Adamec (1998) noted that the eddy kinetic
energy in the Kuroshio Extension region was particularly weak in 1994 until early 1995. Simultaneous sea surface temperature observations showed
a weakening of the north–south temperature
gradient across the current during the summer of
1994, implying a weaker front and hence less
energy source for the eddies. This sea surface temperature change was consistent with the eddy heat
flux estimate using both altimetry and sea surface
temperature data. The implication of the study is
that the eddies are playing a convoluted role in the
overall energetics of the Kuroshio current system.
The eddy Reynolds stress underlying all the
aforementioned studies was computed from gridded altimeter data through spatial interpolations.
Because Reynolds stress is a second-order quantity, it is particularly sensitive to interpolation
errors. The direct estimation of the quantity at
cross-over points discussed in Section 3.3.4.2 is
probably a more robust approach. Using GEOSAT
data, Morrow et al. (1994) computed the Reynolds
stress tensor at the cross-over points in the Southern Ocean to diagnose the momentum balance of
the ACC. They found that the zonally averaged
meridional flux of zonal momentum is too small
by at least two orders of magnitude to balance the
momentum input by wind. This conclusion confirms the importance of the stress generated by
bottom pressure against topography (Munk and
Palmén, 1951; Treguier and McWilliams, 1990).
Wilkin and Morrow (1994) applied the Reynolds
stress determined from altimetry to estimating the
rate of kinetic energy transfer between eddy and
mean flow. The results were compared favourably
with the simulation of an ocean general circulation
model.
3.3.4.5 Eddy scales and dynamics
The statistical information provided by altimetry
on the sea surface currents and eddies is unique
and unavailable from any other observational
techniques. It allows us to survey the spatial and
temporal scales with a regular sampling over the
global oceans for years. Stammer (1997b) conducted a comprehensive analysis of frequency and
wavenumber spectra of the eddy variability using
T/P data. His study has revised the conclusions
from previous studies based on less accurate and
much shorter data records. While he found that
the frequency spectrum has different forms in
dynamically different regions (tropics, low- and
high-energy regions), a universal form exists for
the wavenumber spectrum in extratropical regions.
The universal wavenumber spectrum assumes the
following form:
⌫ 0 (k
~
):135k
~ 90.7 ,
0.18-k
~
-1.006,
135k
~ 92.8 ,
1.006-k
~
-2.057, (3.3.6)
501k
~ 94.6 ,
2.057-k
~
-4.54
where k
~ :k/k 0 , and k 0 is the wavenumber for the
dominant local eddy scale. The important role of
the Rossby radius of deformation in determining
the eddy scales in extratropical regions is clearly
demonstrated in the study. Stammer (1997b) also
found that the geographic distribution of eddy
kinetic energy is to a large extent correlated to that
of the vertical shear of horizontal geostrophic
velocity over the upper 1000 m (the thermal wind).
These findings suggest that the baroclinic instability is a major source of eddy energy over most
of the open ocean outside the tropics. However,
Le Traon and Morrow (2000) considered that
the eddy dynamics in the areas of low eddy
energy might be more linear and subject to wind
forcing.
Shown in Fig. 3.3.18 (see Plate 3.3.18, p. 172)
are the geographic distributions of the eddy temporal and spatial scales computed by Stammer
(1998) from the T/P data as follows:
T:C
91
(0)͵
T 0
0
C ()d
(3.3.7)
where T 0 is the first zero-crossing of the autocorrelation function of the sea surface height, C . The
spatial scales range from 180 km in the tropics to
60 km at high latitudes. The temporal scales are
longest in the subtropical gyres and shortest at
high latitudes with a factor of five difference.
Stammer (1998) demonstrated that these eddy
scales derived from T/P were related to those
derived from the theory of baroclinic instability.
These findings led him to carry the analysis
further to address the eddy diffusion and transport processes using the statistical information
from T/P.
