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New families of pure gravity waves in water of infinite depth |
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| Institution: | 1. School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and Scientific Computing, Xiamen University, Xiamen, Fujian 361005, China;2. Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA;1. DICATAM, Mathematical Division, University of Brescia, Via Valotti 9, 25133 Brescia, Italy;2. SMART Engineering Solutions & Technologies (SMARTEST) Research Centre, eCampus University, Via Isimbardi 10, 22060 Novedrate (CO), Italy;1. DICATAM, University of Brescia, Via Valotti 9, 25133 Brescia, Italy;2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;3. Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan 430072, China |
| Abstract: | Nonlinear periodic gravity waves propagating at a constant velocity at the surface of a fluid of infinite depth are considered. The fluid is assumed to be inviscid and incompressible and the flow to be irrotational. It is known that there are both regular waves (for which all the crests are at the same height) and irregular waves (for which not all the crests are at the same height). We show numerically the existence of new branches of irregular waves which bifurcate from the branch of regular waves. Our results suggest there are an infinite number of such branches. In addition we found additional new branches of irregular waves which bifurcate from the previously calculated branches of irregular waves. |
| Keywords: | Nonlinear gravity waves Bifurcations |
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