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Mathematical Modeling of Moored Ship Motion in Arbitrary Harbor utilizing the Porous Breakwater

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Abstract

The motion of the moored ship in the harbor is a classical hydrodynamics problem that still faces many challenges in naval operations, such as cargo transfer and ship pairings between a big transport ship and some small ships. A mathematical model is presented based on the Laplace equation utilizing the porous breakwater to investigate the moored ship motion in a partially absorbing/reflecting harbor. The motion of the moored ship is described with the hydrodynamic forces along the rotational motion (roll, pitch, and yaw) and translational motion (surge, sway, and heave). The efficiency of the numerical method is verified by comparing it with the analytical study of Yu and Chwang (1994) for the porous breakwater, and the moored ship motion is compared with the theoretical and experimental data obtained by Yoo (1998) and Takagi et al. (1993). Further, the current numerical scheme is implemented on the realistic Visakhapatnam Fishing port, India, in order to analyze the hydrodynamic forces on moored ship motion under resonance conditions. The model incorporates some essential strategies such as adding a porous breakwater and utilizing the wave absorber to reduce the port’s resonance. It has been observed that these tactics have a significant impact on the resonance inside the port for safe maritime navigation. Therefore, the current numerical model provides an efficient tool to reduce the resonance within the arbitrarily shaped ports for secure anchoring.

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References

  • Bakhti, Y., Chioukh, N., Hamoudi, B. and Boukhari, M., 2017. A multidomain boundary element method to analyze the reflection and transmission of oblique waves from double porous thin walls, Journal of Marine Science and Application, 16(3), 276–285.

    Article  Google Scholar 

  • Bellotti, G. and Franco, L., 2011. Measurement of long waves at the harbor of Marina di Carrara, Italy, Ocean Dynamics, 61(12), 2051–2059.

    Article  Google Scholar 

  • Bhautoo, P., Mortensen, S., Hibberd, W., Harkin, A., Kirkegaard, J. and Morley, B., 2015. Moored vessel interaction induced by passing ships at the Port of Brisbane, Australasian Coasts & Ports Conference 2015: 22nd Australasian Coastal and Ocean Engineering Conference and the 15th Australasian Port and Harbour Conference. pp.75–82.

  • Cerrato, A., González, J.A. and Rodríguez-Tembleque, L., 2016. Boundary element formulation of the Mild-Slope equation for harmonic water waves propagating over unidirectional variable bathymetries, Engineering Analysis with Boundary Elements, 62, 22–34.

    Article  MathSciNet  MATH  Google Scholar 

  • Chang, Y.S. and Wang, E.H., 2017. A harbor resonance numerical model with reflecting, absorbing and transmitting boundaries, The Open Construction and Building Technology Journal, 11(1), 413–432.

    Article  Google Scholar 

  • Chen, H.S., 1986. Effects of bottom friction and boundary absorption on water wave scattering, Applied Ocean Research, 8(2), 99–104.

    Article  Google Scholar 

  • Chen, K.H., Chen, J.T., Lin, S.Y. and Lee, Y.T., 2004. Dual boundary element analysis of normal incident wave passing a thin submerged breakwater with rigid, absorbing, and permeable boundaries, Journal of Waterway, Port, Coastal, and Ocean Engineering, 130(4), 179–190.

    Article  Google Scholar 

  • Chou, C.R. and Han, W.Y., 1993. Wave-induced oscillations in harbours with dissipating quays, Costal Engineering in Japan, 36(1), 1–23.

    Google Scholar 

  • Dong, G.H., Gao, J.L., Ma, X.Z., Wang, G. and Ma, Y.X., 2013. Numerical study of low-frequency waves during harbor resonance, Ocean Engineering, 68, 38–46.

    Article  Google Scholar 

  • Dong, G.H., Wang, G., Ma, X.Z. and Ma, Y.X., 2010. Harbor resonance induced by subaerial landslide-generated impact waves, Ocean Engineering, 37(10), 927–934.

    Article  Google Scholar 

  • Dusseljee, D.W., Klopman, G., Van Vledder, G.P. and Riezebos, H.J., 2014. Impact of harbor navigation channels on waves: a numerical modelling guideline, Proceedings of the 34th International Conference on Coastal Engineering, Seoul, Korea.

