energy and scalar variance cascades at scales of
order 100 km. Eddies of these diameters, principally formed by baroclinic instability at large-scale
oceanic fronts, act to stir fluid parcels in a way that
is highly constrained by the stratified nature of the
fluid. Theoretical understanding of this issue has
progressed since the pioneering paper of Gent and
McWilliams (1990). One promising approach for
understanding how the effects of mesoscale eddies
should be parameterized is the Temporal-ResidualMean (TRM) formalism (McDougall and McIntosh,
1996, 2000), which provides the link between the
different views that are apparent from averaging
these turbulent flow fields in height coordinates
and in density coordinates. The TRM framework
reduces the flux parameterization problem from
three dimensions to two and shows how the divergent part of the density flux is skew-symmetric so
that the total advection velocity can be adiabatic.
These ideas are reviewed in Section 5.2.3.
Moving towards smaller scales, shear dispersion
involving internal waves (e.g. Young et al., 1982)
and possibly vortical mode motions (Polzin et al.,
2000b) appear active at horizontal scales of 1 to a
few km. And at thermohaline fronts, intrusions
with similar lateral scales supporting (and possibly
driven by) double diffusive mixing are commonly
observed. Section 5.2.4 gives a brief overview of
research on these motions.
Diapycnal mixing is a broad topic; we will
restrict attention here to the mechanisms and intensity of mixing below the surface boundary layer.
The reader is referred to Large and Nurser (Chapter 5.1), Price (Chapter 5.3), Hanawa and Talley
(Chapter 5.4) and Lazier et al. (Chapter 5.5) for a
discussion of the very significant and important
mixing and resultant water mass modification that
occurs in and about the ocean’s surface layer.
Our presentation on diapycnal mixing is organized
by depth: thermocline processes are discussed in
Section 5.2.5 and abyssal processes in 5.2.6.
Mechanistically, two classes of diapycnal mixing
have been defined: turbulent and double diffusive.
In the former, mechanical energy is expended as 1to-100; cm-scale eddies strain scalar variance to
small scales where it is destroyed by molecular diffusion (see recent reviews by Gregg, 1987, 1998;
Caldwell and Moum, 1995; and Gargett, 1989).
Energetic turbulence mixes heat, salt and other
scalar fields at similar rates. In the ocean interior,
a principal energy source for the turbulence is the
internal wave field, and so our presentation contains extensive discussion of waves. Double diffusive processes (salt fingering and diffusive layering)
become relevant when the vertical gradients of
temperature or salinity have the same sign, and
thus contribute oppositely to the vertical density
gradient (see review by Schmitt, 1994). Due to the
dissimilar molecular diffusivities of heat and salt,
convective motions develop and release the potential energy associated with the unstably-stratified
component. The associated vertical buoyancy
flux is up-gradient. As discussed below, the relative importance of turbulent and double-diffusive
mixing varies within the oceans depending on
the background stratification and internal wave
energy level. Though we don’t pursue the idea further, it should be remembered that heat and salt
fluxes associated with weak turbulence (that does
not completely homogenize water properties) may
also result in up-gradient buoyancy fluxes, again a
consequence of the dissimilar molecular diffusivities for temperature and salinity (Gargett, 1988;
Merryfield et al., 1998).
5.2.2 Background
Basic energy arguments applied to an idealized,
steady ocean suggest a direct connection between
the large-scale flows and mixing. To overcome
friction in a steady ocean circulation, there must be
an input of mechanical energy over each closed
streamline. This concept led Sandström (1916) to
postulate that a closed, steady, buoyancy-driven
circulation can be maintained only if the heating
source is positioned at a lower geopotential than the
cooling source (Huang, 1999). Sandström carried
out simple laboratory experiments that appeared to
confirm this idea, but application to the real ocean
circulation is problematic. Sea level in the tropics
where the oceans are heated is some 1 m higher
(relative to a geopotential surface) than it is in the
polar oceans where cooling occurs. Why then does
a substantial mean thermohaline circulation exist
in the ocean? Jeffreys (1925) proposed that mixing
is capable of redistributing density, leading to a
pressure field of the sense to sustain an overturning circulation in the face of frictional damping.
