and Dillon, 1987; Muench et al., 1990). Microstructure measurements (e.g. Larson and Gregg, 1983;
Osborn, 1988; Padman and Dillon, 1987) have
lent credence to laboratory-derived laws for fluxes
through the diffusive interfaces characteristic of
this instability. Kelley (1984, 1990) in turn derived
expressions for the effective diapycnal heat and
salt diffusivities by this double-diffusive process
that approach 10
94 m
2 s
91 as the density ratio
approaches 1.0. Thus far unclear are the potential
interactions between diffusive layers, internal
waves, shear and turbulence.
More intense mixing also appears to occur in
ocean regions characterized by an energized internal wave field (more energetic than the GM background). The Henyey et al. (1986) model suggests
that the energy flux through the wave field (and
thus the dissipation rate) increases quadratically
with the fine-scale shear spectral level of the internal waves (equivalently as the fourth power of the
fine-scale velocity gradient in the spatial domain;
Gregg, 1989). A weak dependence on the frequency content of the wave field is also suggested
(Henyey, 1991; Polzin et al., 1995). Thus, to identify areas of enhanced mixing in the ocean interior
one might equivalently search for regions of energetic internal waves. These might include sites of
internal wave generation, and/or distortion by, for
example, bottom reflection or the effects of largerscale flows. More on these below.
5.2.5.2 Role of ocean currents
In addition to the shears associated with the
ubiquitous internal waves, there are a handful of
open-ocean current systems that develop internal
instabilities leading to turbulent mixing. Most
notable in this regard are the Equatorial Undercurrent–South Equatorial Current (EUC/SEC) systems
of the tropical Pacific and Atlantic Oceans. Frictional damping and diapycnal heat and buoyancy
fluxes are believed to be of first order importance
in the momentum budget of these currents and the
heat budget of the equatorial waters, respectively.
A series of cruises to the equatorial Pacific conducted in the 1980s examined the turbulence in
this low-latitude environment (e.g. Gregg et al.,
1985; Moum et al., 1989; Lien et al., 1995). These
studies report intense turbulent dissipation above
the undercurrent core, diurnally modulated with
the cycle of air–sea buoyancy exchange. The causal
agent responsible for the diurnal signal in mixing
below the surface layer appears to be highfrequency internal waves that radiate down from
the surface layer (see Wang et al., 1998; Wang
and Muller, 1999). On longer time scales, these
research teams found mixing in the EUC varies
with the strength of the wind stress and the ambient
shear between the SEC and EUC. Averaging over
the diurnal and longer-period fluctuations, mean
diapycnal diffusivities in excess of 10
93 m
2 s
91
were obtained. Mean eddy viscosities also estimated in the EUC/SEC shear flow were comparably large.
At greater depths, remarkable arrays of zonal
jets about the equator have been observed in all
three oceans (Luyten and Swallow, 1976; Firing,
1987, 1988; Ponte et al., 1990). These flows have
been interpreted as long-period, high-mode, equatorially trapped planetary waves (see Muench
et al., 1994). Superimposed on these ‘equatorial
deep jets’ is a spectrum of Kelvin, Rossby, mixed
Rossby–gravity and inertial gravity waves down to
periods of a few days, melding with an internal
wave field of approximate GM shape but enhanced
energy (Eriksen, 1980, 1981; Blumenthal, 1987;
Gregg et al., 1995). Of relevance to our discussion,
Pacific and Atlantic microstructure data from the
equator appears to be modulated by the vertical
shears associated with the equatorial deep jets
(Gregg et al., 1995; K. Polzin, personal communication, 1999). But the long jet time scales imply
that the turbulence does not erode them. These
findings motivated Muench and Kunze (1999) to
investigate wave-mean flow interaction wherein
the jets might be sustained by transfer of energy
from the internal wave field at critical layers.
Their model predicts peak dissipation rates on the
jet flanks of comparable magnitude to what is
observed and significant momentum flux divergences of the sense to sustain jets (though the
study begs the question of the jets’ origin). The
peak dissipations at the jet flanks are not excessively large however, corresponding to diapycnal
diffusivities around 10
94 m
2 s
91
, with values about
the jet cores typically an order of magnitude
smaller. The lower-thermocline tropical waters are
thus characterized by somewhat enhanced diapycnal exchange as compared with mid-latitudes,
largely due to the equatorial deep jets. (On its
own, the equatorial internal wave field, though
more energetic than GM, does not seem to equate
with enhanced mixing, leading Gregg et al. (1995)
5.2 Mixing and Stirring in the Ocean Interior
349
Toole and McDougall
Osborn, 1988; Padman and Dillon, 1987) have
lent credence to laboratory-derived laws for fluxes
through the diffusive interfaces characteristic of
this instability. Kelley (1984, 1990) in turn derived
expressions for the effective diapycnal heat and
salt diffusivities by this double-diffusive process
that approach 10
94 m
2 s
91 as the density ratio
approaches 1.0. Thus far unclear are the potential
interactions between diffusive layers, internal
waves, shear and turbulence.