  • Feng, A.C., Kang, H.S., Zhao, B.B. and Jiang, Z.Y., 2020. Two-dimensional numerical modelling of a moored floating body under sloping seabed conditions, Journal of Marine Science and Engineering, 8(6), 389.

    Article  Google Scholar 

  • Figuero, A., Sande, J., Peña, E., Alvarellos, A., Rabuñal, J.R. and Maciñeira, E., 2019. Operational thresholds of moored ships at the oil terminal of inner port of A Coruña (Spain), Ocean Engineering, 172, 599–613.

    Article  Google Scholar 

  • Gaillard, P., 1982. Numerical calculation of seiche motions in harbours of arbitrary shape, Proceedings of the 18th International Conference on Coastal Engineering, American Society of Civil Engineers, Cape Town, South Africa, pp. 172–191.

    Google Scholar 

  • Gao, J.L., Ji, C.Y., Gaidai, O. and Liu, Y.Y., 2016b. Numerical study of infragravity waves amplification during harbor resonance, Ocean Engineering, 116, 90–100.

    Article  Google Scholar 

  • Gao, J.L., Ji, C.Y., Gaidai, O., Liu, Y.Y. and Ma, X.J., 2017b. Numerical investigation of transient harbor oscillations induced by N-waves, Coastal Engineering, 125, 119–131.

    Article  Google Scholar 

  • Gao, J.L., Ji, C.Y., Liu, Y.Y., Gaidai, O., Ma, X.J. and Liu, Z., 2016a. Numerical study on transient harbor oscillations induced by solitary waves, Ocean Engineering, 126, 467–480.

    Article  Google Scholar 

  • Gao, J.L., Ji, C.Y., Liu, Y.Y., Ma, X.J. and Gaidai, O., 2017a. Influence of offshore topography on the amplification of infragravity oscillations within a harbor, Applied Ocean Research, 65, 129–141.

    Article  Google Scholar 

  • Gao, J.L., Ma, X.Z., Chen, H.Z., Zang, J. and Dong, G.H., 2021. On hydrodynamic characteristics of transient harbor resonance excited by double solitary waves, Ocean Engineering, 219, 108345.

    Article  Google Scholar 

  • Gao, J.L., Ma, X.Z., Dong, G.H., Zang, J., Ma, Y.X. and Zhou, L., 2019b. Effects of offshore fringing reefs on the transient harbor resonance excited by solitary waves, Ocean Engineering, 190, 106422.

    Article  Google Scholar 

  • Gao, J.L., Ma, X.Z., Dong, G.H., Zang, J., Zhou, X.J. and Zhou, L., 2019a. Topographic influences on transient harbor oscillations excited by N-waves, Ocean Engineering, 192, 106548.

    Article  Google Scholar 

  • Gao, J.L., Zhou, X.J., Zhou, L., Zang, J., Chen, Q. and Ding, H.Y., 2018b. Numerical study of harbor oscillations induced by water surface disturbances within harbors of constant depth, Ocean Dynamics, 68(12), 1663–1681.

    Article  Google Scholar 

  • Guerrini, M., Bellotti, G., Fan, Y. and Franco, L., 2014. Numerical modelling of long waves amplification at Marina di Carrara Harbour, Applied Ocean Research, 48, 322–330.

    Article  Google Scholar 

  • Gulshan, Kumar, P. and Rajni, 2020. Moored ship motion analysis in Paradip port under the resonance conditions using 3-D boundary element method, Journal of Marine Science and Technology, 25(4), 1075–1092.

    Article  Google Scholar 

  • Hamanaka, K.I., 1997. Open, partial reflection and incident-absorbing boundary conditions in wave analysis with a boundary integral method, Coastal Engineering, 30(3–4), 281–298.

    Article  Google Scholar 

  • Hildebrand, F.B., 1962. Advanced Calculus for Applications, Prentice-Hall Inc., Eaglewood Cliffs, New Jersey.

