I I Numerical Analysis of Tsunami Propagating on Wide Reef Platform Using Turbulence Model Takahito MIKAMI and Tomoya SHIBAYAMA This paper aims to und
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1 I I Numerical Analysis of Tsunami Propagating on Wide Reef Platform Using Turbulence Model Takahito MIKAMI and Tomoya SHIBAYAMA This paper aims to understand the characteristics of a tsunami propagating over a wide reef platform, which was observed during a field survey of the 2009 Samoan Islands Tsunami, by using a turbulence model. A Large Eddy Simulation (LES) model was used to simulate wave breaking and energy dissipation. The results of the numerical simulations were shown to reproduce well the results of the field survey of the 2009 Samoan Islands Tsunami. In particular after the 2004 Indian Ocean Tsunami, tsunamis propagating over coral reefs were observed in many countries, such as the Maldives, the southwest coast of Sri Lanka and Solomon Islands. The present method may also apply to these countries and contribute to considering regional tsunami mitigation strategies a Satitoa 200km 20 1 b Faleaseela
2 Fernando Hikkaduwa Dodanduwa Hikkaduwa Akuralla Kulhudhuffushi Kunkel Baba Large Eddy Simulation LES 1 Navier-Stokes LES 1 2 u i i p tρ g τ ij SGS 2 f CIP f 0.5 non-slip 3 SOR Successive over-relaxation CIP 3 x y z 1cm0.002s /100 h r =
3 I_78 土木学会論文集B2 海岸工学 Vol. 68 No cm 沖側境界での水深は hi=30cm とした リーフエッ は 分裂した波が発達したまま遡上して砕波する場合に ジには勾配 1/2 の斜面を 海岸線近傍には勾配 1/10 の斜 は 津波本体の静水圧に加えて衝撃砕波圧が発生するこ 面を取り付けている リーフの長さについては とを実験により確かめている リーフの幅が広いほど分 Lr=500cm 750cm 1000cmの3種類を用いた 裂が顕著になり 後続の波が十分に発達すると考えられ 津波は波長の長い規則波 クノイド波の 3 次近似解 るので 幅の広いリーフをもつ地域では 分裂した波の で模擬した 周期 T=30.0s をとし 波高については 遡上とそれらの波が及ぼす作用について十分に考慮する Hi=5.0cm 6.0cm 7.0cm の3種類を用いた 必要がある 2 解析結果 リーフ上での砕波条件については 岩瀬ら 2001 が a 波の変形 本研究とほぼ同様のスケールのもとに水平床を用いた水 まず リーフ上での波の変形に着目する 図-3 にリー 理実験を行って確かめている 実験結果から岩瀬らは フ上での波の変形の様子を示す リーフ上に入射した波 は 徐々に前面の勾配が大きくなっていき ある程度ま で大きくなった後は波高が少しずつ小さくなっていくこ 砕波点における波高水深比 Hb/h は平均的に 3 とがわかる また リーフ上を伝播しながら波峰が 2 つ であるとしている また 水平床におけるソリトン分裂 に分裂していく様子が確認でき Lr=1000cm の場合には 波は伝播に伴い次第に小さくなり砕波が終了する点が存 汀線付近で後続の波の高さが前の波の高さとほぼ同じに 在し 砕波終了時の波高水深比 He/h は平均的に なるまで発達している 以上より リーフ上での津波挙 動について 波峰の分裂と波高の増減の 2 点を大きな特 4 であるとしている 徴として挙げることができる 津波が遠浅な浅海域を伝播する場合 水深変化に伴う 入射波高 Hi=5.0cm の場合には 式 3 の関係を満た 波の非線形項と波数分散項の位相のずれからソリトン分 す程に波高は高まらなかったが 入射波高 Hi=7.0cm の場 裂が発生することが知られている 岩瀬ら 2000 ソ 合には 流速ベクトル図より x= cm 付近で砕 リトン分裂した波の及ぼす影響として 安田ら 2006 波しながら進んでいく様子が確認できた 波を入射させ てから 17.6 秒後 18.8 秒後までの 0.3 秒ごとの流速ベクト ル図を図-4 に示す 図中の破線は式 3 を用いて求め た砕波点における波高 H b 一点鎖線は式 4 を用いて 求めた砕波終了時における波高 He をそれぞれ表わしてい る 波は前面で砕波を起こし 波高を小さくしながらも 図-2 地形条件 図-3 岸に向かって進んでいく様子がわかる サモア諸島でも リーフ上での波の変形 波が入射して16.0 秒後から 1秒ごとの波形
4 b 1 x= cm H i =5.0cm L r 3 1 x=10cm 1W 10 5 x=10cm L r =750cm H i 3 5.0cm 6.0cm 7.0cm
5 LES 5 5. LES 2009 B No pp pp Faainuseiamalie Latu 2010 B2 Vol. 66 No. 1 pp pp pp pp pp Baba, T., Mleczko, R., Burbidge, D., Cummins, P. R. and Thio, H. K. (2008): The effect of the Great Barrier Reef on the propagation of the 2007 Solomon Islands tsunami recorded in northeastern Australia, Pure and Applied Geophysics, Vol. 165, pp Fernando, H. J. S., McCulley, J. L., Mendis, S. G. and Perera, K. (2005): Coral poaching worsens tsunami destruction in Sri Lanka, Eos Transactions, AGU, Vol. 86, No. 33, pp. 301, 304. Kunkel, C. M., Hallberg, R. W. and Oppenheimer, M. (2006): Coral reefs reduce tsunami impact in model simulations, Geophysical Research Letters, Vol. 33, L23612.
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