270
Theory of the Ventilated Thermocline
De Szoeke (1987) applied the three-layer model to the thermocline of the
South Pacific and also found good agreement between the predictions of the
theory and the observed isopycnal depths and dynamic topography. In his
calculation it appears that most of the basin at the density levels which he
considered is covered by the unventilated pool in the western region in an
interesting contrast to the North Atlantic circulation where Huang (1989b)
showed the dominant importance of ventilation. The success of the theory in
both of these limiting cases is strong evidence in favor of the unified theory of
recirculation and ventilation.
Numerical Models
Although numerical models are not adequate surrogates for the natural ocean,
they do contain processes, in particular the interaction of the interior with the
western boundary current, that are absent in the analytical models described in
this chapter. It is therefore of great interest to see to what extent the dynamical
picture which we have developed can be discerned in numerical experiments. In
order to deal with order 1 variations of the depth of the density surfaces
numerical models must abandon the quasi-geostrophic approximation. This
has historically meant that such models utilize what is called the primitive
equations. The equations are "primitive" in the sense that no additional
approximations are used to refine the equations beyond the hydrostatic
approximation. The complexity of these equations means that numerical
experiments are costly and time consuming.
After the construction of the analytical, ventilated-thermocline theory of
Luyten et al. (1983), Cox and Bryan (1984) and Cox (1985) reexamined their
numerical model in the context of simplified basin shapes and boundary
conditions that allowed a useful comparison with the theory (see also Bryan
( 1987) for a discussion of the experiments).
Cox and Bryan (1984) and Cox (1985) describe the results of two central
experiments. In the first experiment a relatively course grid is employed (1 °
meridionally, 1.2° zonally) while in the fine-grid experiment the resolution is
improved (to 1/3° meridionally, 0.4° zonally). The coarse-grid experiment does
not resolve time-dependent synoptic scale eddies, and in their absence mixing is
accomplished by large explicit lateral mixing of momentum and density
(although the momentum balance remains geostrophic and the interior is in
Sverdrup balance.) The mixing parameterization for both momentum and
density mixing is, in the coarse-resolution case, the traditional diffusion
representation, with turbulent mixing coefficients of 10 8 cm 2 s- 1 and 10 7 cm 2 s- 1 ,
respectively. In the fine grid experiment the diffusion is accomplished largely by
the resolved eddies, and the explicit mixing is small and is parameterized in
terms of a biharmonic representation of the mixing terms that acts selectively
on the very small scales. This explicit mixing is not significant in the interior on
the energy-containing scales of motion. The calculations are double-gyre
Theory of the Ventilated Thermocline
De Szoeke (1987) applied the three-layer model to the thermocline of the
South Pacific and also found good agreement between the predictions of the
theory and the observed isopycnal depths and dynamic topography. In his
calculation it appears that most of the basin at the density levels which he
considered is covered by the unventilated pool in the western region in an
interesting contrast to the North Atlantic circulation where Huang (1989b)
showed the dominant importance of ventilation. The success of the theory in
both of these limiting cases is strong evidence in favor of the unified theory of
recirculation and ventilation.
Numerical Models
Although numerical models are not adequate surrogates for the natural ocean,
they do contain processes, in particular the interaction of the interior with the
western boundary current, that are absent in the analytical models described in
this chapter. It is therefore of great interest to see to what extent the dynamical
picture which we have developed can be discerned in numerical experiments. In
order to deal with order 1 variations of the depth of the density surfaces
numerical models must abandon the quasi-geostrophic approximation. This
has historically meant that such models utilize what is called the primitive
equations. The equations are "primitive" in the sense that no additional
approximations are used to refine the equations beyond the hydrostatic
approximation. The complexity of these equations means that numerical
experiments are costly and time consuming.
After the construction of the analytical, ventilated-thermocline theory of
Luyten et al. (1983), Cox and Bryan (1984) and Cox (1985) reexamined their
numerical model in the context of simplified basin shapes and boundary
conditions that allowed a useful comparison with the theory (see also Bryan
( 1987) for a discussion of the experiments).
Cox and Bryan (1984) and Cox (1985) describe the results of two central
experiments. In the first experiment a relatively course grid is employed (1 °
meridionally, 1.2° zonally) while in the fine-grid experiment the resolution is
improved (to 1/3° meridionally, 0.4° zonally). The coarse-grid experiment does
not resolve time-dependent synoptic scale eddies, and in their absence mixing is
accomplished by large explicit lateral mixing of momentum and density
(although the momentum balance remains geostrophic and the interior is in
Sverdrup balance.) The mixing parameterization for both momentum and
density mixing is, in the coarse-resolution case, the traditional diffusion
representation, with turbulent mixing coefficients of 10 8 cm 2 s- 1 and 10 7 cm 2 s- 1 ,
respectively. In the fine grid experiment the diffusion is accomplished largely by
the resolved eddies, and the explicit mixing is small and is parameterized in
terms of a biharmonic representation of the mixing terms that acts selectively
on the very small scales. This explicit mixing is not significant in the interior on
the energy-containing scales of motion. The calculations are double-gyre