with:
db
db dr-db)
-+u Vb +U3--- ,1,- = a
a t '
dz dz dz
divu + dU3 = a
dz
q == J!.... + gz
Po
137
b = f!::2Q g = beT,S)
Po
where (i) is twice the vertical component of the earth rotation vector, q the generalized
pressure, v the vertical eddy viscosity, and X the vertical eddy diffusivity of buoyancy.
Remark: Considering that horizontal length scales are much larger than vertical length scales
and that turbulent fluxes are proportional to the gradient of the mean quantities, the horizontal
turbulent diffusion is neglected as compared with the vertical diffusion. Nevertheless, for the
numerical analysis of the fully three-dimensional problem, we will introduce horizontal
diffusion term. This term will depend on the numerical space discretization and it will be
combined with the sub-grid scale Reynolds stresses.
1.2 Domain boundaries hypothesis
The notations used to specify the boundaries of the studied model are presented
hereafter.
03
1
Yo
[]
[]
Q
OX
CJ;:I CDn
I]
Figure 0: Surface and vertical section of the domain