    MATH  Google Scholar 

  • Hsiao, S.S. and Fang, H.M., 2005. A DRBEM model for harbor oscillation with the effect of energy dissipation, Journal of the Chinese Institute of Engineers, 28(4), 639–646.

    Article  Google Scholar 

  • Ippen, A.T. and Goda, Y., 1963. Wave Induced Oscillations in Harbors: the Solution for a Rectangular Harbor Connected to the Open-Sea, MIT, Washington, DC.

    Google Scholar 

  • Isaacson, M. and Qu, S.Q., 1990. Waves in a harbour with partially reflecting boundaries, Coastal Engineering, 14(3), 193–214.

    Article  Google Scholar 

  • Kaligatla, R.B., Tabssum, S. and Sahoo, T., 2018. Effect of bottom topography on wave scattering by multiple porous barriers, Meccanica, 53(4), 887–903.

    Article  MathSciNet  MATH  Google Scholar 

  • Kaligatla, R.B., Tabssum, S. and Sahoo, T., 2021. Surface gravity wave interaction with a partial porous breakwater in a two-layer ocean having bottom undulations, Waves in Random and Complex Media, 1–32

  • Kofoed-Hansen, H., Kerper, D.R., Sørensen, O.R. and Kirkegaard, J., 2005. Simulation of long wave agitation in ports and harbours using a time-domain Boussinesq model, Proceedings of the Fifth International Symposium on Ocean Wave Measurement and Analysis-Waves, Madrid, Spain, 1–11.

  • Koley, S., Panduranga, K., Almashan, N., Neelamani, S. and Al-Ragum, A., 2020. Numerical and experimental modeling of water wave interaction with rubble mound offshore porous breakwaters, Ocean Engineering, 218, 108218.

    Article  Google Scholar 

  • Kravtchenko, J. and McNown, J.S., 1955. Seiche in rectangular ports, Quarterly of Applied Mathematics, 13(1), 19–26.

    Article  MathSciNet  MATH  Google Scholar 

  • Kumar, P. and Gulshan, 2017. Extreme wave-induced oscillation in paradip port under the resonance conditions, Pure and Applied Geophysics, 174(12), 4501–4516.

    Article  Google Scholar 

  • Kumar, P. and Gulshan, 2018. Theoretical analysis of extreme wave oscillation in Paradip Port using a 3-D boundary element method, Ocean Engineering, 164, 13–22.

    Article  Google Scholar 

  • Kumar, P. and Rupali, 2018. Modeling of shallow water waves with variable bathymetry in an irregular domain by using hybrid finite element method, Ocean Engineering, 165, 386–398.

    Article  Google Scholar 

  • Kumar, P., Priya, P. and Rajni, 2021. Boundary element modeling of multiconnected ocean basin in visakhapatnam port under the resonance conditions, China Ocean Engineering, 35(5), 662–675.

    Article  Google Scholar 

  • Kumar, P., Priya, P. and Rajni, 2022. Mathematical modelling of Visakhapatnam Port utilizing the porous and non-porous breakwaters with finite depth green function, Ocean Dynamics, 72(7), 557–576.

    Article  Google Scholar 

  • Kumar, P., Zhang, H. and Kim, K.I., 2014. Spectral density analysis for wave characteristics in Pohang New Harbor, Pure and Applied Geophysics, 171(7), 1169–1185.

    Article  Google Scholar 

  • Kumar, P., Zhang, H., Kim, K.I. and Yuen, D.A., 2016. Modeling wave and spectral characteristics of moored ship motion in Pohang New Harbor under the resonance conditions, Ocean Engineering, 119, 101–113.

    Article  Google Scholar 

  • Kumar, P., Zhang, H., Yuen, D.A. and Kim, K.I., 2013. Wave field analysis in a harbor with irregular geometry through boundary integral of Helmholtz equation with corner contributions, Computers & Fluids, 88, 287–297.

    Article  MathSciNet  MATH  Google Scholar 

  • Kwak, M., Moon, Y. and Pyun, C., 2012. Computer simulation of moored ship motion induced by harbor resonance in Pohang New Harbor, Coastal Engineering Proceedings, 1(33), waves.68.

