{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:54:52Z","timestamp":1760234092169,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,3,22]],"date-time":"2021-03-22T00:00:00Z","timestamp":1616371200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100005416","name":"Norges Forskningsr\u00e5d","doi-asserted-by":"publisher","award":["Ekstraordin\u00e6re GM 2020 funding attributed to SINTEF Ocean"],"award-info":[{"award-number":["Ekstraordin\u00e6re GM 2020 funding attributed to SINTEF Ocean"]}],"id":[{"id":"10.13039\/501100005416","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Energies"],"abstract":"<jats:p>A typical assumption when performing analytical, numerical, and experimental studies in wave\u2013structure interaction in multi-body problems such as for wave farms and very large floating structures is the homogeneity of the wave field. Important interactions between the floating elements are dependent on the direction, amplitude, and phase of the waves acting on each. Then, wave homogeneity is probably unrealistic in near-shore areas where these installations are to be deployed. In the present work, an existing interaction method, which allows the use of standard boundary element diffraction codes for solving the first order wave structure linear potential for each unique geometry in the problem, is shown to be able to account for inhomogeneous sea states across the domain of a multi-body problem requiring only minimal modification to its implementation. A procedure to use the method to include arbitrary incoming undisturbed wave conditions at each body is presented. A verification study was done by using an artificial numerical configuration to mimic an inhomogeneous wave field in a standard diffraction code, which was used as a reference. The results obtained using the interaction-method based procedure are shown to be in excellent agreement with the reference ones. Furthermore, an example of frequency inhomogeneity of the wave field in a wave farm is shown and the effects on the motion amplitudes and absorbed power are presented illustrating the applicability of the procedure.<\/jats:p>","DOI":"10.3390\/en14061761","type":"journal-article","created":{"date-parts":[[2021,3,22]],"date-time":"2021-03-22T11:13:26Z","timestamp":1616411606000},"page":"1761","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Procedure to Calculate First-Order Wave-Structure Interaction Loads in Wave Farms and Other Multi-Body Structures Subjected to Inhomogeneous Waves"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9821-4781","authenticated-orcid":false,"given":"Jos\u00e9 Miguel","family":"Rodrigues","sequence":"first","affiliation":[{"name":"SINTEF Ocean, Marinteknisk Senter, Otto Nielsens vei 10, 7052 Trondheim, Norway"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,22]]},"reference":[{"key":"ref_1","unstructured":"Rodrigues, J.M., \u00d8kland, O., Fonseca, N., Leira, B., Alsos, H.S., Abrahamsen, B.C., Aksnes, V., and Lie, H. (2020, January 11\u201316). Design and verification of large floating coastal structures: Floating bridges for fjord crossings. Proceedings of the Thirtieth International Ocean and Polar Engineering Conference, Shanghai, China."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Fonseca, N., Chi, Z., Rodrigues, J.M., Ren, N.X., Hellan, O., and Magee, A.R. (2019, January 9\u201314). Hydrodynamic model tests with a large floating hydrocarbon storage facility. Proceedings of the ASME 38th International Conference on Ocean, Offshore and Arctic Engineering, Glasgow, Scotland.","DOI":"10.1115\/OMAE2019-96761"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/S0141-1187(98)00017-0","article-title":"Theoretical and experimental predictions of the hydroelastic response of a very large floating structure in waves","volume":"20","author":"Kagemoto","year":"1998","journal-title":"Appl. Ocean Res."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/0951-8339(93)90025-X","article-title":"Hydrodynamic interaction analyses of very large floating structures","volume":"6","author":"Kagemoto","year":"1993","journal-title":"Mar. Struct."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1016\/j.apor.2009.10.006","article-title":"The effect of sub-optimal control and the spectral wave climate on the performance of wave energy converter arrays","volume":"31","author":"Folley","year":"2009","journal-title":"Appl. Ocean Res."},{"key":"ref_6","unstructured":"Fitzgerald, C., and Thomas, G. (2007, January 11\u201313). A preliminary study on the optimal formation of an array of wave power devices. Proceedings of the 7th European Wave and Tidal Energy Conference, Porto, Portugal."},{"key":"ref_7","unstructured":"WAMIT INC (2020). Wamit User Manual, v7.4., WAMIT INC."},{"key":"ref_8","unstructured":"Babarit, A., and Delhommeau, G. (2015, January 6\u201311). Theoretical and numerical aspects of the open source bem solver nemoh. Proceedings of the 11th European Wave and Tidal Energy Conference (EWTEC2015), Nantes, France."},{"key":"ref_9","unstructured":"(2021, March 20). BUREAU VERITAS. Available online: https:\/\/marine-offshore.Bureauveritas.Com\/hydrostar-software-powerful-hydrodynamic."},{"key":"ref_10","unstructured":"(2021, March 20). SINTEF OCEAN. Available online: https:\/\/www.Sintef.No\/globalassets\/sintef-ocean\/factsheets\/muldif.Pdf."