intense turbulent mixing we might even need to
question the basic Sverdrup vorticity balance.
5.2.7 Discussion
This chapter has summarized recent developments
in the fields of diapycnal mixing in the ocean interior and aspects of dispersion by mesoscale eddies
and smaller scale motions. While these oceanic
stirring and mixing mechanisms operate at quite
disparate horizontal length scales, they are linked
through the scale cascade that ultimately reaches
the dissipative end of the spectrum. Given limitations in computer power, eddy processes must be
parameterized in coarse-resolution ocean and coupled ocean–atmosphere climate models; mixing
processes require parameterization in all models
(apart from direct numerical simulations that are
viable only for very limited spatial domains). Given
the relationships between scales, care must be taken
that parameterizations for one class of motion don’t
adversely impact what occurs on other scales. The
now classic example of this problem was the contamination of diapycnal diffusive fluxes in simulations resulting from a horizontal (as opposed to
isopycnal) stirring parameterization.
A major advance in the field of ocean interior
stirring came about by the realization of Gent
and McWilliams (1990) that oceanic properties
should not be advected in an ocean model by the
Eulerian-mean flow but rather by some appropriate approximation of the Lagrangian velocity.
From this early work it took several years before
the importance of this idea on coarse-resolution
ocean models was realized. The theoretical aspect
of this work has progressed by making connections to the zonally averaged residual-mean theory
of the atmospheric scientists, and the three-dimensional version of this approach, the temporal-residual-mean has been summarized in this chapter. The
realization of the need for this type of extra advection (or equivalently, an extra skew diffusion) has
allowed many modellers to achieve substantial
improvements in ocean simulations including, for
example, the deep ocean temperature field. The
parameterizations used for this skew-diffusion to
date are rather crude and are clearly in need of
refinement.
Great progress has been made over the last 15
years documenting the pattern and intensity of
diapycnal mixing in the ocean. Perhaps the most
significant turbulent mixing occurs in and about
the surface layer where water properties are modified by air–sea exchange as well as by internal
mechanisms. Clearly a first step in building a realistic ocean model is to parameterize accurately surface-layer processes. We direct the reader to Large
and Nurser (Chapter 5.1), Lazier et al. (Chapter
5.5), Price (Chapter 5.3) and Hanawa and Talley
(Chapter 5.4) for detailed discussion. Large (1998)
also presents an excellent discussion of surface
boundary-layer processes and their parameterization. Below the surface-layer environment, a
background level of diapycnal flux is sustained by
the canonical GM internal wave field via wave
breaking. This level is relatively weak, however –
equivalent to a diapycnal diffusivity of about
10
95 m
2 s
91 . Thus to first order, the circulation in
and above the main thermocline might be thought
of as a turbulent surface layer above a stratified,
near-ideal-fluid interior.
On closer inspection of course, one finds oceaninterior regions with diapycnal fluxes above the
background level parameterized by Kϳ 10
95 m
2 s
91
background. One subset involves ocean currents
that directly support turbulent mixing. Marginal
sea overflows and flows through straits are examples here, as perhaps are the equatorial undercurrents (though the turbulent dissipation there is
modulated by diurnally generated high-frequency
internal waves). Getting the mixing in these flows
‘right’ appears key to synthesizing realistic abyssal
stratifications and water properties and sensible
low-latitude circulations. Adoption of critical
Froude- or Richardson-number-based parameterization schemes for mixing in these flows has shown
promise (e.g., Schudlich and Price, 1992; Price and
Baringer, 1994; Price and Yang, 1998). Enhanced
diapycnal flux has also been inferred where the
internal waves are more energetic than the GM
background. Recent parameterizations of mixing
by internal wave instability and breaking exhibit
skill in relating wave field characteristics to dissipation rates. For example, the Henyey et al. (1986)
model with extensions (see Polzin et al., 1995)
yields dissipation estimates within a factor of two
of observations for wave fields ranging to seven
times more energetic than GM. Underlying this
success, however, is a somewhat shaky theoretical
foundation (particularly for wave fields significantly different than GM) that would benefit from
further study. This aside, the relationships between
SECTION 5 FORMATION AND TRANSPORT OF WATER MASSES
354
question the basic Sverdrup vorticity balance.