    Article  Google Scholar 

  • Kwak, M. and Pyun, C., 2013. Numerical analysis of moored ship motion considering harbor resonance in Pohang New Harbor, Proceedings of the 7th International Conference on Asian and Pacific Coasts (APAC 2013), Bali, Indonesia, pp. 750–757.

  • Lee, H.S., Kim, S.D., Wang, K.H. and Eom, S., 2009. Boundary element modeling of multidirectional random waves in a harbor with a rectangular navigation channel, Ocean Engineering, 36(17–18), 1287–1294.

    Article  Google Scholar 

  • Lee, H.S. and Williams, A.N., 2002. Boundary element modeling of multidirectional random waves in a harbor with partially reflecting boundaries, Ocean Engineering, 29(1), 39–58.

    Article  Google Scholar 

  • Lee, J.J., 1971. Wave-induced oscillations in harbours of arbitrary geometry, Journal of Fluid Mechanics, 45(2), 375–394.

    Article  MATH  Google Scholar 

  • Lee, M.M. and Chwang, A.T., 2000. Scattering and radiation of water waves by permeable barriers, Physics of Fluids, 12(1), 54–65.

    Article  MathSciNet  MATH  Google Scholar 

  • Li, Y.C., Liu, Y. and Teng, B., 2006. Porous effect parameter of thin permeable plates, Coastal Engineering Journal, 48(4), 309–336.

    Article  Google Scholar 

  • Linton, C.M. and McIver, P., 2000. Green’s functions for water waves in porous structures, Applied Ocean Research, 22(1), 1–12.

    Article  Google Scholar 

  • López, M. and Iglesias, G., 2013. Artificial Intelligence for estimating infragravity energy in a harbour, Ocean Engineering, 57, 56–63.

    Article  Google Scholar 

  • López, M. and Iglesias, G., 2014. Long wave effects on a vessel at berth, Applied Ocean Research, 47, 63–72.

    Article  Google Scholar 

  • Losada, I.J., Patterson, M.D. and Losada, M.A., 1997. Harmonic generation past a submerged porous step, Coastal Engineering, 31, 281–304.

    Article  Google Scholar 

  • Ma, X.Z., Zheng, Z.J., Zhang, X. and Dong, G.H., 2020. Numerical investigation on special modes with narrow amplification diagram in harbor oscillations, Ocean Dynamics, 70(1), 1–19.

    Article  Google Scholar 

  • Maa, J.P.Y., Tsai, C.H., Juang, W.J. and Tseng, H.M., 2011. A preliminary study on Typhoon Tim induced resonance at Hualien Harbor, Taiwan, Ocean Dynamics, 61(4), 411–423.

    Article  Google Scholar 

  • Mandal, S., Behera, H. and Sahoo, T., 2016. Oblique wave interaction with porous, flexible barriers in a two-layer fluid, Journal of Engineering Mathematics, 100(1), 1–31.

    Article  MathSciNet  MATH  Google Scholar 

  • McIver, P., 1999. Water-wave diffraction by thin porous breakwater, Journal of Waterway, Port, Coastal, and Ocean Engineering, 125(2), 66–70.

    Article  Google Scholar 

  • Mizutani, N. and Mostafa, A.M., 1998. Nonlinear wave-induced seabed instability around coastal structures, Coastal Engineering Journal, 40(2), 131–160.

    Article  Google Scholar 

  • Monserrat, S., Vilibić, I. and Rabinovich, A.B., 2006. Meteotsunamis: atmospherically induced destructive ocean waves in the tsunami frequency band, Natural Hazards and Earth System Sciences, 6(6), 1035–1051.

    Article  Google Scholar 

  • Newman, J.N., 1977. Marine Hydrodynamics, The MIT Press, Cambridge, p. 361.

    Book  Google Scholar 

  • Nishad, C.S., Vijay, K.G., Neelamani, S. and Chen, J.T., 2021. Dual BEM for wave scattering by an H-type porous barrier with nonlinear pressure drop, Engineering Analysis with Boundary Elements, 131, 280–294.