},{"key":"ref_11","unstructured":"(2021, March 20). SINTEF OCEAN. Available online: https:\/\/www.Sintef.No\/en\/software\/sima\/."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1017\/S0022112086000101","article-title":"Interactions among multiple three-dimensional bodies in water waves: An exact algebraic method","volume":"166","author":"Kagemoto","year":"1986","journal-title":"J. Fluid Mech."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1016\/S0029-8018(97)00003-6","article-title":"Analytical solutions of the diffraction problem of a group of truncated vertical cylinders","volume":"25","author":"Yilmaz","year":"1998","journal-title":"Ocean Eng."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Linton, C.M., and McIver, P. (2001). Handbook of Mathematical Techniques for Wave\/Structure Interactions, Chapman & Hall\/CRC.","DOI":"10.1201\/9781420036060"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1402","DOI":"10.1016\/j.oceaneng.2010.06.010","article-title":"Optimal configurations of wave energy device arrays","volume":"37","author":"Child","year":"2010","journal-title":"Ocean Eng."},{"key":"ref_16","first-page":"365","article-title":"A numerical method for huge semisubmersible responses in waves","volume":"98","author":"Yoshida","year":"1990","journal-title":"Trans. Soc. Naval Archit. Mar. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1037","DOI":"10.1016\/S0029-8018(99)00034-7","article-title":"Hydrodynamic interaction forces on multi-moduled structures","volume":"27","author":"Chakrabarti","year":"2000","journal-title":"Ocean Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"e26","DOI":"10.1016\/j.ijome.2013.11.009","article-title":"The cylindrical wave field of wave energy converters","volume":"3","author":"McNatt","year":"2013","journal-title":"Int. J. Mar. Energy"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.oceaneng.2014.11.029","article-title":"A novel method for deriving the diffraction transfer matrix and its application to multi-body interactions in water waves","volume":"94","author":"McNatt","year":"2015","journal-title":"Ocean Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/j.oceaneng.2017.11.026","article-title":"A numerical tool for the frequency domain simulation of large arrays of identical floating bodies in waves","volume":"148","author":"Flavia","year":"2018","journal-title":"Ocean Eng."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"McNatt, J.C., Porter, A., Chartrand, C., and Roberts, J. (2020). The performance of a spectral wave model at predicting wave farm impacts. Energies, 13.","DOI":"10.3390\/en13215728"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Leira, B.J., and Dai, J. (2020, January 23\u201316). Extreme dynamic response of extended bridge structures subjected to inhomogeneous environmental loading. Proceedings of the EURODYN 2020 XI International Conference on Structural Dynamics, Athens, Greece.","DOI":"10.47964\/1120.9285.19806"},{"key":"ref_23","unstructured":"Fonseca, N., and Bachynski, E.E. (2018). LFCS Review Report\u2014Environmental Loads Methods for the Estimation of Loads on Large Floating Bridges, SINTEF Ocean."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.engstruct.2018.02.066","article-title":"Wave load effect analysis of a floating bridge in a fjord considering inhomogeneous wave conditions","volume":"163","author":"Cheng","year":"2018","journal-title":"Eng. Struct."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Xiang, X., Viuff, T., Leira, B., and Oiseth, O. (2018, January 17\u201322). Impact of hydrodynamic interaction between pontoons on global responses of a long floating bridge under wind waves. Proceedings of the ASME 37th International Conference on Ocean, Offshore and Arctic Engineering, Madrid, Spain.","DOI":"10.1115\/OMAE2018-78625"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Belibassakis, K., Bonovas, M., and Rusu, E. (2018). A novel method for estimating wave energy converter performance in variable bathymetry regions and applications. Energies, 11.","DOI":"10.3390\/en11082092"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"102763","DOI":"10.1016\/j.marstruc.2020.102763","article-title":"Inhomogeneous wave load effects on a long, straight and side-anchored floating pontoon bridge","volume":"72","author":"Dai","year":"2020","journal-title":"Mar. Struct."},{"key":"ref_28","unstructured":"Abramowitz, M., and Stegun, I.A. (1964). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables."},{"key":"ref_29","unstructured":"McNatt, C. (2021, March 20). Mwave. Available online: https:\/\/github.com\/cmcnatt\/mwave."}],"container-title":["Energies"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1073\/14\/6\/1761\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:39:18Z","timestamp":1760161158000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1073\/14\/6\/1761"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,22]]},"references-count":29,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2021,3]]}},"alternative-id":["en14061761"],"URL":"https:\/\/doi.org\/10.3390\/en14061761","relation":{},"ISSN":["1996-1073"],"issn-type":[{"type":"electronic","value":"1996-1073"}],"subject":[],"published":{"date-parts":[[2021,3,22]]}}}