4. More generally the moments m, of the wave spectrum are defined as |m, = fos(o

Question

4. More generally the moments m, of the wave spectrum are defined as |m, = fos(odo, the average wave height is given by A=2| aplc HC = (2m. . The normalized probability density function is given by P(S) = Le 12 and 3= 4 Here is the normalized wave amplitude, and m, is the total energy of the spectrum or the integral of s(@) over all frequencies. The significant wave height ,is defined as the average of the highest one third of all the waves , =2| Apls AGI JPISHG = 4.0m, y", the average of the highest one tenth of all the waves is defined as Aymo = 5.1(m)", the design extreme value exceeds the significant value by the ratio Design Extreme - log Ny", where N is the number of *** Significa nt 5198 0.01 encountered waves. In the sea state with significant wave height Hy3 = 5.0m, please find the wave height H, A10 = 5.1(m. )"2; if the ship experiences 2000 waves, what is the largest wave height? (15').

Explanation / Answer

(a) The average wave height (http://www.vos.noaa.gov/MWL/apr_06/waves.shtml)

     = 2/3(or0.64)times of the significant wave height(5.0 metres in this case)

     =0.64X5=   3.20metres

(b) Largest wave height(http://en.ilmatieteenlaitos.fi/significant-wave-height)

     = twice the significant wave height(5 metres here)

     = 10 metres

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