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Solitary Wave on a Conical Island

Motivated by the catastrophe in Babi Island, Indonesia (Yeh et al., 1994), during the 1992 Flores Island tsunami, large-scale laboratory experiments were performed at Coastal Engineering Research Center, Vicksburg, Mississippi, in a 30 m-wide, 25 m-long, and 60 cm-deep wave basin (Fig. 1). Waves were realistically created in the tank by a horizontal wave generator with 60 different paddles each 46 cm-wide and moving independently. These experiments provided runup observations for validating numerical models and supplemented comparisons with analytical results (Kânoglu and Synolakis, 1998).

Figure 1: View of conical island (top) and basin (bottom).
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The detailed experiments are described elsewhere in greater detail (Liu et al., 1995; Briggs et al., 1995; Kânoglu, 1998; Kânoglu and Synolakis, 1998), and at the following site. Data from this experiment can be downloaded here. Briefly, a Directional Spectral Wave Generator (DSWG), located at $\widetilde{x}$ = 12.96 m from the island, generated waves with an initial solitary wave-like profile. The 27.42 m-long DSWG consists of sixty 46 cm-wide and 76 cm-high individual paddles, each of which can be driven independently. This allowed performance of experiments with different wave crest lengths. However, the cases presented here were performed using all the paddles. Experimental results for different wave crest lengths are given in Briggs et al. (1995) and Kânoglu (1998).

In the physical model, a 62.5 cm-high, 7.2 m toe-diameter, and 2.2 m crest-diameter circular island with a 1:4 slope was located in the basin (Fig. 2). Experiments were conducted at two different water depths, 32 cm and 42 cm, but presented here with dimensionless solitary wave heights $\widetilde{H}/\widetilde{d}$ equal to 0.045, 0.091, and 0.181 at 32 cm. Each experiment was repeated at least twice and maximum runup heights around the perimeter of the island were measured at 24 locations. Wavemaker signals were presented in Fig. 4 for these cases to allow direct implementation of these solitary waves as a wavemaker motion in the numerical models. Water-surface time histories were measured with 27 wave gages located around the perimeter of the island (Fig. 3). However, here, time histories of the surface elevation around the circular island are given at four locations, i.e., in the front of the island at the toe and gages closest to the shoreline with the numbers 9, 16, and 22 located at the $0^{\circ }$, $90^{\circ }$, and $% 180^{\circ}$ radial lines, respectively (Figs. 5-7. Maximum runup measurements are given in Fig. 8.

Figure 2: Definition sketch for conical island. All dimensions are in cm. Not to scale.
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Figure 3: Schematic showing gage locations around the conical island. Not to scale.
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Figure: Wavemaker motions for the generation of $\tilde{H}/\tilde{d} = 0.045 $, 0.091, and 0.181 solitary waves. Target wave heights are given in the insets.
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Figure: Laboratory data for the time histories of surface elevation for a $\tilde{H}/\tilde{d} = 0.045 $ solitary wave at four gages and $\tilde{d} = 32$ cm. Gage 6 is located at the toe of the conical island on 0$^{\circ }$ radial line. Gages 9, 16, and 22 are the gages closest to the shoreline on the $0^{\circ }$, $90^{\circ }$, and $180^{\circ }$ radial lines, respectively. Initial wave is defined half-wavelength (L/2, i.e., gages 1 to 4) away from the toe of the conical island.
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Figure: Laboratory data for the time histories of surface elevation for a $\tilde{H}/\tilde{d} = 0.091$ solitary wave at four gages and $\tilde{d} = 32$ cm. Gage 6 is located at the toe of the conical island on 0$^{\circ }$ radial line. Gages 9, 16, and 22 are the gages closest to the shoreline on the $0^{\circ }$, $90^{\circ }$, and $180^{\circ }$ radial lines, respectively. Initial wave is defined half-wavelength (L/2, i.e., gages 1 to 4) away from the toe of the conical island.
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Figure: Laboratory data for the time histories of surface elevation for a $\tilde{H}/\tilde{d} = 0.181$ solitary wave at four gages and $\tilde{d} = 32$ cm. Gage 6 is located at the toe of the conical island on $0^{\circ }$ radial line. Gages 9, 16, and 22 are the gages closest to the shoreline on the $0^{\circ }$, $90^{\circ }$, and $180^{\circ }$ radial lines, respectively. Initial wave is defined half-wavelength (L/2, i.e., gages 1 to 4) away from the toe of the conical island.
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Figure: Maximum runup heights from the laboratory data for three solitary waves $\tilde{H}/\tilde{d} = 0.045 $, 0.091, and 0.181 and $\tilde{d} = 32$ cm. Initial waves are defined half-wavelength (L/2, i.e., gages 1 to 4) away from the toe of the conical island.
\includegraphics[height=5in]{SP3053_figA23_helvetica.eps}

These experiments were used as benchmark tests for validating 2+1 numerical codes in the 1995 Friday Harbor, Seattle, Washington Long-Wave Runup Models Workshop (Yeh et al., 1996).

References:

Briggs, M.J., C.E. Synolakis, G.S. Harkins, and D. Green (1995): Laboratory experiments of tsunami runup on a circular island. Pure Appl. Geophys., 144, 569-593.

Kânoglu, U. (1998): The runup of long waves around piecewise linear bathymetries. Ph.D. Thesis, University of Southern California, Los Angeles, California, 90089-2531, 273 pp.

Kânoglu, U., and C.E. Synolakis (1998): Long wave runup on piecewise linear topographies. J. Fluid Mech., 374, 1-28.

Liu, P.L.-F., Y.-S. Cho, M.J. Briggs, U. Kânoglu, and C.E. Synolakis (1995): Runup of solitary waves on a circular island. J. Fluid Mech., 320, 259-285.

Yeh, H., P.L.-F. Liu, and C.E. Synolakis (1996): Long-Wave Runup Models. World Scientific, 403 pp.