(order in €) 
koi = Lo1 eo e( (1): 
kon = Mor — M1 oe (EES 
ko3 = Mos — 3uoitlen + 2u4G; 22 G82) 
kio = 10 a (2). 
Ky = 411-1001 4 ey ()) (12.111) 
kz = M12 — Wigton — 2uo11 + 21045; pe(ecee) 
k0 = M20 — Mio ... (+e) 
koy = M21 — 21011 —Motl20 + 27 qulo1 »4 =) 
kao = 30 — 341020 + 23 (eRe) 
Following these general formulations by Vinje, M. Hineno®’ calculated the proba- 
bility distribution function of the wave height, treating the wave process as nonlinear, as 
was mentioned in Section 9.2.1, and will be summarized as follows. 
From these relations with u,,, the order of kp, in€’s was obtained, which is a 
smallness parameter that appeared in Eq. 12.100 as is listed in Eq. 12.111. Expanding 
Eg. 12.110 arounde =0 into a Taylor series and truncating at O(€) gives 
1 1 1 = 
p(21, 22) = =| | exp — k20(0)81- ko2(0)63 
x [1+ hotoo) += Kso(0)(0 1)? += kox(0)(i82)° 
= Kt 0G0 1083) | eH9:2:+6222) dO dO>, (12.112) 
: re) 
where k;j(0) = ben k;(0) = =e ke 
€=0° 
After manipulation, 
357 
