越洋海啸波传播数学模型的研究
|
摘要
应用内外解匹配的方法和驻相法推导了柱坐标系下地震引起的水面波动方程的解,即推导了地震海啸波生成与传播的理论方程,并对越洋地震海啸理论方程进行了求解。基于Boussinesq方程出发,建立了二维越洋海啸波传播数学模型,并对越洋海啸进行了数值计算,计算方法采用有限差分方法,差分格式采用交替方向隐格式(Alternating Direction Implicit即ADI方法)。利用越洋海啸计算模式对发生在大洋中的地震海啸进行了模拟,将数值模拟结果与地震海啸波理论方程的计算结果进行了比较,两种计算结果吻合较好。
In this paper, we used the method of matching inner and out solutions and the stationary phased method to derive the solution of the wave equation in cylindrical coordinates for the water surface after earthquake, which is the theoretical equation of earthquake tsunami. We then applied this equation to calculate the transoceanic tsunami. Based on the Boussinesq equation, a 2D trans-oceanic tsunami wave propagation mathematical model was built, and was used to simulate the trans-ocean tsunami. In this model, the calculation was performed with the finite difference method, and the difference scheme with the Alternating Direction Implicit, that is ADI method. With the trans-ocean tsunami numerical calculation model, an earthquake tsunami was calculated; and the results were in good consistency with that of the earthquake-induced wave calculated by the theoretical wave equation for water surface.
In this paper, we used the method of matching inner and out solutions and the stationary phased method to derive the solution of the wave equation in cylindrical coordinates for the water surface after earthquake, which is the theoretical equation of earthquake tsunami. We then applied this equation to calculate the transoceanic tsunami. Based on the Boussinesq equation, a 2D trans-oceanic tsunami wave propagation mathematical model was built, and was used to simulate the trans-ocean tsunami. In this model, the calculation was performed with the finite difference method, and the difference scheme with the Alternating Direction Implicit, that is ADI method. With the trans-ocean tsunami numerical calculation model, an earthquake tsunami was calculated; and the results were in good consistency with that of the earthquake-induced wave calculated by the theoretical wave equation for water surface.
引文
[1]包澄澜,叶琳.海啸灾害与预警[J].海洋预报,2005,22(1):1-4.
[2]于福江,叶琳,王喜年.1994年发生在台湾海峡的一次地震海啸的数值模拟[J].海洋学报,2001,23(6):32-39.
[3]祝会兵,于颖,戴世强.海啸数值计算研究进展[J].水动力学研究与进展,2006,21(6):714-723.
[4]姚远,蔡树群,王盛安.海啸波数值模拟的研究现状[J].海洋科学进展,2007,25(4):487-494.
[5]李伟,朱元清,王本龙,等.海啸在冲绳海槽和东海浅水大陆架地形上产生和传播的数值模拟[J].地震地磁观测与研究,2007,28(5):138-142.
[6]温瑞智,公茂盛,谢礼立.海啸预警系统及我国海啸减灾任务[J].自然灾害学报,2006,15(3):1-7.
[7]刘双庆,朱元清,薛艳,等.多种海啸触发类型的流固耦合数值模拟初步研究[J].地震地磁观测与研究,2007,28(5):130-137.
[8]陈颙.海啸的成因与预警系统[J].自然杂志,2005,27(1):4-7.
[9]易家训.流体力学[M].章克本,张涤明,陈启强等译.北京:高等教育出版社,1982.464-469.
[10]钱伟长.奇异摄动理论及其在力学中的应用[M].北京:科学出版社,1981.87-131.
[11]梅强中.水波动力学[M].北京:科学出版社,1984.22-39.
[2]于福江,叶琳,王喜年.1994年发生在台湾海峡的一次地震海啸的数值模拟[J].海洋学报,2001,23(6):32-39.
[3]祝会兵,于颖,戴世强.海啸数值计算研究进展[J].水动力学研究与进展,2006,21(6):714-723.
[4]姚远,蔡树群,王盛安.海啸波数值模拟的研究现状[J].海洋科学进展,2007,25(4):487-494.
[5]李伟,朱元清,王本龙,等.海啸在冲绳海槽和东海浅水大陆架地形上产生和传播的数值模拟[J].地震地磁观测与研究,2007,28(5):138-142.
[6]温瑞智,公茂盛,谢礼立.海啸预警系统及我国海啸减灾任务[J].自然灾害学报,2006,15(3):1-7.
[7]刘双庆,朱元清,薛艳,等.多种海啸触发类型的流固耦合数值模拟初步研究[J].地震地磁观测与研究,2007,28(5):130-137.
[8]陈颙.海啸的成因与预警系统[J].自然杂志,2005,27(1):4-7.
[9]易家训.流体力学[M].章克本,张涤明,陈启强等译.北京:高等教育出版社,1982.464-469.
[10]钱伟长.奇异摄动理论及其在力学中的应用[M].北京:科学出版社,1981.87-131.
[11]梅强中.水波动力学[M].北京:科学出版社,1984.22-39.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心