• Gargett, A. E., 1994: Observing turbulence with a modified acoustic Doppler current profiler. J. Atmos. Oceanic Technol., 11, 15921610, doi:10.1175/1520-0426(1994)011<1592:OTWAMA>2.0.CO;2.

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  • Gargett, A. E., 1999: Velcro measurement of turbulence kinetic energy dissipation rate ε. J. Atmos. Oceanic Technol., 16, 19731993, doi:10.1175/1520-0426(1999)016<1973:VMOTKE>2.0.CO;2.

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    • Search Google Scholar
    • Export Citation
  • Gargett, A. E., and J. R. Wells, 2007: Langmuir turbulence in shallow water. Part 1. Observations. J. Fluid Mech., 576, 2761, doi:10.1017/S0022112006004575.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gargett, A. E., and C. E. Grosch, 2014: Turbulence process domination under the combined forcings of wind stress, the Langmuir vortex force, and surface cooling. J. Phys. Oceanogr., 44, 4467, doi:10.1175/JPO-D-13-021.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gargett, A. E., T. R. Osborn, and P. W. Nasmyth, 1984: Local isotropy and the decay of turbulence in a stratified fluid. J. Fluid Mech., 144, 231280, doi:10.1017/S0022112084001592.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gargett, A. E., J. R. Wells, A. E. Tejada-Martínez, and C. E. Grosch, 2004: Langmuir supercells: A mechanism for sediment resuspension and transport in shallow seas. Science, 306, 19251928, doi:10.1126/science.1100849.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gargett, A. E., A. E. Tejada-Martínez, and C. E. Grosch, 2008: Measuring turbulent large-eddy structures with an ADCP. 1. Vertical velocity variance. J. Mar. Res., 66, 157189, doi:10.1357/002224008785837149.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gargett, A. E., A. E. Tejada-Martínez, and C. E. Grosch, 2009: Measuring turbulent large-eddy structures with an ADCP. 2. Horizontal velocity variance. J. Mar. Res., 67, 569595, doi:10.1357/002224009791218823.

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    • Export Citation
  • Greene, A. D., P. J. Hendricks, and M. C. Gregg, 2015: Using an ADCP to estimate turbulent kinetic energy dissipation rate in sheltered coastal waters. J. Atmos. Oceanic Technol., 32, 318333, doi:10.1175/JTECH-D-13-00207.1.

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    • Search Google Scholar
    • Export Citation
  • Holt, J. T., 1998: Experiments on Kelvin-Helmholtz billows influenced by boundaries. Geophys. Astrophys. Fluid Dyn., 89, 205233, doi:10.1080/03091929808203686.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kolmogoroff, A. N., 1941: The local structure of turbulence in an incompressible viscous fluid for very large Reynolds number. Dokl. Akad. Nauk SSSR, 30, 301–305.

  • Moum, J. N., 1996: Energy-containing scales of turbulence in the ocean thermocline. J. Geophys. Res., 101, 14 09514 109, doi:10.1029/96JC00507.

  • Pope, S. B., 2000: Turbulent Flows. Cambridge University Press, 771 pp.

    • Crossref
    • Export Citation
  • Salehipour, H., W. Peltier, and A. Mashayek, 2015: Turbulent diapycnal mixing in stratified shear flows: The influence of Prandtl number on mixing efficiency and transition at high Reynolds number. J. Fluid Mech., 773, 178223, doi:10.1017/jfm.2015.225.

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    • Search Google Scholar
    • Export Citation
  • Smyth, W. D., J. N. Moum, and D. R. Caldwell, 2001: The efficiency of mixing in turbulent patches: Inferences from direct simulations and microstructure observations. J. Phys. Oceanogr., 31, 19691992, doi:10.1175/1520-0485(2001)031<1969:TEOMIT>2.0.CO;2.

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    • Search Google Scholar
    • Export Citation
  • Tejada-Martínez, A. E., and C. E. Grosch, 2007: Langmuir turbulence in shallow water. Part 2. Large-eddy simulation. J. Fluid Mech., 576, 63108, doi:10.1017/S0022112006004587.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., 2002: The axial coherence of Kelvin–Helmholtz billows. Quart. J. Roy. Meteor. Soc., 128, 15291542, doi:10.1002/qj.200212858307.

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    • Search Google Scholar
    • Export Citation
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    Profiles as a function of scaled height above the bottom of , the natural logarithm of turbulent kinetic energy dissipation rate normalized with H and the surface stress velocity used to force an LES of Langmuir supercells. Estimates are determined both directly from LES results (heavy line) and as large-eddy estimates and made with the same rms vertical velocity (averaged over both horizontal dimensions) but different length scales, (light line) and (dashed line), respectively: both estimates use calibration constant = 1 (Gargett 1999). The dashed line is a best-case scenario for the estimate, obtained when the horizontal transect is normal to the long axis of the supercells: because of the substantial anisotropy of Langmuir circulations, any other path would yield larger , hence even smaller εh.

