2011
DOI: 10.1016/j.oceaneng.2011.07.001
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Three dimensional wave scattering by arrays of elliptical and circular cylinders

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Cited by 31 publications
(10 citation statements)
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“…Mathieu functions have the advantage of decreasing significantly the numerical tasks and reducing the algebraic manipulations with respect to methods based on integral and hypersingular integral equations. For this reason, their applications can be found in several surface wave diffraction phenomena of the first (Chen and Mei, 1973;Williams and Darwiche, 1988;Chatjigeorgiou and Mavrakos, 2010;Chatjigeorgiou, 2011) and second order (Chatjigeorgiou and Mavrakos, 2012) and other fields involving elliptic structures (Stamnes and Spjelkavik, 1995;Ruby, 1995;Gutiérrez-Vega, 2000;Gutiérrez-Vega et al, 2003). Hereafter we summarize the method of solution adopted in Michele et al (2016b).…”
Section: Leading Order Problem -First Harmonic Response To Incident Wavesmentioning
confidence: 99%
“…Mathieu functions have the advantage of decreasing significantly the numerical tasks and reducing the algebraic manipulations with respect to methods based on integral and hypersingular integral equations. For this reason, their applications can be found in several surface wave diffraction phenomena of the first (Chen and Mei, 1973;Williams and Darwiche, 1988;Chatjigeorgiou and Mavrakos, 2010;Chatjigeorgiou, 2011) and second order (Chatjigeorgiou and Mavrakos, 2012) and other fields involving elliptic structures (Stamnes and Spjelkavik, 1995;Ruby, 1995;Gutiérrez-Vega, 2000;Gutiérrez-Vega et al, 2003). Hereafter we summarize the method of solution adopted in Michele et al (2016b).…”
Section: Leading Order Problem -First Harmonic Response To Incident Wavesmentioning
confidence: 99%
“…Linton & Evans 1993;Porter & Evans 1999;Thompson, Linton & Porter 2008). Notable extensions to problems involving non-circular cylinders, truncated cylinders, second-order theory and ice covered surfaces are described by Chatjigeorgiou (2011), Zheng et al (2020b), Wolgamot, Eatock Taylor & Taylor (2015), Malenica, Eatock Taylor & Huang (1999) and Ren, Wu & Ji (2018). It is worth remarking here that if the cylinder is not uniform in the depth (i.e.…”
Section: Introductionmentioning
confidence: 99%
“…In the current multiply-connected domain problem (see Fig. 1), enforcement of the outer boundary condition at ξ 2 = ξ O can be achieved by direct application of the classical addition theorems for elliptical wave (Mathieu) functions [6,7]. Accordingly, following the classical notation presented in Meixner and Schäfke [19], the wave fields associated with the elliptical perforation coordinates (ξ 1 , η 1 ) can expediently be expressed in terms of the general elliptical membrane coordinates (ξ 2 , η 2 ) by making use of the following useful relationships:…”
Section: Formulationmentioning
confidence: 99%