Abstract
A mathematical model based on the three-dimensional (3-D) boundary element method (BEM), including porous and non-porous breakwaters, is developed to determine the wave trapping characteristics of porous breakwater over the partially reflecting walls with variable bathymetry. In this formulation, a special form of Green’s function is utilized to solve the Laplace equation in the 3-D domain to enhance the numerical accuracy. The order of convergence of the present numerical scheme shows a better convergence rate than simple Green’s function. The numerical scheme with and without the porous breakwater is compared with the analytical studies of Yu et al. (1994) and Lee (1969), respectively. In addition, the numerical simulation for sloping bathymetry is conducted and compared with the analytical results of Wang et al. (2011). The numerical validation exhibits good agreement with and without porous breakwaters. Based on validation, the current numerical scheme is implemented on the realistic Visakhapatnam Port, Andhra Pradesh, India, at four different synthetic key locations S1 to S4 to analyze the hydrodynamic performance of porous and non-porous breakwaters. Wave amplification is determined for different porosity parameters, including variable linear resistance and inertial coefficient, and different reflecting coefficients of the port wall. Moreover, the wave amplitude within the Visakhapatnam Port is also estimated through a contour plot with and without porous breakwaters to identify the safe location for the moored ship. Overall, the porosity of the breakwaters and partial reflection coefficient on the port wall plays a significant role in inducing or reducing the resonance inside the port.
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The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.
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Acknowledgements
The current research work is supported by Department of Applied Sciences (Mathematics), National Institute of Technology Delhi. We are thankful to the reviewers for their insightful and valusble suggestions to improve our manuscript.
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This work was financially supported by the Department of Applied Science (Mathematics), National Institute of Technology, Delhi.
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Kumar, P., Priya, P. & Rajni Mathematical modelling of Visakhapatnam Port utilizing the porous and non-porous breakwaters with finite depth green function. Ocean Dynamics 72, 557–576 (2022). https://doi.org/10.1007/s10236-022-01519-7
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DOI: https://doi.org/10.1007/s10236-022-01519-7