5.2.7 Discussion
This chapter has summarized recent developments
in the fields of diapycnal mixing in the ocean interior and aspects of dispersion by mesoscale eddies
and smaller scale motions. While these oceanic
stirring and mixing mechanisms operate at quite
disparate horizontal length scales, they are linked
through the scale cascade that ultimately reaches
the dissipative end of the spectrum. Given limitations in computer power, eddy processes must be
parameterized in coarse-resolution ocean and coupled ocean–atmosphere climate models; mixing
processes require parameterization in all models
(apart from direct numerical simulations that are
viable only for very limited spatial domains). Given
the relationships between scales, care must be taken
that parameterizations for one class of motion don’t
adversely impact what occurs on other scales. The
now classic example of this problem was the contamination of diapycnal diffusive fluxes in simulations resulting from a horizontal (as opposed to
isopycnal) stirring parameterization.
A major advance in the field of ocean interior
stirring came about by the realization of Gent
and McWilliams (1990) that oceanic properties
should not be advected in an ocean model by the
Eulerian-mean flow but rather by some appropriate approximation of the Lagrangian velocity.
From this early work it took several years before
the importance of this idea on coarse-resolution
ocean models was realized. The theoretical aspect
of this work has progressed by making connections to the zonally averaged residual-mean theory
of the atmospheric scientists, and the three-dimensional version of this approach, the temporal-residual-mean has been summarized in this chapter. The
realization of the need for this type of extra advection (or equivalently, an extra skew diffusion) has
allowed many modellers to achieve substantial
improvements in ocean simulations including, for
example, the deep ocean temperature field. The
parameterizations used for this skew-diffusion to
date are rather crude and are clearly in need of
refinement.
Great progress has been made over the last 15
years documenting the pattern and intensity of
diapycnal mixing in the ocean. Perhaps the most
significant turbulent mixing occurs in and about
the surface layer where water properties are modified by air–sea exchange as well as by internal
mechanisms. Clearly a first step in building a realistic ocean model is to parameterize accurately surface-layer processes. We direct the reader to Large
and Nurser (Chapter 5.1), Lazier et al. (Chapter
5.5), Price (Chapter 5.3) and Hanawa and Talley
(Chapter 5.4) for detailed discussion. Large (1998)
also presents an excellent discussion of surface
boundary-layer processes and their parameterization. Below the surface-layer environment, a
background level of diapycnal flux is sustained by
the canonical GM internal wave field via wave
breaking. This level is relatively weak, however –
equivalent to a diapycnal diffusivity of about
10
95 m
2 s
91 . Thus to first order, the circulation in
and above the main thermocline might be thought
of as a turbulent surface layer above a stratified,
near-ideal-fluid interior.
On closer inspection of course, one finds oceaninterior regions with diapycnal fluxes above the
background level parameterized by Kϳ 10
95 m
2 s
91
background. One subset involves ocean currents
that directly support turbulent mixing. Marginal
sea overflows and flows through straits are examples here, as perhaps are the equatorial undercurrents (though the turbulent dissipation there is
modulated by diurnally generated high-frequency
internal waves). Getting the mixing in these flows
‘right’ appears key to synthesizing realistic abyssal
stratifications and water properties and sensible
low-latitude circulations. Adoption of critical
Froude- or Richardson-number-based parameterization schemes for mixing in these flows has shown
promise (e.g., Schudlich and Price, 1992; Price and
Baringer, 1994; Price and Yang, 1998). Enhanced
diapycnal flux has also been inferred where the
internal waves are more energetic than the GM
background. Recent parameterizations of mixing
by internal wave instability and breaking exhibit
skill in relating wave field characteristics to dissipation rates. For example, the Henyey et al. (1986)
model with extensions (see Polzin et al., 1995)
yields dissipation estimates within a factor of two
of observations for wave fields ranging to seven
times more energetic than GM. Underlying this
success, however, is a somewhat shaky theoretical
foundation (particularly for wave fields significantly different than GM) that would benefit from
further study. This aside, the relationships between
SECTION 5 FORMATION AND TRANSPORT OF WATER MASSES
354