup>10</sup>�<sup>3</sup>

. The Sommerfeld radiation condition is

f g ð Þ η þ h V ¼ 0, (1)

� KV

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>U</sup><sup>2</sup> <sup>þ</sup> <sup>V</sup><sup>2</sup> <sup>p</sup> <sup>η</sup> <sup>þ</sup> <sup>h</sup> , (2)

> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>U</sup><sup>2</sup> <sup>þ</sup> <sup>V</sup><sup>2</sup> <sup>p</sup> <sup>η</sup> <sup>þ</sup> <sup>h</sup> ,

> > , and

�<sup>1</sup> and

(3)

� KU

applying a finite difference method. The fundamental equations are

<sup>∂</sup><sup>x</sup> f g ð Þ <sup>η</sup> <sup>þ</sup> <sup>h</sup> <sup>U</sup> <sup>þ</sup>

∂η ∂y � 1 ρ ∂P ∂y þ Ah

∂η <sup>∂</sup><sup>x</sup> � <sup>1</sup> ρ ∂P ∂x þ Ah

meteotsunamis are summarized.

∂U ∂t þ ∂U<sup>2</sup> ∂x þ

> ∂V ∂t þ

of waves.

100.0 m<sup>2</sup>

84

2. Numerical model and calculation conditions

Natural Hazards - Risk, Exposure, Response, and Resilience

∂η ∂t þ ∂

<sup>∂</sup><sup>y</sup> <sup>¼</sup> fV � <sup>g</sup>

<sup>∂</sup><sup>y</sup> ¼ �fU � <sup>g</sup>

<sup>∂</sup>ð Þ UV

<sup>∂</sup>ð Þ UV ∂x þ ∂V<sup>2</sup>

tional acceleration g = 9.8 m/s<sup>2</sup>

seawater density ρ = 1035.0 kg/m<sup>3</sup>

and long-wave generation

/s, respectively.

The still water depth in East China Sea near the main island of Kyushu. The point indicated with ① is located off the mouth of Urauchi Bay, where the huge harbor oscillation of 3.0 m in total amplitude was observed. The still water depth is around 800 m at the deepest site in Okinawa Trough.

#### Figure 6.

Typical four patterns for the high-pressure profiles of atmospheric-pressure waves, propagating rightward. Pmax is the maximum value of pressure, while P0 is a stable value of pressure, where P0 = 0 in (a), P0 = Pmax in (b), and P0 < Pmax in (c) and (d).

pressure data, where the atmospheric pressure P is a deviation from the value of pressure for an average atmospheric-pressure condition. It should be noted that an atmospheric-pressure wave is not a pressure wave in fluids, including a sound wave and a shock wave, but the propagation of an atmospheric-pressure profile.

An atmospheric-pressure wave of pattern (a), for example, has three parameters, that is, wavelength L, the maximum value of pressure, Pmax, and phase velocity Cp, where these values are kept constant before the wave stops in the numerical calculation. The pressure profile for an atmospheric-pressure wave of pattern (a) is described as

$$P(\mathbf{x}, t\_0) = \begin{cases} \frac{p\_{\text{max}}}{2} \left\{ 1 + \cos \left[ \frac{2\pi}{L} (\mathbf{x} - \mathbf{x}\_c) \right] \right\} & (|\mathbf{x} - \mathbf{x}\_c| \le L/2), \\ 0 & (|\mathbf{x} - \mathbf{x}\_c| > L/2), \end{cases} \tag{4}$$

where the initial position of the pressure peak, xc, is at the longitude of 124°E.

3.2 The long waves on the days when large harbor oscillation occurred in

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

(d) shown in Figure 6 are described for x � xc j j≤L=2 as

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

The pressure profiles for atmospheric-pressure waves of patterns (b), (c), and

ð Þc : P xð Þ¼ ; t<sup>0</sup> P0f g 1 þ cos 2½ � πð Þ x � xc =L =2

ð Þ <sup>d</sup> : P xð Þ¼ ; <sup>t</sup><sup>0</sup> <sup>0</sup>:05e<sup>κ</sup>P0f g <sup>1</sup> <sup>þ</sup> cos 6½ � <sup>π</sup>ð Þ <sup>x</sup> � xc <sup>=</sup><sup>L</sup> <sup>=</sup><sup>4</sup>

respectively, while P(x, t0) = P0(x < xc � L/2) and P(x, t0) = 0.0 (x > xc + L/2). In Eq. (7), xd is the initial position of the second pressure peak, and the power κ is