Based on dimensional arguments, the eddy diffusion coefficient, , should be proportional to vЈlЈ,
where vЈ and lЈ are the eddy velocity and length
scales, respectively. Since vЈϳ(K E )
1/2
, lЈϳ(K E )
1/2 T bc,
SECTION 3 NEW WAYS OF OBSERVING THE OCEAN
168
energy in the Kuroshio Extension region was particularly weak in 1994 until early 1995. Simultaneous sea surface temperature observations showed
a weakening of the north–south temperature
gradient across the current during the summer of
1994, implying a weaker front and hence less
energy source for the eddies. This sea surface temperature change was consistent with the eddy heat
flux estimate using both altimetry and sea surface
temperature data. The implication of the study is
that the eddies are playing a convoluted role in the
overall energetics of the Kuroshio current system.
The eddy Reynolds stress underlying all the
aforementioned studies was computed from gridded altimeter data through spatial interpolations.
Because Reynolds stress is a second-order quantity, it is particularly sensitive to interpolation
errors. The direct estimation of the quantity at
cross-over points discussed in Section 3.3.4.2 is
probably a more robust approach. Using GEOSAT
data, Morrow et al. (1994) computed the Reynolds
stress tensor at the cross-over points in the Southern Ocean to diagnose the momentum balance of
the ACC. They found that the zonally averaged
meridional flux of zonal momentum is too small
by at least two orders of magnitude to balance the
momentum input by wind. This conclusion confirms the importance of the stress generated by
bottom pressure against topography (Munk and
Palmén, 1951; Treguier and McWilliams, 1990).
Wilkin and Morrow (1994) applied the Reynolds
stress determined from altimetry to estimating the
rate of kinetic energy transfer between eddy and
mean flow. The results were compared favourably
with the simulation of an ocean general circulation
model.
3.3.4.5 Eddy scales and dynamics
The statistical information provided by altimetry
on the sea surface currents and eddies is unique
and unavailable from any other observational
techniques. It allows us to survey the spatial and
temporal scales with a regular sampling over the
global oceans for years. Stammer (1997b) conducted a comprehensive analysis of frequency and
wavenumber spectra of the eddy variability using
T/P data. His study has revised the conclusions
from previous studies based on less accurate and
much shorter data records. While he found that
the frequency spectrum has different forms in
dynamically different regions (tropics, low- and
high-energy regions), a universal form exists for
the wavenumber spectrum in extratropical regions.
The universal wavenumber spectrum assumes the
following form:
⌫ 0 (k
~
):135k
~ 90.7 ,
0.18-k
~
-1.006,
135k
~ 92.8 ,
1.006-k
~
-2.057, (3.3.6)
501k
~ 94.6 ,
2.057-k
~
-4.54
where k
~ :k/k 0 , and k 0 is the wavenumber for the
dominant local eddy scale. The important role of
the Rossby radius of deformation in determining
the eddy scales in extratropical regions is clearly
demonstrated in the study. Stammer (1997b) also
found that the geographic distribution of eddy
kinetic energy is to a large extent correlated to that
of the vertical shear of horizontal geostrophic
velocity over the upper 1000 m (the thermal wind).
These findings suggest that the baroclinic instability is a major source of eddy energy over most
of the open ocean outside the tropics. However,
Le Traon and Morrow (2000) considered that
the eddy dynamics in the areas of low eddy
energy might be more linear and subject to wind
forcing.
Shown in Fig. 3.3.18 (see Plate 3.3.18, p. 172)
are the geographic distributions of the eddy temporal and spatial scales computed by Stammer
(1998) from the T/P data as follows:
T:C
91
(0)͵
T 0
0
C ()d
(3.3.7)
where T 0 is the first zero-crossing of the autocorrelation function of the sea surface height, C . The
spatial scales range from 180 km in the tropics to
60 km at high latitudes. The temporal scales are
longest in the subtropical gyres and shortest at
high latitudes with a factor of five difference.
Stammer (1998) demonstrated that these eddy
scales derived from T/P were related to those
derived from the theory of baroclinic instability.
These findings led him to carry the analysis
further to address the eddy diffusion and transport processes using the statistical information
from T/P.
Based on dimensional arguments, the eddy diffusion coefficient, , should be proportional to vЈlЈ,
where vЈ and lЈ are the eddy velocity and length
scales, respectively. Since vЈϳ(K E )
1/2
, lЈϳ(K E )
1/2 T bc,
SECTION 3 NEW WAYS OF OBSERVING THE OCEAN
168