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Full text: 29: The Operational Circulation Model of BSH (BSHcmod)

44 
Concerning the wave propagation direction as a function of A and q> we have the 
following elliptic system of partial differential equations 
3(cos<9) d(cos^smi9) _ 
dA d(p 
3(sin<9) d(cos(pcos9) 
dA d(p 
It can be seen at this point that in spherical co-ordinates the rays of wave propagation are 
not straight lines but must be curved. 
Waves are uncorrelated with mean flow and with what has been taken into account as 
irregular turbulent fluctuation. As with irregular sub-scale fluctuation, a residual comes 
from self-correlation only. However, compared to totally irregular fluctuations (turbulence), 
we are in a much better position regarding the fluctuation effect. Since we have a better 
picture of waves than of turbulence, modelling of this net effect is not as vague as in the 
case of irregular fluctuations. 
As has been mentioned above, the radiation stress calculated by Dolata & Rosenthal 
coincides with the Reynolds average of the wave momentum. (Note however that this 
conclusion was not explicitly drawn in their paper.) We arrive at the result 
u’u —\a 2 co 2 
cosh 2 (k(H + z)) 
sinh 2 (£W) 
sin" 6 
mV = \a 2 (o 2 
vV = -~a 2 co 2 
cosh 2 (k(H + z)) . 
AA — cos 9 sin 6 
sinh(/W) 
cosh 2 (&(W + z)) 2 a 
At —cos 6 
sinh 2 (Af/) 
mV = 0 
v V = 0 
In our vertically resolved model, the wave effect is taken into account at any depth, all the 
way from surface to bottom. To achieve that, we use the two-dimensional surface fields 
of waves as provided by numerical simulation (WAM) as well as the vertical profile of 
radiation stress. As a simplification we assume that the entire wave energy is 
concentrated in a single wave of peak frequency and mean direction.
	        
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