56
The main objective of the hydrodynamic model study is thus the evaluation of the vertical
fluxes, to test the hypothesis that it is mainly the Anadyr stream which is fuelling the huge
biological production of the Bering Strait region.
The three-dimensional model. The hydrodynamic model study - extensively discussed
in Deleersnijder (1992), Nihoul et al. (1993a) and Deleersnijder (1994a) - is carried out in an
ecological perspective. It concentrates on the summer period, when the region of interest is
virtually free of sea ice. The computational domain is a 700 km x 700 km shallow sea area,
where the sea depth is $ 70 m (Fig. 6).
Since the ultimate aim of the study is the understanding of the biological activity, it is
deemed appropriate to devote most of the attention to the general circulation, i.e., the flow
averaged over a sufficiently long time, say one week to one month, so that the meso-scale
processes are filtered out. In the domain of interest, the general circulation is associated with
much of the kinetic energy, in marked contrast to what is observed in most shelf seas.
The model set-up is described in detail in Deleersnijder (l994a). Here it is sufficient to say
that the water is forced to enter the domain through the southern boundary, that steady solutions
are examined, and that no wind stress is applied. Three reasons leads to neglecting the wind
forcing. First, the intent is to simulate the steady state background flow, i.e., the circulation
free of wind-induced variability. Second, it is believed that the wind stress is not a major
forcing in the domain of interest, although, over the whole Bering-Chukchi shelf, the wind
stress certainly plays a major role. Third, the plume of cold water downstream of the Anadyr
Strait does not seem to obey the classical wind-induced coastal upwelling scenario. Wind data
indeed indicates that the wind stress is hardly ever directed so as to drive coastal upwelling
(Deleersnijder, 1992). Therefore, it is found appropriate to look for an upwelling mechanism in
which the wind stress has no significant role.
The equations of the model are solved numerically in the sigma-coordinate system (Phillips,
1957). Accordingly, the physical space-time coordinates are transformed to new coordinates as
follows:
( _ _
)
(
z+h)
t,'X,y,z=u = t,x,Y,-- ,
T/+h
(28)
where h and T/ denote the unperturbed sea depth and the sea surface elevation, respectively.
Hence, the actual height of a water column is H = h + T/. In the sigma-coordinate system, the
surface (z = f/) and the bottom (z = -h) of the sea are coordinate surfaces. The latter is defined
as u = 0, while the former corresponds to u = 1.
Along with the transformed vertical coordinate u, it is customary to use a new vertical
velocity, defined as iii = DIu, where D I represents the material derivative operator, i.e., D 1=
a/at + u. 'i1 + wa/az. With the transformed vertical velocity, the impermeability of the surface
and the bottom is easily taken into account by prescribing iii = 0 at u = I, O.
In the sigma-space, the generic equation (7) is transformed to
H- 1 [a(~lfI} + V.(HulfI) + a(Hw lfI)] =
at
au
QI/f + H-1V.(HA VlfI} + H- 2 ~(K alfl), (29)
I/f
au I/f au
The main objective of the hydrodynamic model study is thus the evaluation of the vertical
fluxes, to test the hypothesis that it is mainly the Anadyr stream which is fuelling the huge
biological production of the Bering Strait region.
The three-dimensional model. The hydrodynamic model study - extensively discussed
in Deleersnijder (1992), Nihoul et al. (1993a) and Deleersnijder (1994a) - is carried out in an
ecological perspective. It concentrates on the summer period, when the region of interest is
virtually free of sea ice. The computational domain is a 700 km x 700 km shallow sea area,
where the sea depth is $ 70 m (Fig. 6).
Since the ultimate aim of the study is the understanding of the biological activity, it is
deemed appropriate to devote most of the attention to the general circulation, i.e., the flow
averaged over a sufficiently long time, say one week to one month, so that the meso-scale
processes are filtered out. In the domain of interest, the general circulation is associated with
much of the kinetic energy, in marked contrast to what is observed in most shelf seas.
The model set-up is described in detail in Deleersnijder (l994a). Here it is sufficient to say
that the water is forced to enter the domain through the southern boundary, that steady solutions
are examined, and that no wind stress is applied. Three reasons leads to neglecting the wind
forcing. First, the intent is to simulate the steady state background flow, i.e., the circulation
free of wind-induced variability. Second, it is believed that the wind stress is not a major
forcing in the domain of interest, although, over the whole Bering-Chukchi shelf, the wind
stress certainly plays a major role. Third, the plume of cold water downstream of the Anadyr
Strait does not seem to obey the classical wind-induced coastal upwelling scenario. Wind data
indeed indicates that the wind stress is hardly ever directed so as to drive coastal upwelling
(Deleersnijder, 1992). Therefore, it is found appropriate to look for an upwelling mechanism in
which the wind stress has no significant role.
The equations of the model are solved numerically in the sigma-coordinate system (Phillips,
1957). Accordingly, the physical space-time coordinates are transformed to new coordinates as
follows:
( _ _
)
(
z+h)
t,'X,y,z=u = t,x,Y,-- ,
T/+h
(28)
where h and T/ denote the unperturbed sea depth and the sea surface elevation, respectively.
Hence, the actual height of a water column is H = h + T/. In the sigma-coordinate system, the
surface (z = f/) and the bottom (z = -h) of the sea are coordinate surfaces. The latter is defined
as u = 0, while the former corresponds to u = 1.
Along with the transformed vertical coordinate u, it is customary to use a new vertical
velocity, defined as iii = DIu, where D I represents the material derivative operator, i.e., D 1=
a/at + u. 'i1 + wa/az. With the transformed vertical velocity, the impermeability of the surface
and the bottom is easily taken into account by prescribing iii = 0 at u = I, O.
In the sigma-space, the generic equation (7) is transformed to
H- 1 [a(~lfI} + V.(HulfI) + a(Hw lfI)] =
at
au
QI/f + H-1V.(HA VlfI} + H- 2 ~(K alfl), (29)
I/f
au I/f au