References
91
velocity on the side wall, have turned out to have an influence on the total
solution far beyond our expectations. This implies that the solutions which we
do achieve depend on the least reliable part of our physical theory. It is
common in present-day numerical modeling to choose a parameterization of
turbulent mixing and the associated boundary condition in order to achieve a
numerical "solution" that is judged to be realistic or at least pleasing to the
investigator. There is nothing wrong with such a strategy as a device to obtain
flows for analysis of their dynamics, but we must distinguish such solutions
from a completely deductive theory for the circulation, which is after all our
ultimate goal.
The homogeneous ocean model has also been used to investigate other
important dynamical issues connected to a more detailed description of the
circulation. Among the most important of these is the issue of determining the
latitude of separation of the western boundary current from the coast and its
intrusion into the interior. Such interesting issues are beyond the scope of the
present book, and the interested reader is referred to recent work by Cessi
(1991), Deng (1993), and Haidvogel et al. (1992). Suffice it to say that in each of
these treatments, small-scale dissipation once more appears as a determining
factor in the gross dynamics of the large-scale flow.
The following chapters concentrate on theories for the vertical structure of
the oceanic general circulation. In almost all cases these theories are incomplete
in the sense that their dynamics is limited to the region outside of the western
boundary current region. They therefore suffer all the uncertainties and dynamic ambiguities of the Sverdrup theory. Indeed, except for the discussion in
Chapter 6 of equatorial dynamics, they all take the Sverdrup theory as a
starting point for determining of the vertical average of the flow field in the
interior. The reader must therefore bear in mind that from a purely deductive
point of view these theories are fundamentally incomplete and depend on
strong assumptions about the possibility of completing the solution in the
western regions without fundamentally disturbing the interior. We may believe
that the Sverdrup theory is justified from an observational point of view, although, as we saw in Chapter 1, this is still itself a controversi!ll point. We also
use the theory freely as a building block for more complicated theories of the
stratified ocean circulation. We must admit, however, that we have so far fallen
short of our goal in deciding the issue on first principles.
References
Barcilon, V. Large Rossby number wind-driven barotropic ocean circulation.
Batchelor, G.K., 1969: Computation of the energy spectrum in homogeneous two- dimensional
turbulence. Phys. Fluids.(Supplement II), 12, 233-238.
Blandford, R. R., 1971: Boundary conditions in homogeneous ocean models. Deep Sea Res.,18,
739-751.
Boning, C.W., 1986: On the influence of frictional parameterization in wind-driven ocean
circulation models. Dyn. of Atm. and Oceans. 10, 63-92.
91
velocity on the side wall, have turned out to have an influence on the total
solution far beyond our expectations. This implies that the solutions which we
do achieve depend on the least reliable part of our physical theory. It is
common in present-day numerical modeling to choose a parameterization of
turbulent mixing and the associated boundary condition in order to achieve a
numerical "solution" that is judged to be realistic or at least pleasing to the
investigator. There is nothing wrong with such a strategy as a device to obtain
flows for analysis of their dynamics, but we must distinguish such solutions
from a completely deductive theory for the circulation, which is after all our
ultimate goal.
The homogeneous ocean model has also been used to investigate other
important dynamical issues connected to a more detailed description of the
circulation. Among the most important of these is the issue of determining the
latitude of separation of the western boundary current from the coast and its
intrusion into the interior. Such interesting issues are beyond the scope of the
present book, and the interested reader is referred to recent work by Cessi
(1991), Deng (1993), and Haidvogel et al. (1992). Suffice it to say that in each of
these treatments, small-scale dissipation once more appears as a determining
factor in the gross dynamics of the large-scale flow.
The following chapters concentrate on theories for the vertical structure of
the oceanic general circulation. In almost all cases these theories are incomplete
in the sense that their dynamics is limited to the region outside of the western
boundary current region. They therefore suffer all the uncertainties and dynamic ambiguities of the Sverdrup theory. Indeed, except for the discussion in
Chapter 6 of equatorial dynamics, they all take the Sverdrup theory as a
starting point for determining of the vertical average of the flow field in the
interior. The reader must therefore bear in mind that from a purely deductive
point of view these theories are fundamentally incomplete and depend on
strong assumptions about the possibility of completing the solution in the
western regions without fundamentally disturbing the interior. We may believe
that the Sverdrup theory is justified from an observational point of view, although, as we saw in Chapter 1, this is still itself a controversi!ll point. We also
use the theory freely as a building block for more complicated theories of the
stratified ocean circulation. We must admit, however, that we have so far fallen
short of our goal in deciding the issue on first principles.
References
Barcilon, V. Large Rossby number wind-driven barotropic ocean circulation.
Batchelor, G.K., 1969: Computation of the energy spectrum in homogeneous two- dimensional
turbulence. Phys. Fluids.(Supplement II), 12, 233-238.
Blandford, R. R., 1971: Boundary conditions in homogeneous ocean models. Deep Sea Res.,18,
739-751.
Boning, C.W., 1986: On the influence of frictional parameterization in wind-driven ocean
circulation models. Dyn. of Atm. and Oceans. 10, 63-92.