A Mathematical Model for Investigating The Resonance Phenomenon in Lakes

Magdalena, Ikha; Karima, Nadhira; Rif'atin, H. Q.

doi:10.1016/j.wavemoti.2020.102669

Cited by 5 publications

(1 citation statement)

References 17 publications

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“…More complicated bottom topographies, such as semi-closed quartic, triangular (right-angled), trapezoidal, and coupled rectangular type, are rarely studied analytically due to the complexities of the basin depth formula. One of the rare studies that have investigated the quartic basin using an analytical approach was published by Chrystal [1] and Magdalena et al [13]. However, they only provided the resonant period for closed quartic basin.…”

Section: Introductionmentioning

confidence: 99%

Resonant Periods of Seiches in Semi-Closed Basins with Complex Bottom Topography

Magdalena

Karima

Rif'atin

2021

Fluids

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Seiches and resonances are two closely related phenomena that can cause damage to coastal areas. Seiches that occur in a basin at a distinct period named the resonant period may generate resonance when a wave induced by external forces enters the basin and has the same period as the seiches. Studying this period has become essential if we want to understand the resonance better. Thus, in this paper, we derive the resonant period in various shapes of semi-closed basin using the shallow water equations. The equations are then solved analytically using the separation of variables method and numerically using the finite volume method on staggered grid to discover the resonant period for each basin. To validate the numerical scheme, we compare its results against the analytical resonant periods, resulting in a very small error for each basin, suggesting that the numerical model is quite reliable in the estimation of the analytical resonant period. Further, resonant wave profiles are also observed. It is revealed that, in the coupled rectangular basin, the maximum wave elevation is disproportionate to the ratio of the length of the basin, while, in the trapezoidal basin, the ratio of the depth of the basin has no significant impact on the maximum wave elevation.

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Section: Introductionmentioning

confidence: 99%