40 
The model is not yet complete inasmuch as we also need a formula for velocity scale. To 
this end, we postulate an integral similar to that applied to length scale. 
V u v (z)= jV(z + S)A(z + 5) 
0 
v[( z )= f y/{z-S)K{z-S) 
dd u 
dô 
{z,S) 
ç-z 
J 
r dO l ^ 
v dS ; 
dö= K \y/{z + ô)d u {z,5)dô 
0 
H+z 
dö=K \y{z-ö)6\z,8)dö 
Again, the upper and lower integrals have to be put together. As for length scale, it must 
match up with the logarithmic boundary layer. Thus, after evaluation of the two integrals 
we choose the maximum value as the definite result. 
K (z)=max(F “ (z),V [ (z)) 
Finally, in our model, to end up with eddy viscosity, we set up a relaxation equation 
dt 4 
We believe that such damping (integration in time) is permissible because none of the 
processes involved has a frequency that is substantially greater than shear. (The factor of 
4 in the denominator comes from a crude estimation.) 
It should be kept in mind that our construct has developed from simple reflections about 
mixing length. Its novel features do not constitute a radical revision but a moderate 
modification of an existing standard. 
DYNAMIC BOUNDARY CONDITIONS AT SURFACE AND BOTTOM 
To calculate shear stress at the sea surface and bottom, i.e. the boundary conditions for 
vertical flux of horizontal momentum, a quadratic formulation from the boundary layer 
theory is used. 
At the sea surface it reads: 
«V 
< air 
r <p, 
P water 
Pa 
'CD 
'CD 
where 
Wx-Jwi + wi 
w ç jwl + w; 
C D 
Wà, Wcp 
Pair 
wind drag coefficient 
Co = (0.63+0.066 W/(m/s)) 10' 3 
components of surface wind 
density of the air. 
At the sea bottom it reads: 
T Xb = ru Vu 2 + v 2 
(Smith and Banke, 1975)