抛物型对称海脊引导波完整解析理论

越洋海啸能够被大洋海脊引导并沿海脊传播至远场地区，虽然传播速度较慢，但携带较大的能量，会对远场地区造成灾害影响，相关研究对于提高海啸传播特性本质的认识具有重要意义。本文基于线性长波方程，推导出了抛物型对称海脊引导波完整解析理论。研究表明对称型海脊同时存在对称与反对称引导波，其自由水面波动可以表示为虚宗量Bessel函数形式。利用海脊中心对称条件给出了描述其频率与波数的频散关系。基于所提理论进一步分析讨论了引导波的运动特性，包括频散关系、波速度、能量传播速度与波面空间分布等。本研究为揭示地形坡度由脊顶至两侧逐渐增加的海脊引导波运动特征，预测实际越洋海啸中最具威胁性海啸波的到达时间提供了理论依据。

Complete analytical solutions for guided waves along a parabolic symmetrical ridge

Transoceanic tsunamis can be guided by oceanic ridges and transferred large energy with slower velocity, hitting far-field regions and causing disaster effects. Therefore, the study on guided waves is crucial to improve the understanding of tsunami propagation characteristics. Based on the linear shallow water equation, the complete analytical solutions for guided waves over a parabolic symmetric ridge are derived. It is shown that both symmetric and anti-symmetric guided waves can exist along symmetric ridges and the free surface is described using the modified Bessel functions. Dispersion relationships, determining the relationship between the wave frequency and the wavenumber, are obtained from the continuity of water surface and velocity at the top of the ridge. The kinematic characteristics of guided waves, such as phase velocity, group velocity and surface spatial distribution are further revealed. This paper theoretically elaborates the guided waves over the ridge with its topographic slope generally increasing from the top to the bottom and provides the formulas to predicate the arrival time of the most threatening waves for the actual transoceanic tsunamis.