5. Tsunami in the Vicinity of a Wave Origin[III]
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概要
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In the numerical study of a tsunami, the most difficult question is the way in which the oscillatory factors cosω*t* and J0(k*r*), which are included in the integrand of the integration a*∫cosω*t*/cosh k*J0(k*r*)J1(k*a*)dk*, are to be transformed into a form suitable for numerical calculation. For this purpose, Filon's method is available, which makes the the above integration possible for large values of t* and r*. Since we have no available information with regard to the efficiency of this method, two examples of the integration are presented to check the efficiency of Filon's method in comparison with that devised by Simpson. In this paper, using Filon's method, the calculations of the above integration are carried out for values r* in the range 25 to 50. Subsequently, the following conclusions have been arrived at: - (1) notwithstanding an uniform elevation of a circular portion of the bottom, a saddle-shaped valley appears at the first intumescence of the waves, (2) the toe of the waves appears to advance at a speed of the long wave velocity for a tsunami of near-field, while the intumescences of the later phase are propagated with less than the velocity of a long wave, (3) the elevation of the first crest is in amount larger than the depression.数値実験的に津波を取り扱うときにおこる最も困難な点は形式的な積分表示に含まれている振動因子cosω*t*,J0(k*r*)がt*およびr*の増加につれて,数値積分の能率を著しく低下させることである.これを避けるためにFilonの方法というのが存在する.筆者はこれを用いて,すでに報告ずみの第1,第2報に続いて,波源域近傍の津波の解析をr*が25から50の範囲について試みた.そして次の結論を得た.
- 1965-07-15
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