6. Numerical calculation for harbor oscillation in harbors of various shapes

#### 6.1 Numerical calculation conditions

Meteotsunamis can be amplified to be heavier through harbor oscillation, as well as shoaling. In this chapter, we discuss oscillation in harbors of various shapes, by applying the numerical model based on the nonlinear shallow water equations, that is, Eqs. (1)–(3). The Coriolis coefficient f and horizontal eddy viscosity coefficient Ah are 0.0 s<sup>1</sup> and 30.0 m<sup>2</sup> /s, respectively. Illustrated in Figure 22 is an example of computational domains, where the harbor of a horizontally rectangular shape, we call, an I-type harbor. A train of incident regular waves, the wave height of which is 0.2 m, enters the computational domain through its leftward boundary and then propagates inside the harbor, leading to harbor oscillation.

The target harbors are model harbors of various shapes, as well as an actual bay, where the horizontal shapes of the model harbors are I-type, L-type, C-type, and

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 dimen-

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

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

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

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

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.

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

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

gh � � p . Although both the values of R and kl for

sionless wave number, that is, 2πl= T ffiffiffiffiffi

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

same harbor-axis length.

computational domains.

Figure 25.

Figure 26.

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shown in Figure 25.

Figure 22.

The computational domain for harbor oscillation in an I-type harbor. The incident waves, the wave height of which is 0.2 m, enter the computational domain through its leftward boundary.

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.
