Decomposing damped incident and reflected waves using correlation and quasi-linearization methods |
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| Institution: | 1. Coastal Engineer, Coast & Harbor Engineering A Division of Hatch Mott MacDonald, formerly with Johns Hopkins University, 110 Main St, Suite 103, Edmonds, WA 98020, USA;2. Williard & Lillian Hackerman Professor of Civil Engineering, Johns Hopkins University, Baltimore, MD 21218-2682, USA;3. Professor of Civil Engineering, Johns Hopkins University, Baltimore, MD 21218-2682, USA;1. State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023, China;2. Department of Mechanical Engineering, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark |
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| Abstract: | Water waves propagating over a layer of soft mud or submerged aquatic vegetation can drastically attenuate over distances comparable to several wave lengths. The attenuation in the case of mud has been found previously to be reasonably described by an exponential decay. Waves reflect from beaches and any structures that they impact. The reflected waves affect wave heights measured in the field or laboratory wave basins.Decomposition of small amplitude waves into incident and reflected waves is a linear problem. However, the presence of the exponential damping introduces nonlinearity to the decomposition problem and requires an iterative process for solving the problem. Despite considerable experimental research on attenuation of waves over mud, none of the existing methods for decomposition of incident and reflected waves have accounted for this case.Here, the Newton Algorithm was used to account for the effect of wave decay over mud by quasi-linearizing the nonlinear equations. Also, a second method using a new error function and a commercial nonlinear solver was proposed in both time and frequency domain. The performance of both methods has been verified using artificial as well as laboratory data. |
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