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.