into reordered stable profiles and displacements. The 3D appearance (Fig. 2a) so well
captured by 17th century clouds and landscape painters is completely absent in the flat
2D image (Fig. 2b) from which the turbulent displacements (Fig. 2c) are removed.
The raw turbulence parameter estimates for every sensor and every (1 s) profile are
averaged over depth, hereafter indicated by <…>, and time, indicated by […].
Thorpe [9, 36] proposed to average over individual turbulent overturns, but as
smaller overturns exist in larger ones that even may exceed the range of moored
sensors (cf., Fig. 2), it was decided to average over the full vertical range of
T-sensors when it is equal to or less than 100 m [32]. Commonly, about 5% of the
T-sensors show electronic or calibration problems and their data are linearly
interpolated between neighboring sensors. This affects the turbulence parameter
estimates by less than 10%, well within the standard error in the estimates due to the
procedure.
Observations
In the examples given in this section, areas are avoided where the temperaturedensity relationship is not tight. Although the locally established apparent thermal
expansion coefficients vary considerably for different regions between 0.05 and
0.3 kg m
−3 °C
−1 and their ‘tightness’ between 1 and 10% of the mean value, the
standard errors in turbulence parameters are always about a factor of two. This is
equivalent to errors in microstructure profiler data after considerable and careful
post-processing (Oakey 1991, pers. comm.). The factor of two error is confirmed by
comparing moored T-sensor overturn estimates above a seamount slope with nearby
shipborne lowered ADCP/CTD data estimates using Gregg [52]’s shear-scaling [32].
In the Open Ocean Far Away from Topography
The stratified open ocean interior is permanently in motion, not merely by surface
waves but especially also by internal waves with typical amplitudes of several tens
of meters (e.g., [53–55]). The weakly turbulent motions are smooth, albeit not
perfectly sinusoidal in shape, and have relatively large vertical coherent scales with
near-zero phase difference over the range of thermistors (‘local vertical mode-1’), at
both tidal and near-buoyancy frequencies. Amplitudes vary continuously for
motions within any particular finite frequency band; evidence of intermittency. Due
to straining, the thickness of strongly stratified layers drops below 1 m, while
weakly stratified layers can exceed tens of meters. In the Canary Basin [55], the
mean Ozmidov scale ≈ 0.4 m (obtained from high-resolution shipborne
CTD-data). The mean interior turbulence parameters are estimated as [<ε>] ≈ 10
−9
m
2 s
−3 and [] ≈ 2 × 10
−5 m
2 s
−1 , which is equivalent to values estimated for
other, upper 2000 m, open ocean regions [52] and for, e.g., the summer stratified
High-Resolution Observations of Internal Wave Turbulence …
135
captured by 17th century clouds and landscape painters is completely absent in the flat
2D image (Fig. 2b) from which the turbulent displacements (Fig. 2c) are removed.
The raw turbulence parameter estimates for every sensor and every (1 s) profile are
averaged over depth, hereafter indicated by <…>, and time, indicated by […].
Thorpe [9, 36] proposed to average over individual turbulent overturns, but as
smaller overturns exist in larger ones that even may exceed the range of moored
sensors (cf., Fig. 2), it was decided to average over the full vertical range of
T-sensors when it is equal to or less than 100 m [32]. Commonly, about 5% of the
T-sensors show electronic or calibration problems and their data are linearly
interpolated between neighboring sensors. This affects the turbulence parameter
estimates by less than 10%, well within the standard error in the estimates due to the
procedure.
Observations
In the examples given in this section, areas are avoided where the temperaturedensity relationship is not tight. Although the locally established apparent thermal
expansion coefficients vary considerably for different regions between 0.05 and
0.3 kg m
−3 °C
−1 and their ‘tightness’ between 1 and 10% of the mean value, the
standard errors in turbulence parameters are always about a factor of two. This is
equivalent to errors in microstructure profiler data after considerable and careful
post-processing (Oakey 1991, pers. comm.). The factor of two error is confirmed by
comparing moored T-sensor overturn estimates above a seamount slope with nearby
shipborne lowered ADCP/CTD data estimates using Gregg [52]’s shear-scaling [32].
In the Open Ocean Far Away from Topography
The stratified open ocean interior is permanently in motion, not merely by surface
waves but especially also by internal waves with typical amplitudes of several tens
of meters (e.g., [53–55]). The weakly turbulent motions are smooth, albeit not
perfectly sinusoidal in shape, and have relatively large vertical coherent scales with
near-zero phase difference over the range of thermistors (‘local vertical mode-1’), at
both tidal and near-buoyancy frequencies. Amplitudes vary continuously for
motions within any particular finite frequency band; evidence of intermittency. Due
to straining, the thickness of strongly stratified layers drops below 1 m, while
weakly stratified layers can exceed tens of meters. In the Canary Basin [55], the
mean Ozmidov scale
CTD-data). The mean interior turbulence parameters are estimated as [<ε>] ≈ 10
−9
m
2 s
−3 and [
−5 m
2 s
−1 , which is equivalent to values estimated for
other, upper 2000 m, open ocean regions [52] and for, e.g., the summer stratified
High-Resolution Observations of Internal Wave Turbulence …
135