A Mathematical Model for Investigating The Resonance Phenomenon in Lakes

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. (C) 2020 Elsevier B.V. All rights reserved.