    Article  MathSciNet  MATH  Google Scholar 

  • Ohyama, T. and Tsuchida, M., 1995. Development of a partially three-dimensional model for ship motion in a harbor with arbitrary bathymetry, 24th International Conference on Coastal Engineering, ASCE, Kobe, Japan, pp. 871–885.

    Google Scholar 

  • Ohyama, T. and Tsuchida, M., 1997. Expanded mild-slope equations for the analysis of wave-induced ship motion in a harbor, Coastal Engineering, 30(1–2), 77–103.

    Article  Google Scholar 

  • Panchang, V., Zhang, J.F. and Demirbilek, Z., 2008. Incorporating rubble mound jetties in elliptic harbor wave models, Journal of Waterway, Port, Coastal, and Ocean Engineering, 134(1), 40–52.

    Article  Google Scholar 

  • Pessao, J., Fonseca, N. and Soares, C.G., 2015. Numerical study of the coupled motion responses in waves of side-by-side LNG floating systems, Applied Ocean Research, 51, 350–366.

    Article  Google Scholar 

  • Priya, P., Kumar, P. and Rajni, 2023. Mathematical modelling of nonlinear pressure drops in arbitrarily shaped port utilizing dual boundary element method, Ocean Engineering, 275, 114154.

    Article  Google Scholar 

  • Rabinovich, A.B., 1997. Spectral analysis of tsunami waves: Separation of source and topography effects, Journal of Geophysical Research: Oceans, 102(C6), 12663–12676.

    Article  Google Scholar 

  • Rupali, Kumar, P. and Rajni, 2021. Moored ship motion under the resonance conditions with breakwaters: A coupled numerical approach, Ocean Engineering, 241, 110022.

    Article  Google Scholar 

  • Sakakibara, S. and Kubo, M., 2008. Characteristic of low-frequency motions of ships moored inside ports and harbors on the basis of field observations, Marine Structures, 21(2–3), 196–223.

    Article  Google Scholar 

  • Santos, J.A., Pinheiro, L.V., Abdelwahab, H.S., Fortes, C.J., Pedro, F. G.L., Capitão, R.P., Hinostroza, M.A. and Soares, C.G., 2019. Physical modelling of motions and forces on a moored ship at the Leixões port, Defect and Diffusion Forum, 396, 60–69.

    Article  Google Scholar 

  • Sawaragi, T., Aoki, S. and Hamamoto, S., 1989. Analysis of hydrody-namic forces due to waves acting on a ship in a harbour of arbitrary geometry, 8th International Conference on Offshore Mechanics and Arctic Engineering, British Maritime Technology, The Hague, Netherlands, pp. 117–123.

    Google Scholar 

  • Sawaragi, T. and Kubo, M., 1982. The motions of a moored ship in a harbor basin, 18th International Conference on Coastal Engineering, American Society of Civil Engineers, Cape Town, South Africa, pp. 2743–2762.

    Google Scholar 

  • Sharma, A., Panchang, V.G. and Kaihatu, J.M., 2014. Modeling nonlinear wave-wave interactions with the elliptic mild slope equation, Applied Ocean Research, 48, 114–125.

    Article  Google Scholar 

  • Shi, X.Y., Zhang, N.C., Chen, C.P., Jiang, H.Z. and Cui, L., 2014. Experimental study of characteristics of motions of a large mooring ship in long-period waves, Journal of Marine Science and Technology, 22(2), 240–246.

    Google Scholar 

  • Sulisz, W., 2005. Wave propagation in channel with side porous caves, Journal of Waterway, Port, Coastal, and Ocean Engineering, 131(4), 162–170.

    Article  Google Scholar 

  • Sulisz, W., 2015. Wave propagation in a converging channel of arbitrary configuration, China Ocean Engineering, 29(5), 771–782.

    Article  Google Scholar 

  • Tabssum, S., Kaligatla, R.B. and Sahoo, T., 2020a. Gravity wave interaction with a porous breakwater in a two-layer ocean of varying depth, Ocean Engineering, 196, 106816.

    Article  Google Scholar 

  • Tabssum, S., Kaligatla, R.B. and Sahoo, T., 2020b. Surface gravity wave interaction with a partial porous breakwater in the presence of bottom undulation, Journal of Engineering Mechanics, 146(9), 04020088.

