marginal sea overflows: see below). Knowledge of
mixing in the ocean interior is thus intimately
linked to an understanding of the flow field associated with internal waves. In the 1970s, a spectral
model of the canonical internal wave field was
developed by Garrett and Munk (1972a, commonly referred to as the GM prescription). With
updates (Garrett and Munk, 1975; Cairns and
Williams, 1976; Gregg and Kunze, 1991), this
model remains a valid baseline description of the
climatological wave field. One of the first applications of GM was a statistical prediction for the
amount of mixing supported by shear instability
within the wave field (Garrett and Munk, 1972b).
Pinkel and Anderson (1997a,b) recently revisited
this topic with application to the upper ocean.
Wave–wave interaction models were subsequently
developed to build dynamical understanding of the
observed internal wave spectrum (McComas and
Bretherton, 1977; McComas and Müller, 1981;
Henyey and Pomphrey, 1983; Müller et al., 1986).
These also led to estimates of the turbulent mixing
rate in terms of the rate at which energy in the
internal wave field moves through wavenumber
space towards vertical scales of order 10 m (where
shear and advective instabilities are presumably
active and the energy is ultimately dissipated).
With statements about the mixing efficiency (⌫),
these models yield predictions for the turbulent
buoyancy flux, (⌫ ), associated with a given internal wave field, or if preferred, the diapycnal eddy
diffusivity: K :⌫N
92 . (Here, is the dissipation
rate of turbulent kinetic energy per unit mass.)
Polzin et al. (1995) investigated several of the
wave–wave interaction models and found that
Henyey et al.’s (1986) predictions had greatest
consistency with observed dissipation rates, as was
previously observed by Gregg (1989), although the
robustness of this model derivation can be debated
(in particular, the heavy reliance on interactions
between motions of similar scale that violates basic
model assumption: C. Garrett, personal communication, 1999). Importantly, the Henyey et al. model
suggests a small diffusivity associated with the
canonical GM wave field: K
GM
:710
96 m
2 s
91
,
independent of depth and stratification (as suggested by Figure 5.2.2).
The somewhat greater diapycnal dispersion
of the NATRE tracer as compared with the
temperature- and velocity-microstructure-based estimates appears to be due to an additional mixing
mechanism: double diffusion. Ruddick et al. (1997)
and St Laurent and Schmitt (1999) found evidence
of salt fingering in the relative sizes of the turbulent kinetic energy and thermal dissipation rate
estimates, most notable when the latter investigators conditionally sampled for low density ratio
and high Richardson number. Based on data collected in the month prior to the tracer injection and
using a salt-finger flux model together with an estimate of the turbulent mixing that was occurring, St
Laurent and Schmitt derived an average effective
salt diffusivity of 0.13<0.0110
94 m
2 s
91 at
the isopycnal where the tracer was injected
(Fig. 5.2.3b). Their estimate is consistent with the
diapycnal diffusivity deduced from the tracer dispersion during the first 6 months of Ledwell
et al.’s experiment. (SF 6 should mix in a similar
fashion as salt in this ocean environment.) Additionally, their estimate of the diapycnal buoyancy
flux convergence caused by salt fingers and the
occasional turbulent mixing event was consistent
with Ledwell et al.’s observation that the tracer
sank relative to the density field over the course of
the experiment.
The intensity of double-diffusive mixing is a
strong function of the density ratio. Although the
salt-finger fluxes were relatively weak in the
NATRE region where the density ratio approached
1.6, there are extensive ocean regions characterized by ratios closer to 1.0 (Schmitt, 1981). Here
we might expect average diapycnal fluxes to
exceed those associated with the background GM
internal wave field, with the added complication
that the effective heat and salt diffusivities may
differ substantially. Using laboratory-based flux
laws and measurements in the salt-fingeringfavourable thermohaline staircase southeast of
Barbados in the tropical Atlantic Ocean, Schmitt
(1988) and Kunze (1990) estimated the vertical
diffusivity for salt to be 1–210
94 m
2 s
91 . As the
staircase region encompasses approximately onequarter of the area of the Atlantic between 10 and
15 °N, salt fingering may dominate the diapycnal
salt flux at these latitudes (Schmitt, 1998). Fingering may also be important for removing mixedlayer density-compensated thermohaline variability
soon after subduction (Rudnick and Ferrari, 1999;
Schmitt, 1999). At high latitudes, the characteristic
thermohaline stratification of cold, fresh above
warmer, more saline waters supports the diffusive
layering mode of double diffusion (e.g. Padman
SECTION 5 FORMATION AND TRANSPORT OF WATER MASSES
348
mixing in the ocean interior is thus intimately
linked to an understanding of the flow field associated with internal waves. In the 1970s, a spectral
model of the canonical internal wave field was
developed by Garrett and Munk (1972a, commonly referred to as the GM prescription). With
updates (Garrett and Munk, 1975; Cairns and
Williams, 1976; Gregg and Kunze, 1991), this
model remains a valid baseline description of the
climatological wave field. One of the first applications of GM was a statistical prediction for the
amount of mixing supported by shear instability
within the wave field (Garrett and Munk, 1972b).
