Longuet-Higgins (1952) . The fraction r of waves that are larger than a 

 given value of H/H^^ is the exceedence probability for that H/H^^^ . The 

 average value of waves higher than a given H/H^^^ is the integral from that 

 H/Hrms ^o infinity of the normalized heights weighted by the pdf and divided 

 by the area over the same limits under the weighting function (i.e., the pdf). 

 The general forms for r and H^'^VHrms ^^® 



The terms in square brackets are the dimensionless pdf models under considera- 

 tion (Equation 10 for the Rayleigh model or Equation 13 for the Modified 

 Rayleigh model). Where the above integrals have no simple analytic form, 

 numerical methods are used for evaluation. The simple trapezoid rule with 

 increments of AH/H^3 = 0.001 and an upper limit of integration of 6.0 (in 

 place of infinity) has been found to yield quite accurate results . 



Bimodal Test Data Generation 



50. The above definitions are used to establish criteria for simulating 

 a Rayleigh process using discrete inverse Fourier transform techniques to 

 produce time series from unimodal , band- limited, white spectra having given 

 bandwidths and numbers of component waves. Once such criteria are estab- 

 lished, a bimodal spectrum can be constructed of two unimodal spectra, each of 

 which yields a Rayleigh wave height distribution by itself. Wave height 

 distributions derived from such bimodal spectra can then be compared with test 

 models to determine the quality of representation. 



51. Since each mode in such a bimodal spectrum yields a Rayleigh wave 

 height distribution by itself, the details of the mode structure (bandwidth 

 and number of component wave trains) are no longer important. The two primary 

 variables in bimodal tests are a measure of modal separation in the frequency 

 domain and the relative amount of energy in one mode compared with the other. 

 Modal separation is important because the two modes could be very close to 

 each other and so just yield a slightly wider unimodal spectrum (and 



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