A method has yet to be found to properly parameterize such wave-breaking
motions, in the context of the large-scale ocean circulation. One of the unknowns is to
relate to the proper scaling of topography. As the term ‘rough topography’ [9, 31] is
somewhat imprecise in quantification, it would be better to consider the slope angle, in
relation with the internal wave angles for given stratification, and the length scales of
the slope-determination in association with the internal wave length scales. Apart
from such modeling constraints, an encouraging recent tracer-release experiment near
the Mid-Atlantic Ridge integrated over yearlong periods showed upslope motions that
can only be balanced by diffusivities of about K z = 5 × 10
−3 m
2 s
−1 (Ledwell 2017,
pers. comm.). It will be shown in this paper that such values are within a factor of two
similar to those determined from high-resolution temperature sensors moored in
various deep-ocean topographic regions. Under conditions of very high Reynolds
numbers in the ocean that are not achieved in laboratories and a tight
temperature-density relationship, such observations prove adequate in quantifying
internal wave turbulence because of many 1-Hz yearlong sampled realizations of true
vertical profiles under very little mooring motion.
Instrumentation and Data
Quantifying Internal Wave Turbulent Mixing:
Lowered Instruments
Most turbulence measurements in the ocean have been performed using free-falling
(few free-ascending) microstructure profilers, either loosely tethered to the ship or
freely operating. These profilers carry shear probes and fast-response temperature
(sometimes also conductivity) sensors that more or less resolve the Kolmogorov
scales of smallest turbulence dissipation overturns that are about 0.1–0.01 s in time
and 0.001–0.01 m in space, under ocean conditions. For statistical reasons, the raw
several 100 Hz sampled data are divided in blocks of a few seconds long to give
estimates of turbulence dissipation rate and eddy diffusivity. The disadvantages of this
instrumentation are its relatively slow vertical speed of about 0.7 m s
−1 , its 1D profiling of essentially 3D physical processes and its costs: a full ocean depth apparatus
requires financing over 0.5 million US dollars and not many exist in the community.
A simpler but more commonly useable method was proposed by Thorpe [36] to
infer turbulence estimates from standard oceanographic Conductivity Temperature
Depth CTD data. This shipborne equipment also collects vertical (1D) profiles of
ocean quantities at a slightly higher speed of just under 1 m s
−1 while sampling at a
rate of 24 Hz for modern equipment. The turbulence estimation method is by
reordering vertical density profiles into statically stable ones and keeping track of the
displacements. Thus after some averaging to reduce noise the larger
energy-containing turbulent eddies are resolved but not the (Kolmogorov) dissipation
scales. In essence this is not a problem, provided some assumptions are made.
130
H. van Haren
motions, in the context of the large-scale ocean circulation. One of the unknowns is to
relate to the proper scaling of topography. As the term ‘rough topography’ [9, 31] is
somewhat imprecise in quantification, it would be better to consider the slope angle, in
relation with the internal wave angles for given stratification, and the length scales of
the slope-determination in association with the internal wave length scales. Apart
from such modeling constraints, an encouraging recent tracer-release experiment near
the Mid-Atlantic Ridge integrated over yearlong periods showed upslope motions that
can only be balanced by diffusivities of about K z = 5 × 10
−3 m
2 s
−1 (Ledwell 2017,
pers. comm.). It will be shown in this paper that such values are within a factor of two
similar to those determined from high-resolution temperature sensors moored in
various deep-ocean topographic regions. Under conditions of very high Reynolds
numbers in the ocean that are not achieved in laboratories and a tight
temperature-density relationship, such observations prove adequate in quantifying
internal wave turbulence because of many 1-Hz yearlong sampled realizations of true
vertical profiles under very little mooring motion.
Instrumentation and Data
Quantifying Internal Wave Turbulent Mixing:
Lowered Instruments
Most turbulence measurements in the ocean have been performed using free-falling
(few free-ascending) microstructure profilers, either loosely tethered to the ship or
freely operating. These profilers carry shear probes and fast-response temperature
(sometimes also conductivity) sensors that more or less resolve the Kolmogorov
scales of smallest turbulence dissipation overturns that are about 0.1–0.01 s in time
and 0.001–0.01 m in space, under ocean conditions. For statistical reasons, the raw
several 100 Hz sampled data are divided in blocks of a few seconds long to give
estimates of turbulence dissipation rate and eddy diffusivity. The disadvantages of this
instrumentation are its relatively slow vertical speed of about 0.7 m s
−1 , its 1D profiling of essentially 3D physical processes and its costs: a full ocean depth apparatus
requires financing over 0.5 million US dollars and not many exist in the community.
A simpler but more commonly useable method was proposed by Thorpe [36] to
infer turbulence estimates from standard oceanographic Conductivity Temperature
Depth CTD data. This shipborne equipment also collects vertical (1D) profiles of
ocean quantities at a slightly higher speed of just under 1 m s
−1 while sampling at a
rate of 24 Hz for modern equipment. The turbulence estimation method is by
reordering vertical density profiles into statically stable ones and keeping track of the
displacements. Thus after some averaging to reduce noise the larger
energy-containing turbulent eddies are resolved but not the (Kolmogorov) dissipation
scales. In essence this is not a problem, provided some assumptions are made.
130
H. van Haren