Jin Wu 
k,is the wave-number at the spectral maximum; ky is the maximum 
wave-number where the influence of surface tension is negligible; k, 
is the neutrally stable wave-number, B and B' are the spectral coef- 
ficients for the gravity and the capillary ranges, respectively; finally, 
f (@)is a dimensionless function specifying the directional distribu- 
tion of wave components (Schule et al. 1971) where 9 = 0 indicates 
the wind direction, The wave-number ky can be expressed as 
| 
I= deesBgtie Bs shy (8) 
wherein pis the density of water, gis the gravitational acceleration 
and T is the surface tension. The neutrally stable wave-number cor- 
responds to the wavelength at which the energy input from the wind 
is balanced by the energy dissipation through viscosity. This specific 
wavelength was expressed by Miles (1962) as a function of the wind 
shear velocity. 
It is considered for the equilibrium wave spectra that high- 
frequency wave components spread isotropically. In this case f (0 ) 
equals to unity and the one-dimensional spectra, identical in all direc- 
tions, becomes 
v¥(k)=(B/2 7 )kK? and W(k)=(B'/27)k? (9) 
In laboratories, owing to narrowness of the tank the waves propagate 
predominantly in the direction of the wind. The spectra may be consi- 
dered to be unidirectional and may be described by (9) in the direction 
of the wind. 
The mean square slope of the wind-disturbed water surface, 
s*, can be obtained from the directional wave-number spectrum 
WV (k), or 
=z f [oe) 2 =a A 
s = j k* w (k) dk (10) 
The integration should cover the possible range of the wave-number. 
Substituting (7) into (10), we have (Phillips 1966) 
s°= B fy (ky/k,) + BI Ln (k,/ky ) (11) 
The first term on the right-hand side of (11) represents the contribu- 
tion of gravity waves to the mean-square surface slope, and the se- 
cond term on the right-hand side represents the contribution of capil- 
lary waves. 
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