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A mathematical model for investigating the resonance phenomenon in lakes
Magdalena I.a, Karima N.a, Rif’atin H.Q.a
a Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, 40132, Indonesia
[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]© 2020 Elsevier B.V.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.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Numerical scheme,Resonance phenomena,Shallow water equations,Wave amplitudes,Wave period[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Natural wave period,Resonance in lakes,Shallow water equation[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text][{‘$’: ‘This work is supported by Research Grant from Institut Teknologi Bandung and Ministry of Research and Technology of the Republic of Indonesia .’}, {‘$’: ‘This work is supported by Research Grant from Institut Teknologi Bandung and Ministry of Research and Technology of the Republic of Indonesia.’}][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text]https://doi.org/10.1016/j.wavemoti.2020.102669[/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]