Abstract. Run-up is defined as sea wave up-rush on a beach. Run-up height is affected by many factors, including the shape of the bay. As an archipelagic country, Indonesia consists of thousands of islands with bays of diverse profiles, including Palu Bay, which is a well-known example of a bay with a drastically-increasing wave run-up height. In the case of the 2018 Palu tsunami, scientists found that the incident wave was amplified by the shape of the bay. The amplifying wave played a large role in the significant increase of run-up height. The run-up in question caused severe inundation, which led to a high number of casualties and damages. Therefore a mathematical model will be constructed to investigate the wave run-up. The bay's geometry will be approximated using three linearly-inclined channel types: one of parabolic cross-section, one of triangular cross-section, and a plane beach. We use the generalized nonlinear shallow water equations, which is then solved analytically using a hodograph-type transformation. As a result, the nonlinear shallow water equation system can be reduced to a one-dimensional linear equation system. Assuming the incident wave is sinusoidal, we can obtain a simple formula for calculating maximum run-up height on the shoreline.

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估算2018年帕卢海啸最大起伏高度的数学公式

摘要。加速被定义为海滩上的海浪涌动。爬升高度受许多因素影响，包括海湾的形状。作为一个群岛国家，印度尼西亚由成千上万个岛屿组成，这些岛屿的海湾轮廓各异，其中包括帕卢湾（Palu Bay），这是波浪上升高度急剧增加的海湾的一个著名例子。就2018年帕卢海啸而言，科学家发现入射波被海湾的形状放大了。放大波在上升高度的显着增加中起很大作用。有问题的起步事故造成了严重的洪水泛滥，导致大量人员伤亡和破坏。因此，将建立一个数学模型来研究波浪的上升。海湾的几何形状将使用三种线性倾斜的通道类型进行近似估算：抛物线横截面，三角形横截面之一，和平面海滩。我们使用广义的非线性浅水方程，然后使用Hodograph型变换进行解析求解。结果，非线性浅水方程组可以简化为一维线性方程组。假设入射波为正弦波，我们可以得到一个简单的公式来计算海岸线上的最大上升高度。