62
(J
Wuw = - f V.(H fi) dO" .
o
(32)
Consequently one has to analyse the behaviour of Hfi in order to understand the distribution
ofwuw'
The direction of u with respect to 0 is measured by the angle {3, which may be calculated
from sin{3 = e z • (ii x u) / (Iiillul). Angle {3 is positive if u is "on the left of 0", and is negative
otherwise. For each water column, the veering S is defined as S = {3max - {3min' if the point
where {3 = f3 is closer to the bottom than that where {3 = {3 . . Otherwise, S = f3 . - {3 .
max
mtn
mm
max
The mean veering is about 12 0 • The veering is positive in 2556 verticals out of a total of 2690.
In 95% of the verticals of the computational domain, the direction of u is qualitatively in
agreement with that of the bottom Ekman spiral, i.e., u is on the left ofo near the bottom and
on the right near the surface.
The qualitative properties of Hfi are accounted for in the following Taylor expansion of Hfi
truncated at two terms:
H fi = (H fi)" + (H fi).i '
(33)
with
(34)
where a" and a.i are positive constants. Relations (33) and (34) are by no means intended to
provide a reliable approximation to the vertical profiles of Hfi. Instead, (33)-(34) are simply
intuitively appealing formulae having some of the modelled properties of Hfi: in (33)-(34), the
depth average of ltil is a linearly increasing function of 101 (Fig. 9), and the veering is always
positive.
Let w uw ." and wuw . .i denote the upwelling velocity related, through (32), to (H fi)"and
(H fi).1' respectively. Accordingly, Wuw = w UWJ1 + wuw . ..l'
Introducing the two contributions to the transport Hfi defined in (34), taking the depthintegrated continuity equation, V.(Hii) = 0, into account, it is readily seen that wuw = Wuw .1
and w UWJ1 = O. The same calculations may be carried out with the modelled field of Hfi. To do
so, the following definitions are introduced
(35)
The corresponding upwelling velocities may then be evaluated. According to the model results,
the latter obey
[ Iwuw JI- wuwlms ' Iwuw . .i - wuwlms ] =
[0.72, 0.28] ( IWuw."l ms + IWuw)ms)' (36)
where, for a given variable s, Islms represents (Islrmi. This clearly supports the wellfoundedness of the splitting (34), for the modelled upwelling velocity is mostly associated with
the variations of (H ti).i' while the role of (H fi)" is less important in this respect.
(J
Wuw = - f V.(H fi) dO" .
o
(32)
Consequently one has to analyse the behaviour of Hfi in order to understand the distribution
ofwuw'
The direction of u with respect to 0 is measured by the angle {3, which may be calculated
from sin{3 = e z • (ii x u) / (Iiillul). Angle {3 is positive if u is "on the left of 0", and is negative
otherwise. For each water column, the veering S is defined as S = {3max - {3min' if the point
where {3 = f3 is closer to the bottom than that where {3 = {3 . . Otherwise, S = f3 . - {3 .
max
mtn
mm
max
The mean veering is about 12 0 • The veering is positive in 2556 verticals out of a total of 2690.
In 95% of the verticals of the computational domain, the direction of u is qualitatively in
agreement with that of the bottom Ekman spiral, i.e., u is on the left ofo near the bottom and
on the right near the surface.
The qualitative properties of Hfi are accounted for in the following Taylor expansion of Hfi
truncated at two terms:
H fi = (H fi)" + (H fi).i '
(33)
with
(34)
where a" and a.i are positive constants. Relations (33) and (34) are by no means intended to
provide a reliable approximation to the vertical profiles of Hfi. Instead, (33)-(34) are simply
intuitively appealing formulae having some of the modelled properties of Hfi: in (33)-(34), the
depth average of ltil is a linearly increasing function of 101 (Fig. 9), and the veering is always
positive.
Let w uw ." and wuw . .i denote the upwelling velocity related, through (32), to (H fi)"and
(H fi).1' respectively. Accordingly, Wuw = w UWJ1 + wuw . ..l'
Introducing the two contributions to the transport Hfi defined in (34), taking the depthintegrated continuity equation, V.(Hii) = 0, into account, it is readily seen that wuw = Wuw .1
and w UWJ1 = O. The same calculations may be carried out with the modelled field of Hfi. To do
so, the following definitions are introduced
(35)
The corresponding upwelling velocities may then be evaluated. According to the model results,
the latter obey
[ Iwuw JI- wuwlms ' Iwuw . .i - wuwlms ] =
[0.72, 0.28] ( IWuw."l ms + IWuw)ms)' (36)
where, for a given variable s, Islms represents (Islrmi. This clearly supports the wellfoundedness of the splitting (34), for the modelled upwelling velocity is mostly associated with
the variations of (H ti).i' while the role of (H fi)" is less important in this respect.