The parameters of each pattern are evaluated based on the GPV pressure data on the days when large harbor oscillation occurred in Urauchi Bay. For example, the time variation of GPV pressure distribution on February 25, 2009, when the largest harbor oscillation was observed in Urauchi Bay from 2009 to 2018, is shown in

Figure 10 shows the pressure profiles along three latitudes of 30.0, 30.5, and 31.0°N, at 3:00 on February 25, 2009, according to the GPV pressure data shown in Figure 9. An atmospheric-pressure wave, where the pressure gap was 4–5 hPa, and the total wavelength was 80–120 km, traveled almost eastward over East China Sea, at the phase velocity of around 140 km/h from 3:00 to 4:00, 120 km/h from 4:00 to 5:00, and 150 km/h from 5:00 to 6:00, such that the wave profile of the atmospheric pressure on the day is described with pattern (d), where the mean values of the

The time variation of the GPV pressure distribution on February 25, 2009, when the huge harbor oscillation of 3.0 m in total amplitude was observed in Urauchi Bay. The GPV pressure data were published by Japan

parameters, that is, L, Pmax, and Cp, are 90.0 km, 4.0 hPa, and 38.6 m/s,

ð Þ b : P xð Þ¼ ; t<sup>0</sup> P0f g 1 � sin ½ � πð Þ x � xc =L =2, (5)

<sup>þ</sup> <sup>P</sup>0f g <sup>1</sup> � sin ½ � <sup>π</sup>ð Þ <sup>x</sup> � xc <sup>=</sup><sup>L</sup> <sup>=</sup>2, (6)

<sup>þ</sup> <sup>P</sup>0f g <sup>1</sup> � sin 3½ � <sup>π</sup>ð Þ <sup>x</sup> � xc � xd <sup>=</sup><sup>L</sup> <sup>=</sup>2, (7)

Urauchi Bay

0.02x.

Figure 9.

respectively.

Figure 9.

87

Meteorological Agency.

Figure 7.

The water surface displacements at Point ① indicated in Figure 5, for various values of Pmax. The wave profile of atmospheric pressure is pattern (a), where L = 10.0 km, Cp = 20.0 m/s, and Pmax = 1.0, 2.0, or 3.0 hPa. The still water depth is about 22.0 m at Point ①.

Figure 7 shows the numerical calculation results of water surface displacements at Point ① indicated in Figure 5, owing to an assumed atmospheric-pressure wave of pattern (a), where L = 10.0 km, Cp = 20.0 m/s, and Pmax = 1.0, 2.0, or 3.0 hPa. Point ① is located off the mouth of Urauchi Bay, where the huge harbor oscillation of 3.0 m in total amplitude was observed, as mentioned above. The wave height of the generated long waves at Point ① is almost in proportion to Pmax, which has been also confirmed at the other monitoring points near Danjyo Islands or Uji Islands. According to Figure 7, many long waves propagate through Point ①, owing to the travel of one atmospheric-pressure wave.

Shown in Figure 8 is the wave height and period of the long wave with the maximum wave height at Point ① indicated in Figure 5, for various values of Cp, where the wave profile of atmospheric pressure is pattern (a); L = 30.0 km and Pmax = 1.0 hPa; the waves are defined using the zero-up-cross method. Inside the area from 125.5 to 127.0°E, and from 30.0 to 32.5°N, the average value of still water depth is 80 m, or 100 m, over the continental shelf, such that the Proudman resonance for long ocean waves can occur when the phase velocity of an atmospheric-pressure wave, Cp, is around the phase velocity of linear shallow water waves, that is, ffiffiffiffiffi gh p ≈30 m=s. According to Figure 8, the wave height of the long ocean waves increases as Cp is close to 32.0 m/s.

Figure 8.

The wave height and period of the long wave with the maximum wave height at point ① indicated in Figure 5, for various values of Cp. The wave profile of atmospheric pressure is pattern (a), where L = 30.0 km and Pmax = 1.0 hPa.

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