THE NEAR-SURFACE LAYER OF THE OCEAN
d) In order to estimate H, the equation,
2
2 ( )
u
u t
V
V H
(3.23)
is solved by an iteration method, where
2 ( )
ut
V H is determined using the
discrete version of integral (3.22). The iteration process starts from a very
small initial dissipation rate
12
10
2
.
1
u
H
W kg
-1 and finishes at the value
of H that satisfies Eq. (3.23) with 1% accuracy.
e) The dissipation rate estimates obtained from 0.1-s segments are then
averaged within overlapping 10 cm depth bins over the 10-min record
segments. In order to account for the intermittent nature of turbulence, the
mean dissipation rate and the confidence intervals are calculated using
formulas of Baker and Gibson (1987). These formulae assume a lognormal
distribution of the turbulence dissipation rate.
Note that the fluctuation of the mean flow speed during a 0.1-s interval is
much smaller than for a segment including the full pitching period. The
reduction of the mean flow fluctuation facilitates the use of Taylor’s
hypothesis of frozen turbulence under conditions of high seas and strong
pitching of the ship. Figure 3-11a, b demonstrates two examples of the
averaged vertical profile of dissipation rate H obtained with this algorithm.
The example shown in Figure 3-11b was taken under high wind and wave
conditions. The confidence intervals in Figure 3-11b are bigger than in
Figure 3-11a in part because a larger percentage of points were removed due
to the probe surfacing or entering bubble clouds.
For further analysis, we use the dissipation rates calculated from short
segments according to the method described above. The dissipation rates
calculated for a month long COARE cruise are plotted in Figure 3-12 as a
function of wind speed. The cases when the ship speed was less than 2 m s
-1
or the ship course or speed varied more than 10% are excluded from these
statistics. Note that the data in Figure 3-12 are not sorted by depth.
The equivalent electronics noise level of the velocity sensor,
10
1.8 10
n
H
u
W kg
-1 , shown in Figure 3-12 by a horizontal line is obtained
by processing the laboratory noise record via steps a) through d). According
to Figure 3-12, this noise level is much less than the dissipation rate that is
typically observed in the near-surface layer of the ocean. No noise correction
is therefore required.
To elucidate possible influence by surface waves on the dissipation rate
estimation, we have calculated the wave kinetic energy in the wavenumber
band that is used here for dissipation rate estimates. The theoretical variance
is calculated using the Pierson and Moskowitz (1964) spectrum (multiplied
by
2
Z , where
2 f
Z S ), surface wave dispersion relationship
g
k
/
2
Z
,
170
d) In order to estimate H, the equation,
2
2 ( )
u
u t
V
V H
(3.23)
is solved by an iteration method, where
2 ( )
ut
V H is determined using the
discrete version of integral (3.22). The iteration process starts from a very
small initial dissipation rate
12
10
2
.
1
u
H
W kg
-1 and finishes at the value
of H that satisfies Eq. (3.23) with 1% accuracy.
e) The dissipation rate estimates obtained from 0.1-s segments are then
averaged within overlapping 10 cm depth bins over the 10-min record
segments. In order to account for the intermittent nature of turbulence, the
mean dissipation rate and the confidence intervals are calculated using
formulas of Baker and Gibson (1987). These formulae assume a lognormal
distribution of the turbulence dissipation rate.
Note that the fluctuation of the mean flow speed during a 0.1-s interval is
much smaller than for a segment including the full pitching period. The
reduction of the mean flow fluctuation facilitates the use of Taylor’s
hypothesis of frozen turbulence under conditions of high seas and strong
pitching of the ship. Figure 3-11a, b demonstrates two examples of the
averaged vertical profile of dissipation rate H obtained with this algorithm.
The example shown in Figure 3-11b was taken under high wind and wave
conditions. The confidence intervals in Figure 3-11b are bigger than in
Figure 3-11a in part because a larger percentage of points were removed due
to the probe surfacing or entering bubble clouds.
For further analysis, we use the dissipation rates calculated from short
segments according to the method described above. The dissipation rates
calculated for a month long COARE cruise are plotted in Figure 3-12 as a
function of wind speed. The cases when the ship speed was less than 2 m s
-1
or the ship course or speed varied more than 10% are excluded from these
statistics. Note that the data in Figure 3-12 are not sorted by depth.
The equivalent electronics noise level of the velocity sensor,
10
1.8 10
n
H
u
W kg
-1 , shown in Figure 3-12 by a horizontal line is obtained
by processing the laboratory noise record via steps a) through d). According
to Figure 3-12, this noise level is much less than the dissipation rate that is
typically observed in the near-surface layer of the ocean. No noise correction
is therefore required.
To elucidate possible influence by surface waves on the dissipation rate
estimation, we have calculated the wave kinetic energy in the wavenumber
band that is used here for dissipation rate estimates. The theoretical variance
is calculated using the Pierson and Moskowitz (1964) spectrum (multiplied
by
2
Z , where
2 f
Z S ), surface wave dispersion relationship
g
k
/
2
Z
,
170