Pinkel and Anderson (1997a,b) recently revisited
this topic with application to the upper ocean.
Wave–wave interaction models were subsequently
developed to build dynamical understanding of the
observed internal wave spectrum (McComas and
Bretherton, 1977; McComas and Müller, 1981;
Henyey and Pomphrey, 1983; Müller et al., 1986).
These also led to estimates of the turbulent mixing
rate in terms of the rate at which energy in the
internal wave field moves through wavenumber
space towards vertical scales of order 10 m (where
shear and advective instabilities are presumably
active and the energy is ultimately dissipated).
With statements about the mixing efficiency (⌫),
these models yield predictions for the turbulent
buoyancy flux, (⌫ ), associated with a given internal wave field, or if preferred, the diapycnal eddy
diffusivity: K :⌫N
92 . (Here, is the dissipation
rate of turbulent kinetic energy per unit mass.)
Polzin et al. (1995) investigated several of the
wave–wave interaction models and found that
Henyey et al.’s (1986) predictions had greatest
consistency with observed dissipation rates, as was
previously observed by Gregg (1989), although the
robustness of this model derivation can be debated
(in particular, the heavy reliance on interactions
between motions of similar scale that violates basic
model assumption: C. Garrett, personal communication, 1999). Importantly, the Henyey et al. model
suggests a small diffusivity associated with the
canonical GM wave field: K
GM
:710
96 m
2 s
91
,
independent of depth and stratification (as suggested by Figure 5.2.2).
The somewhat greater diapycnal dispersion
of the NATRE tracer as compared with the
temperature- and velocity-microstructure-based estimates appears to be due to an additional mixing
mechanism: double diffusion. Ruddick et al. (1997)
and St Laurent and Schmitt (1999) found evidence
of salt fingering in the relative sizes of the turbulent kinetic energy and thermal dissipation rate
estimates, most notable when the latter investigators conditionally sampled for low density ratio
and high Richardson number. Based on data collected in the month prior to the tracer injection and
using a salt-finger flux model together with an estimate of the turbulent mixing that was occurring, St
Laurent and Schmitt derived an average effective
salt diffusivity of 0.13<0.0110
94 m
2 s
91 at
the isopycnal where the tracer was injected
(Fig. 5.2.3b). Their estimate is consistent with the
diapycnal diffusivity deduced from the tracer dispersion during the first 6 months of Ledwell
et al.’s experiment. (SF 6 should mix in a similar
fashion as salt in this ocean environment.) Additionally, their estimate of the diapycnal buoyancy
flux convergence caused by salt fingers and the
occasional turbulent mixing event was consistent
with Ledwell et al.’s observation that the tracer
sank relative to the density field over the course of
the experiment.
The intensity of double-diffusive mixing is a
strong function of the density ratio. Although the
salt-finger fluxes were relatively weak in the
NATRE region where the density ratio approached
1.6, there are extensive ocean regions characterized by ratios closer to 1.0 (Schmitt, 1981). Here
we might expect average diapycnal fluxes to
exceed those associated with the background GM
internal wave field, with the added complication
that the effective heat and salt diffusivities may
differ substantially. Using laboratory-based flux
laws and measurements in the salt-fingeringfavourable thermohaline staircase southeast of
Barbados in the tropical Atlantic Ocean, Schmitt
(1988) and Kunze (1990) estimated the vertical
diffusivity for salt to be 1–210
94 m
2 s
91 . As the
staircase region encompasses approximately onequarter of the area of the Atlantic between 10 and
15 °N, salt fingering may dominate the diapycnal
salt flux at these latitudes (Schmitt, 1998). Fingering may also be important for removing mixedlayer density-compensated thermohaline variability
soon after subduction (Rudnick and Ferrari, 1999;
Schmitt, 1999). At high latitudes, the characteristic
thermohaline stratification of cold, fresh above
warmer, more saline waters supports the diffusive
layering mode of double diffusion (e.g. Padman
SECTION 5 FORMATION AND TRANSPORT OF WATER MASSES
348