More intense mixing also appears to occur in
ocean regions characterized by an energized internal wave field (more energetic than the GM background). The Henyey et al. (1986) model suggests
that the energy flux through the wave field (and
thus the dissipation rate) increases quadratically
with the fine-scale shear spectral level of the internal waves (equivalently as the fourth power of the
fine-scale velocity gradient in the spatial domain;
Gregg, 1989). A weak dependence on the frequency content of the wave field is also suggested
(Henyey, 1991; Polzin et al., 1995). Thus, to identify areas of enhanced mixing in the ocean interior
one might equivalently search for regions of energetic internal waves. These might include sites of
internal wave generation, and/or distortion by, for
example, bottom reflection or the effects of largerscale flows. More on these below.
5.2.5.2 Role of ocean currents
In addition to the shears associated with the
ubiquitous internal waves, there are a handful of
open-ocean current systems that develop internal
instabilities leading to turbulent mixing. Most
notable in this regard are the Equatorial Undercurrent–South Equatorial Current (EUC/SEC) systems
of the tropical Pacific and Atlantic Oceans. Frictional damping and diapycnal heat and buoyancy
fluxes are believed to be of first order importance
in the momentum budget of these currents and the
heat budget of the equatorial waters, respectively.
A series of cruises to the equatorial Pacific conducted in the 1980s examined the turbulence in
this low-latitude environment (e.g. Gregg et al.,
1985; Moum et al., 1989; Lien et al., 1995). These
studies report intense turbulent dissipation above
the undercurrent core, diurnally modulated with
the cycle of air–sea buoyancy exchange. The causal
agent responsible for the diurnal signal in mixing
below the surface layer appears to be highfrequency internal waves that radiate down from
the surface layer (see Wang et al., 1998; Wang
and Muller, 1999). On longer time scales, these
research teams found mixing in the EUC varies
with the strength of the wind stress and the ambient
shear between the SEC and EUC. Averaging over
the diurnal and longer-period fluctuations, mean
diapycnal diffusivities in excess of 10
93 m
2 s
91
were obtained. Mean eddy viscosities also estimated in the EUC/SEC shear flow were comparably large.
At greater depths, remarkable arrays of zonal
jets about the equator have been observed in all
three oceans (Luyten and Swallow, 1976; Firing,
1987, 1988; Ponte et al., 1990). These flows have
been interpreted as long-period, high-mode, equatorially trapped planetary waves (see Muench
et al., 1994). Superimposed on these ‘equatorial
deep jets’ is a spectrum of Kelvin, Rossby, mixed
Rossby–gravity and inertial gravity waves down to
periods of a few days, melding with an internal
wave field of approximate GM shape but enhanced
energy (Eriksen, 1980, 1981; Blumenthal, 1987;
Gregg et al., 1995). Of relevance to our discussion,
Pacific and Atlantic microstructure data from the
equator appears to be modulated by the vertical
shears associated with the equatorial deep jets
(Gregg et al., 1995; K. Polzin, personal communication, 1999). But the long jet time scales imply
that the turbulence does not erode them. These
findings motivated Muench and Kunze (1999) to
investigate wave-mean flow interaction wherein
the jets might be sustained by transfer of energy
from the internal wave field at critical layers.
Their model predicts peak dissipation rates on the
jet flanks of comparable magnitude to what is
observed and significant momentum flux divergences of the sense to sustain jets (though the
study begs the question of the jets’ origin). The
peak dissipations at the jet flanks are not excessively large however, corresponding to diapycnal
diffusivities around 10
94 m
2 s
91
, with values about
the jet cores typically an order of magnitude
smaller. The lower-thermocline tropical waters are
thus characterized by somewhat enhanced diapycnal exchange as compared with mid-latitudes,
largely due to the equatorial deep jets. (On its
own, the equatorial internal wave field, though
more energetic than GM, does not seem to equate
with enhanced mixing, leading Gregg et al. (1995)
5.2 Mixing and Stirring in the Ocean Interior
349
Toole and McDougall