1076 
the turbulent layer 
= p(y aP kowx2), 
and in the laminar layer 
(16) 
A = jy = pp (17) 
Here wu is the viscosity and » the kinematic viscosity 
of the air, k) is von Karman’s universal turbulence 
constant (ko = 0.4), and wx is the “friction velocity” 
which is defined by the equation 
wx = V7/p 
where 7 is the shearing stress. This is defined as r = 
A dw/dz and is supposed, near the sea surface, to be 
independent of height and equal to 7, the wind stress 
at the sea surface. The friction velocity can be ex- 
pressed by the wind at any level w: 
(18) 
where y is the resistance coefficient which, according 
to von Karman, can be obtained from the equation 
wt jin = 554 7 in 
ko Vv 
(20) 
The thickness of the laminar layer 6 is supposed to 
depend on the viscosity and the stress as expressed by 
the friction velocity: 
5=r—, 
Wx’ 
(21) 
where A is a constant for which von Karman found the 
value 11.5, whereas Montgomery [16] obtained 7.8. 
In the following applications we shall use von Ka4rm4n’s 
value, } = 11.5, but the choice is not of great im- 
portance. 
The picture given above of the variation with height 
of the eddy viscosity appears fully applicable when 
turning to the eddy diffusivity. We must indeed expect 
that next to the sea surface there exists a layer through 
which the flux of water vapor takes place by molecular 
diffusion, and it seems reasonable that the thickness 
of this layer equals that of the laminar layer. In the 
turbulent layer the eddy diffusivity must then be 
= p(k + kywxz), (22) 
where « is the coefficient of diffusion of water vapor 
through air. For values of z >> 6 this eddy diffusivity 
differs only imperceptibly from the eddy viscosity. 
The flux of water vapor through the two layers is 
then 
Caren (g\ 
Es px (@) = 
where the indices / and ¢ indicate that the differentials 
apply to the laminar and the turbulent layer, respec- 
tively. By integration, remembering that z = 0 at the 
Fee) 2 (23) 
MARINE METEOROLOGY 
top of the laminar layer where q = q;: 
E E x 
@—-G@=—6=—~, (24) 
pk pW, K 
Zz #H K + ko Wx 2 
Cl ae In Tee Sore (25) 
Adding and considering that « is small compared to 
kowxz for z >> 6, we obtain: 
E Kp wx Eee) 
ath ey ae a lye ete , (26 
Ola aa, | so” o- + (26) 
or, introducing w, 
[WEY fe (27) 
Mito = + In — i 
Therefore: 
i—1 
re = | Mo? +In fume] (28) 
Here the ratio v/x is independent of temperature (v/x 
= 0.602), but « increases a little with temperature 
(at OC x = 0.22, at 20C «x = 0.25 cm? sec). With x 
= 0.24 cm? sec and a = 800 cm, I, is shown in Fig. 
2 as a function of w. 
According to Rossby [19], the sea surface has the 
character of a hydrodynamically smooth surface at 
wind velocities up to 6-7 m sec! as measured at a 
height of about 8 m. At wind velocities exceeding 7-8 
m sec“ the sea surface appears to be hydrodynamically 
rough. 
Over a rough.surface the eddy viscosity mcreases 
linearly with height and has, at the surface itself (¢ = 
0), a value which is much larger than that of the 
ordinary viscosity: 
A = kypwx (2 + 20). (29) 
Here 2 is the ‘‘roughness length” of the surface. The 
resistance coefficient y is determined by 
ko 
~ pete 
20 
(30) 
When this concept is applied to conditions over the 
ocean the question arises as to where to place the zero 
level. No wind profiles have been measured at high 
wind velocities when large waves have been present, 
and we have, therefore, no knowledge of the wind 
distribution very close to the sea surface. 
Using other features—the angle between surface wind 
(e.g., wind at about 8 m) and pressure gradient, the 
ratio between surface wind and gradient wind—Rossby 
arrived at the conclusion that over the ocean the 
roughness length is independent of the wind velocity 
and equal to about 0.6 cm. This result is substantiated 
by the facts that with z9 = 0.6 em and with 800 cm 
< z < 1500 cm, equation (80) renders 7 values in 
agreement with those found by entirely different 
methods, and that these y values have been applied 
OO0 EE a, 
