Abstract The resonance phenomena in parabolic and quartic lakes are investigated using a mathematical model. The model that we use here is formulated from Shallow Water Equations. We solve the model analytically so as to derive the fundamental natural wave period that can result in resonance in a closed basin. Further, a staggered finite volume method is implemented to solve the model numerically. The numerical model is then validated by simulating a resonance phenomenon in a rectangular closed basin. Moreover, simulations are conducted to simulate the resonance phenomena and approximate the natural resonant period in the parabolic and quartic shaped basins. The simulations demonstrate that the obtained analytical natural resonant periods actually generate a resonance in both types of basin, with the maximum wave amplitude in the parabolic type is larger than it is in the quartic type. Further, the numerical scheme constructed can estimate the natural resonant period very well for both types of basin.

中文翻译：

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研究湖泊共振现象的数学模型

摘要 使用数学模型研究了抛物线湖和四方湖中的共振现象。我们在这里使用的模型是根据浅水方程制定的。我们对模型进行解析求解，以推导出可导致封闭盆地共振的基本自然波浪周期。此外，采用交错有限体积法对模型进行数值求解。然后通过模拟矩形封闭盆地中的共振现象来验证数值模型。此外，还进行了模拟以模拟抛物线形和四次形盆地中的共振现象并近似自然共振周期。模拟表明，获得的分析自然共振周期实际上在两种类型的盆地中都产生了共振，抛物线型的最大波幅大于四次型的波幅。此外，构建的数值方案可以很好地估计两种类型盆地的自然共振周期。