Graduate Thesis Or Dissertation
 

Random wave velocity field from periodic theory

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/6108vf82v

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  • Random waves are often expressed as a mathematical superposition of an infinite number of sinusoidal components. The mean square spectral density of the water surface elevation is often called the wave spectrum. The zero upcrossing wave heights usually have a Rayleigh probability distribution. However, the design wave concept is still used for design of many marine structures. It is common to use periodic wave theory to predict the velocity distribution in the design wave even though it is known that actual waves are quite irregular and their shape and kinematics may not conform to the periodic theory. The purpose of this study is to examine the validity of applying periodic wave theory to a wave in a random wave train. The magnitude of the errors are quantified in a statistical manner. The experiments were conducted in the Wave Research Facility at Oregon State University wherein random waves were generated with a flap-type wave board, resulting in a Bretschneider type spectrum with significant wave heights from 2.0 to 2.8 feet and significant periods from 2.5 to 2.8 seconds. The water particle velocities were measured with a hot film anemometer. The observed maximum horizontal and vertical velocities of each zero uperossing wave were compared with predicted ones from the linear wave theory. The relative error is expressed as ε = umeasured⁻upredicted/upredicted. The relative error turned out to be normally distributed and the standard deviation varied from 0.1 to 0.6 according to the size of the wave sample, although the mean value of the error remained almost constant. The error was smallest for the large waves which gives confidence to use of periodic theories for the design wave concept even though random waves are experienced by the structure.
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