Abstract
Existing methods, such as Discrete Integration Algorithm (DIA) or Multiple DIA (MDIA) for evaluating Boltzmann integral to assess the nonlinear energy transfer within a given energy spectrum at a given location, do not account for all the contributing wave resonating quadruplets (QPs) for want of computational ease in the wave models such as WAM and WWIII. By virtue of employing the state-of-the-art Gauss–Legendre Quadrature Method (GLQM), the transfer integral becomes free of singularities, and fast estimation of all the contributing QPs is possible; and hence, this method provides both accuracy and efficiency. It also works for different frequency and angular resolutions of the input spectral grid. In this paper, GLQM is validated with EXACT-NL and WRT methods for a theoretical spectrum. It is then applied to a measured spectrum of a moored buoy of National Institute of Ocean Technology, off Machilipattinam (DS5) in deep waters for evaluating the nonlinear QP interactions based on one-month data during July 2005. A characteristic monthly averaged 1D frequency spectrum has been chosen which represented a double-peaked sea-dominated spectrum. It is then fitted with a theoretical JONSWAP spectrum with 99.5% confidence. The nonlinear energy transfer rate (Snl) between the higher and lower frequencies of this fitted spectrum has been evaluated using GLQM and are quantified. The nonlinear coupling between the sea and swell parts is found to be absent as the ratio of the swell and sea frequencies is less than 0.6 (Masson in J Phys Oceanogr 23:1249–1258, 1993 [1]). Few hypothetical cases have been studied to understand Snl behaviour further.
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Acknowledgements
This work is a part of the research project (Sanction No. 25 (0275)/17/EMR-II) funded by CSIR, New Delhi, India, to the third author. The authors thank INCOIS and MOES for providing the moored buoy data. We thank the Director, Dr. S.S.C. Shenoi and the Group Head of CEE group Dr. M. V. Ramanamurthy, for giving an opportunity to conduct the work. We thank the technical and scientific staff who assisted in the field data collection.
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Kamalakannan, M., Kalyani, M., Prabhakar, V., Jena, B.K., Venkatesan, R. (2019). Assessment of Nonlinear Quadruplet Interactions for Measured Spectra in Deep Waters on the East Coast of India Through Gauss–Legendre Quadrature Method. In: Murali, K., Sriram, V., Samad, A., Saha, N. (eds) Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018). Lecture Notes in Civil Engineering, vol 22. Springer, Singapore. https://doi.org/10.1007/978-981-13-3119-0_53
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DOI: https://doi.org/10.1007/978-981-13-3119-0_53
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