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Joint statistical distribution of two-point sea surface elevations in finite water depth
Institution:1. Department of Power & Control Engineering, School of Electrical & Computer Engineering, Shiraz University, Shiraz, Iran;2. Grenoble-Alpes University G2Elab, Grenoble, France;1. Faculty of Electrical Engineering and Computer Science, Ningbo University, Ningbo 315211, China;2. Electrical Engineering and Computer Science Department, University of Missouri, Columbia, MO 65211, USA;3. College of Electronics and Information Engineering, Shenzhen University, Shenzhen 518060, China
Abstract:Based on the second-order random wave solutions of water wave equations in finite water depth, a joint statistical distribution of two-point sea surface elevations is derived by using the characteristic function expansion method. It is found that the joint distribution depends on five parameters. These five parameters can all be determined by the water depth, the relative position of two points and the wave-number spectrum of ocean waves. As an illustrative example, for fully developed wind-generated sea, the parameters that appeared in the joint distribution are calculated for various wind speeds, water depths and relative positions of two points by using the Donelan and Pierson spectrum and the nonlinear effects of sea waves on the joint distribution are studied.
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