EVAPORATION FROM THE OCEANS 
successfully to such problems as the generation of wind 
waves and the maintenance of the equatorial currents 
[25]. 
We may therefore state that at wind velocities above 
6-7 m sec“ the eddy viscosity in the lower layer above 
the sea surface behaves as 7f the sea surface were a 
rough surface (7) = 0.6 em) located about 8 m below 
the level at which ship observations are ordinarily 
made. The next question is then, How does the eddy 
diffusivity behave? If z is not small, the eddy dif- 
fusivity must be practically equal to the eddy viscosity, 
but what happens when z approaches zero? It appears 
quite probable that in this case, as well, we must 
introduce a layer next to the boundary surface through 
which the flux of water vapor takes place by ordinary 
diffusion. In 1937 the present writer argued as follows 
[23, p. 4]: 
One can conceive that for a short time a mass of air comes 
to rest in one of the hollows of the surface. This mass of air 
will immediately give off its momentum to the surface, but 
the vapor pressure will not immediately attain the value which 
is characteristic of the surface. As long as this mass remains 
at rest, its vapor contents will be increased by processes of 
ordinary diffusion, supposing that it originally was lower than 
the equilibrium pressure corresponding to the temperature 
and salinity of the surface. After a short time the air mass will 
be removed and replaced by another, and similar processes 
will be repeated. In order to describe these processes one can 
introduce a boundary layer, the thickness of which is a sta- 
tistical quantity representative of the average conditions and 
within which the transport of water vapor takes place through 
ordinary diffusion. 
A much more extreme view has been advanced by 
Millar [14] and Montgomery [16], who assume that 
even over a rough surface the laws pertaining to a 
smooth surface apply to a distance Z from the boundary 
surface, but that at that height an abrupt transition 
to “rough” conditions takes place. 
So far, five different attempts have been made to 
discuss the evaporation from a rough surface, based on 
different assumptions as to the character of the dif- 
fusivity close to the surface. These assumptions can be 
described as follows: 
1. Next to the surface there is a true diffusion layer 
followed by an intermediate layer of thickness Z in 
which the eddy diffusivity corresponds to that over a 
smooth surface, A = p(x + kowx,.z), where wx, 1S 
obtained from equation (20). At Z the eddy diffusivity 
suddenly imcreases to the value of the eddy viscosity 
over a rough surface, and forz > Z, A = kopwxr (¢ + 20) 
where wx, is obtained from equation (80) [14, 16]. 
2. Next to the surface there is a true diffusion layer 
of thickness 6 = dv/wx,;, where wx, applies to a rough 
surface. From the top of this layer the eddy dif- 
fusivity increases at the same rate as the eddy viscosity 
above a rough surface. These assumptions agree with 
those of Bunker and others [4] if their notations are 
made to correspond to those that apply to conditions 
above a rough surface. 
3. Next to the surface there is a true diffusion layer 
of thickness 6 = \v/wx,, where wx, applies to a rough 
1077 
surface. At the top of this layer the diffusivity in- 
creases abruptly from the molecular value to the value 
over a rough surface: A = kopwx, (6 + 2), and for z 
> oF A = kopwx,(z + 20) [23]. 
4. There exists no layer of true diffusion. The eddy 
diffusivity is at all levels identical with the eddy vis- 
cosity, A = kopws,(z + 2) (Sverdrup [24]). 
5. The character of the diffusivity corresponds to 
that assumed under (1), but at the top of the inter- 
mediate layer, at 2 = Z, the vertical flux of water 
vapor increases abruptly from Hy) to EH where E)/E 
= (wx:/Wxr)? [18]. 
On the basis of these assumptions it is possible to 
compute I',. The results are: 
‘a a | Wkr v ko We Z\ | 
i, Pe = E Z oP ci (rts? + In | , (31) 
Vv ko Wx, a a 
2. Ts = (dko~ + 1 (32) 
=i 
Vv a 
3 n= (rte? az aa a -) ’ (33) 
=i 
A. By = (in “) 2 (34) 
=il 
By Des (nf = 76 Bs) 2 (35) 
0 *S 
In Fig. 2 five I, curves, referred to a = 800 cm, are 
shown as functions of the wind velocity, corresponding 
to the five sets of assumptions. The curve marked (1) 
to) 2 4 6 8 10 12 14 16 18 20 
WIND VELOCITY (M SEC~!) 
Fig. 2.—Theoretical values of the evaporation coefficient 
as function of the wind velocity at 800 em, computed on the 
basis of different assumptions, and observed values shown by 
dots. 
is plotted according to values given by Montgomery 
[16], taking into account that here we refer I, to a 
height of 8 m, whereas he used 4 m. When computing 
I, in cases (2) and (3), the question arises as to what 
value to assign to X. It is not obvious that the value for 
a smooth surface (A = 11.5) is applicable, but lacking 
means of determining a better value, we have used it. 
It may be observed that, on the basis of Montgomery’s 
humidity measurements, Sverdrup [23] found \ = 27.5, 
but this value seems doubtful because it was derived 