Huang’s (1999) closed-tube model for the thermohaline circulation, which demonstrates how the
flow is controlled principally by diffusion of density when heating occurs at a higher potential than
SECTION 5 FORMATION AND TRANSPORT OF WATER MASSES
338
order 100 km. Eddies of these diameters, principally formed by baroclinic instability at large-scale
oceanic fronts, act to stir fluid parcels in a way that
is highly constrained by the stratified nature of the
fluid. Theoretical understanding of this issue has
progressed since the pioneering paper of Gent and
McWilliams (1990). One promising approach for
understanding how the effects of mesoscale eddies
should be parameterized is the Temporal-ResidualMean (TRM) formalism (McDougall and McIntosh,
1996, 2000), which provides the link between the
different views that are apparent from averaging
these turbulent flow fields in height coordinates
and in density coordinates. The TRM framework
reduces the flux parameterization problem from
three dimensions to two and shows how the divergent part of the density flux is skew-symmetric so
that the total advection velocity can be adiabatic.
These ideas are reviewed in Section 5.2.3.
Moving towards smaller scales, shear dispersion
involving internal waves (e.g. Young et al., 1982)
and possibly vortical mode motions (Polzin et al.,
2000b) appear active at horizontal scales of 1 to a
few km. And at thermohaline fronts, intrusions
with similar lateral scales supporting (and possibly
driven by) double diffusive mixing are commonly
observed. Section 5.2.4 gives a brief overview of
research on these motions.
Diapycnal mixing is a broad topic; we will
restrict attention here to the mechanisms and intensity of mixing below the surface boundary layer.
The reader is referred to Large and Nurser (Chapter 5.1), Price (Chapter 5.3), Hanawa and Talley
(Chapter 5.4) and Lazier et al. (Chapter 5.5) for a
discussion of the very significant and important
mixing and resultant water mass modification that
occurs in and about the ocean’s surface layer.
Our presentation on diapycnal mixing is organized
by depth: thermocline processes are discussed in
Section 5.2.5 and abyssal processes in 5.2.6.
Mechanistically, two classes of diapycnal mixing
have been defined: turbulent and double diffusive.
In the former, mechanical energy is expended as 1to-100; cm-scale eddies strain scalar variance to
small scales where it is destroyed by molecular diffusion (see recent reviews by Gregg, 1987, 1998;
Caldwell and Moum, 1995; and Gargett, 1989).
Energetic turbulence mixes heat, salt and other
scalar fields at similar rates. In the ocean interior,
a principal energy source for the turbulence is the
internal wave field, and so our presentation contains extensive discussion of waves. Double diffusive processes (salt fingering and diffusive layering)
become relevant when the vertical gradients of
temperature or salinity have the same sign, and
thus contribute oppositely to the vertical density
gradient (see review by Schmitt, 1994). Due to the
dissimilar molecular diffusivities of heat and salt,
convective motions develop and release the potential energy associated with the unstably-stratified
component. The associated vertical buoyancy
flux is up-gradient. As discussed below, the relative importance of turbulent and double-diffusive
mixing varies within the oceans depending on
the background stratification and internal wave
energy level. Though we don’t pursue the idea further, it should be remembered that heat and salt
fluxes associated with weak turbulence (that does
not completely homogenize water properties) may
also result in up-gradient buoyancy fluxes, again a
consequence of the dissimilar molecular diffusivities for temperature and salinity (Gargett, 1988;
Merryfield et al., 1998).
5.2.2 Background
Basic energy arguments applied to an idealized,
steady ocean suggest a direct connection between
the large-scale flows and mixing. To overcome
friction in a steady ocean circulation, there must be
an input of mechanical energy over each closed
streamline. This concept led Sandström (1916) to
postulate that a closed, steady, buoyancy-driven
circulation can be maintained only if the heating
source is positioned at a lower geopotential than the
cooling source (Huang, 1999). Sandström carried
out simple laboratory experiments that appeared to
confirm this idea, but application to the real ocean
circulation is problematic. Sea level in the tropics
where the oceans are heated is some 1 m higher
(relative to a geopotential surface) than it is in the
polar oceans where cooling occurs. Why then does
a substantial mean thermohaline circulation exist
in the ocean? Jeffreys (1925) proposed that mixing
is capable of redistributing density, leading to a
pressure field of the sense to sustain an overturning circulation in the face of frictional damping.
Huang’s (1999) closed-tube model for the thermohaline circulation, which demonstrates how the
flow is controlled principally by diffusion of density when heating occurs at a higher potential than
SECTION 5 FORMATION AND TRANSPORT OF WATER MASSES
338