be shown later how tn, depends upon fetch and are two nondimensional parameters to be called 
wind velocity. The value of ftnin determines wave steepness and wave age. 
whether equation (47), the duration equation, or According to (6) and (52) 
(48), the fetch equation, is to be used for deter- dE 2dH 2ds 4d WdE 2d) aide 
mining the characteristics of the significant waves. Hd; dx ddr’ B dz Hiding Ae B di 
The meaning of equations (47) and (48) can be (54a, b) 
further illustrated. Let the subscript ‘‘z’’ denote : ; : 
steady state conditions and the subscript ‘t”’ Assuming that 6 is a function of 6 only: 
transient state conditions. Let dé __di dp | dé _d5 dB 
Hs _CdE | be _dE eR dx dBdz dt dB dt 
ATT DD Grp OT Rs ; With these substitutions and the expressions 
for Ry and Fy already given in (89) and (40), the 
equations for the steady state and the transient 
state can be written in the form 
denote the increments of energy going into the 
increase of wave height, and let 
lig = ne | Re= 7 a (50a, b) % —2Agu-2p-*e os 4B _ Ag U-1g-2! +a(1 =A 
be the increments of energy going into the increase Dames dB aa 6 dB 
of wave velocity for the steady and the transient (55a, b) 
state, respectively. Equations (48) and (47) can) Shore the upper sign (+) refers to BX 1. 
then be written: Equations (55) relate the dependent variables 
Rort Raz=RrtRy | ReitRa=Rr+Ry (Sla,b) 46 and @ to the independent variables z and ¢. 
The Fundamental Equation Complete solutions can be found in one of two 
ways: 
According to equation (4) 1. Eliminate either 5 or 6 (or the equivalent 
on Qn i dimensional terms H, 7) from the equations by 
H Cai miGie kee (52) deriving solutions of the type 5=6 (z,t)on the basis 
where of completely independent considerations. The 
5 A 8 C (53a, b) study of wave dispersion, for example, does indi- 
-—F> ? — . . : ° 
L U : cate solutions 7=T (z,t) which, when substituted 
WAVE STEEPNESS AGAINST RATIO WAVE VELOCITY TO WIND VELOCITY 
omaha T ] ] er Sea altel T 7 inc 
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“7 <2 Sh Nestanlte eal ay Bie | 
o e | i) | | 
oO 6}, — i —— —— cles — Sar a | 18 + 
z2 e@, 5 6 @ | PXNFCco oO | 18 
a § @ oe 8 | 
Ww 5 ! |) CI { + 20 
rs | o® & Te | | | | 
o I O Gh | | | 
dita ee Pej Nf 0 goo |, okie Nee 
z o| * co e] ee mal 
z=; EAS Oo. 0 Bolo F | | ie oY 
; ra sa T 5 Saar ee. —e 
f © 10 568 @ POV tmim Ciro 40 
te) as ~ ars 
; i | | ° jo oo t= 8 i iliag 
| | a—~— 9 
1 al ! | | ee +-==4100 
eo a 
° () 22 3 4 5 & 7 u 12 13 14 LBs} 16 17 18 
8 9 10 
WAVE AGE, B 
Figure 5.—Relation betweer: wave steepness and wave age. Observed values shown by symbols, assumed 
relationship shown by full drawn line. 
15 
