Distribution of the nonlinear random ocean wave period |
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| Authors: | HOU Yijun LI Mingjie SONG Guiting SI Guangcheng QI Peng HU Po |
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| Institution: | [1]Hey Laboratory of Ocean Circulation and Waves, Chinese Academy of Sciences, Qingdao 266071, China [2]Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China [3]Graduate School of the Chinese Academy of Sciences, Beijing 100049, China |
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| Abstract: | Because of the intrinsic difficulty in determining distributions for wave periods, previous studies on wave period distribution
models have not taken nonlinearity into account and have not performed well in terms of describing and statistically analyzing
the probability density distribution of ocean waves. In this study, a statistical model of random waves is developed using
Stokes wave theory of water wave dynamics. In addition, a new nonlinear probability distribution function for the wave period
is presented with the parameters of spectral density width and nonlinear wave steepness, which is more reasonable as a physical
mechanism. The magnitude of wave steepness determines the intensity of the nonlinear effect, while the spectral width only
changes the energy distribution. The wave steepness is found to be an important parameter in terms of not only dynamics but
also statistics. The value of wave steepness reflects the degree that the wave period distribution skews from the Cauchy distribution,
and it also describes the variation in the distribution function, which resembles that of the wave surface elevation distribution
and wave height distribution. We found that the distribution curves skew leftward and upward as the wave steepness increases.
The wave period observations for the SZFII-1 buoy, made off the coast of Weihai (37°27.6′ N, 122°15.1′ E), China, are used
to verify the new distribution. The coefficient of the correlation between the new distribution and the buoy data at different
spectral widths (ν=0.3?0.5) is within the range of 0.968 6 to 0.991 7. In addition, the Longuet-Higgins (1975) and Sun (1988)
distributions and the new distribution presented in this work are compared. The validations and comparisons indicate that
the new nonlinear probability density distribution fits the buoy measurements better than the Longuet-Higgins and Sun distributions
do. We believe that adoption of the new wave period distribution would improve traditional statistical wave theory. |
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| Keywords: | random ocean wave nonlinearity wave period distribution |
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