Chapter 5. SPATIALLY-COHERENT STRUCTURES
as the wind speed, heat fluxes, presence of rain, diurnal warming and so on.
An interface may be clearly seen, for example, in the salinity record but fall
below the detection level in the temperature and/or density record(s). Some
interfaces are therefore found simultaneously in two or three of these
variables while others appear clearly in only one variable. We will hereafter
refer to the sharp frontal interfaces found in density, salinity, and
temperature records as the density, salinity, and temperature interfaces
respectively.
In Figure 5-30, statistical properties of the density, salinity, and
temperature interfaces obtained from bow records during four TOGA
COARE cruises of the R/V Moana Wave are summarized in the form of
histograms. The first, second, and third rows in Figure 5-30 correspond to
the density, salinity, and temperature interfaces. The total number of sharp
fronts found in density, N U = 326, in salinity, N S = 751, and in temperature,
N T = 412. The statistics presented in Figure 5-30 include the cross-front
difference of density, salinity, and temperature (left column) and the density
ratio R for the density, salinity, and temperature interfaces expressed in
terms of the Turner angle (the right column).
In the oceanographic literature,
)
arctan(R
Tu
is known as the Turner
angle (Ruddick and Turner, 1979), where R is defined as in (5.24). The
Turner angle is positive when temperature and salinity tend to compensate
each other in density. For compensated fronts R = 1 and Tu = S/4. For fronts
with no temperature difference ('T = 0), R = 0 and Tu = 0, while for fronts
with no salinity difference (
0
S
'
), R f and Tu = S/2
As emphasized by Ferrari and Rudnick (2000), the advantage of using
the Turner angle instead of the density ratio number is that the infinite scale
of R is replaced by a finite one running from –S/2 to S/2. Also, the
temperature dominated regions (
f
R
1
) and salinity-dominated regions
(
1
0
R
) occupy the same space on the Tu scale, which in particular
means that the ensemble averaging over Tu may be more accurate than that
over R.
According to Figure 5-30, the average density ratio number defined as
= tan () is relatively small for density interfaces ( = 0.2), is
larger for salinity interfaces ( = 0.5), and approaches unity for
temperature interfaces ( = 0.9). (The operator <> here denotes ensemble
averaging). The interpretation is that all density interfaces and a part of the
salinity interfaces are not compensated interfaces, while the majority of the
temperature interfaces appear to be compensated interfaces.
Figure 5-31 shows the dependence of sharp frontal interfaces on the
wind-to-ship angle, T, (the left column) and on the wind speed, a
U (the right
column) separately for the density, salinity, and temperature interfaces (the
first, second, and third rows respectively). Salinity and temperature
329
as the wind speed, heat fluxes, presence of rain, diurnal warming and so on.
An interface may be clearly seen, for example, in the salinity record but fall
below the detection level in the temperature and/or density record(s). Some
interfaces are therefore found simultaneously in two or three of these
variables while others appear clearly in only one variable. We will hereafter
refer to the sharp frontal interfaces found in density, salinity, and
temperature records as the density, salinity, and temperature interfaces
respectively.
In Figure 5-30, statistical properties of the density, salinity, and
temperature interfaces obtained from bow records during four TOGA
COARE cruises of the R/V Moana Wave are summarized in the form of
histograms. The first, second, and third rows in Figure 5-30 correspond to
the density, salinity, and temperature interfaces. The total number of sharp
fronts found in density, N U = 326, in salinity, N S = 751, and in temperature,
N T = 412. The statistics presented in Figure 5-30 include the cross-front
difference of density, salinity, and temperature (left column) and the density
ratio R for the density, salinity, and temperature interfaces expressed in
terms of the Turner angle (the right column).
In the oceanographic literature,
)
arctan(R
Tu
is known as the Turner
angle (Ruddick and Turner, 1979), where R is defined as in (5.24). The
Turner angle is positive when temperature and salinity tend to compensate
each other in density. For compensated fronts R = 1 and Tu = S/4. For fronts
with no temperature difference ('T = 0), R = 0 and Tu = 0, while for fronts
with no salinity difference (
0
S
'
), R f and Tu = S/2
As emphasized by Ferrari and Rudnick (2000), the advantage of using
the Turner angle instead of the density ratio number is that the infinite scale
of R is replaced by a finite one running from –S/2 to S/2. Also, the
temperature dominated regions (
f
R
1
) and salinity-dominated regions
(
1
0
R
) occupy the same space on the Tu scale, which in particular
means that the ensemble averaging over Tu may be more accurate than that
over R.
According to Figure 5-30, the average density ratio number defined as
larger for salinity interfaces (
temperature interfaces (
averaging). The interpretation is that all density interfaces and a part of the
salinity interfaces are not compensated interfaces, while the majority of the
temperature interfaces appear to be compensated interfaces.
Figure 5-31 shows the dependence of sharp frontal interfaces on the
wind-to-ship angle, T, (the left column) and on the wind speed, a
U (the right
column) separately for the density, salinity, and temperature interfaces (the
first, second, and third rows respectively). Salinity and temperature
329