    Article  Google Scholar 

  • Takagi, K., Naito, S. and Hirota, K., 1993. Hydrodynamic forces acting on a floating body in a harbor of arbitrary geometry, The Third International Offshore and Polar Engineering Conference, International Society of Offshore and Polar Engineers, Singapore.

    Google Scholar 

  • Tsay, T.K., Zhu, W. and Liu, P.L.F., 1989. A finite element model for wave refraction, diffraction, reflection and dissipation, Applied Ocean Research, 11(1), 33–38.

    Article  Google Scholar 

  • Venkateswarlu, V., Vijay, K.G. and Nishad, C.S., 2021. Iterative dual boundary element analysis of a wavy porous plate near an inclined seawall, Ocean Engineering, 235, 109242.

    Article  Google Scholar 

  • Vijay, K.G., He, S.Y., Zhao, Y., Liu, Y. and Sahoo, T., 2020. Gravity wave interaction with a submerged wavy porous plate, Ships and Offshore Structure, 15(S1), S123–S133.

    Article  Google Scholar 

  • Wang, D.X., Sun, D.P. and Dong, S., 2022. Numerical investigation into effect of the rubble mound inside perforated caisson breakwaters under random sea states, Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment, 236(1), 48–61.

    Google Scholar 

  • Wang, G., Dong, G.H., Perlin, M., Ma, X.Z. and Ma, Y.X., 2011. An analytic investigation of oscillations within a harbor of constant slope, Ocean Engineering, 38(2–3), 479–486.

    Article  Google Scholar 

  • Watai, R.A., Ruggeri, F., Tannuri, E.A., Santos, N.F., Tavares, B.R. and dos Santos, J.M.G., 2018. An analysis methodology for the passing ship problem considering real-time simulations and moored ship dynamics: Application to the Port of Santos, in Brazil, Applied Ocean Research, 80, 148–165.

    Article  Google Scholar 

  • Yip, T.L. and Chwang, A.T., 1998. Water wave control by submerged pitching porous plate, Journal of Engineering Mechanics, 124(4), 428–434.

    Article  Google Scholar 

  • Yoo, B.S., 1998. An Analysis of Ship Motion in a Harbor, Ph.D. Thesis, Seoul National University, South Korea.

    Google Scholar 

  • Yu, X.P., 1995. Diffraction of water waves by porous breakwaters, Journal of Waterway, Port, Coastal, and Ocean Engineering, 121(6), 275–282.

    Article  Google Scholar 

  • Yu, X.P. and Chwang, A.T., 1994. Wave-induced oscillation in harbor with porous breakwaters, Journal of Waterway, Port, Coastal, and Ocean Engineering, 120(2), 125–144.

    Article  Google Scholar 

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Acknowledgements

This work is accomplished at the Department of Applied Sciences (Mathematics), National Institute of Technology Delhi, India. The authors would like to acknowledge the reviewers for their sincere suggestions to improve the manuscript.

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Authors and Affiliations

  1. Government Model Sanskriti Senior Secondary School Ganaur, Sonipat, 131101, India

    Gulshan

  2. Department of Applied Sciences (Mathematics), National Institute of Technology, Delhi, 110036, India

    Prachi Priya, Prashant Kumar &  Gulshan

  3. JindalGobal Business School, O. P. Jindal Global University, Sonepat, 131001, India

    Rajni

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  1. Prachi Priya
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Contributions

Prachi Priya: Conceptualization, Methodology, Validation, Data curation, Writing - original draft. Prashant Kumar: Conceptualization, Visualization, Investigation, Supervision, Writing - review & editing. Gulshan: Investigation, Writing - review & editing. Rajni: Investigation, Writing - review & editing.

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Correspondence to Prashant Kumar.

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Priya, P., Kumar, P., Gulshan et al. Mathematical Modeling of Moored Ship Motion in Arbitrary Harbor utilizing the Porous Breakwater. China Ocean Eng 37, 738–752 (2023). https://doi.org/10.1007/s13344-023-0062-y

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