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Comment on “Using an ADCP to Estimate Turbulent Kinetic Energy Dissipation Rate in Sheltered Coastal Waters”

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  • 1 Institute of Ocean Sciences, Sidney, British Columbia, Canada, and Old Dominion University, Norfolk, Virginia
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Abstract

Greene et al. revisit the suggestion that the turbulent kinetic energy dissipation rate could be estimated through a “large-eddy estimate,” employing acoustic measurements of velocity fields associated with the largest energy-containing scales of ocean turbulence. While the large-eddy estimate as originally proposed used vertical velocity and a vertical eddy length scale, Greene et al. chose instead to substitute a horizontal length scale for the latter. This comment argues that combining a horizontal scale for length with a vertical velocity scale produces a large-eddy estimate of the dissipation rate that is accurate only if the energy-containing eddies are isotropic, and that this condition is highly unlikely in naturally occurring ocean turbulence, subject as it is to influences of stratification, vertical shear, and/or the presence of horizontal boundaries. The problem is documented using data from a large-eddy simulation of Langmuir supercells.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Ann Gargett, gargettann@gmail.com

The original article that was the subject of this comment/reply can be found at http://journals.ametsoc.org/doi/abs/10.1175/JTECH-D-13-00207.1.

Abstract

Greene et al. revisit the suggestion that the turbulent kinetic energy dissipation rate could be estimated through a “large-eddy estimate,” employing acoustic measurements of velocity fields associated with the largest energy-containing scales of ocean turbulence. While the large-eddy estimate as originally proposed used vertical velocity and a vertical eddy length scale, Greene et al. chose instead to substitute a horizontal length scale for the latter. This comment argues that combining a horizontal scale for length with a vertical velocity scale produces a large-eddy estimate of the dissipation rate that is accurate only if the energy-containing eddies are isotropic, and that this condition is highly unlikely in naturally occurring ocean turbulence, subject as it is to influences of stratification, vertical shear, and/or the presence of horizontal boundaries. The problem is documented using data from a large-eddy simulation of Langmuir supercells.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Ann Gargett, gargettann@gmail.com

The original article that was the subject of this comment/reply can be found at http://journals.ametsoc.org/doi/abs/10.1175/JTECH-D-13-00207.1.

1. Comment

The paper of Greene et al. (2015) revisits a suggestion that acoustic measurements of velocity fields associated with the largest scales of ocean turbulence could be used to estimate a small-scale parameter, the turbulent kinetic energy dissipation rate , through a “large-eddy estimate,”
e1
where , , and are typical velocity, time, and length scales of the largest energy-containing eddies of the turbulence (Gargett 1994, 1999). It is widely accepted (Pope 2000) that these energy-containing scales are almost always anisotropic, since they bear the imprint of the instability process(es) that supply them with energy and/or that of nearby boundaries. This is true regardless of whether the Reynolds number is sufficiently high to produce local isotropy (Kolmogoroff 1941), that is, an inertial subrange of isotropic eddies between these energy-containing scales and the dissipation scales that irreversibly remove their energy. In the ocean, stable stratification, vertical shear, and/or horizontal boundaries all conspire to produce anisotropy of energy-containing scales such that a characteristic vertical length scale is normally smaller than a characteristic horizontal length scale . From continuity, , that is, characteristic turbulent vertical velocity is smaller than characteristic horizontal velocity by the length scale ratio . Thus, when energy-containing eddies are anisotropic, a characteristic time scale of their decay through irreversible transfer to dissipation scales,
e2
must be calculated with the appropriate combination of velocity/length scales, that is, as either or . Gargett (1994, 1999) used acoustic measurements of vertical velocity to calculate a characteristic vertical velocity as the rms value of averaged () over , a large-eddy vertical length scale determined by a zero-crossing algorithm. The time scale associated with these choices is .

For reasons that are not explained, the authors of the paper under discussion did not investigate the algorithm as originally suggested but instead choose to compute and use a horizontal length scale with a velocity scale defined as the rms value of over ; that is, they use an implicit decay time scale that is neither of the appropriate time scales in Eq. (2). Provided that the energy-containing scales of the turbulence are isotropic, there will be no difference between this definition and those of Eq. (2). Comparing spectra from a vertical beam and one canted 60° from vertical, Green et al. (2015, p. 325) argue that “close agreement between the spectra of the two components suggests that the flow is isotropic” at the horizontal scale of 30 m used for their computation of , hence that “the horizontal correlation scale is a reasonable surrogate for the vertical,” that is, that the turbulence is isotropic. However, while 30 m may be within an inertial subrange for some of the values of reported, some of the observed spectra do not exhibit clear and/or extensive inertial subranges (Greene et al. 2015, their Fig. 5). Moreover, the location within an inertial subrange merely suggests local isotropy, that is, isotropy at scales small enough that the turbulence has become independent of the larger scales at which energy resides. In the same vein, the referenced observations of Gargett et al. (1984) show only that local isotropy is guaranteed if a buoyancy Reynolds number is sufficiently large: in that study, measurements of energy-containing scales were contaminated by vehicle motion, hence nothing could be deduced about their degree of isotropy.

Anisotropy of energy-containing scales with < is the most likely oceanic norm, so in general and a choice of horizontal rather than vertical length scale does matter. How much can it matter? To illustrate, I consider Langmuir supercells (Gargett et al. 2004; Gargett and Wells 2007), full-depth Langmuir circulations that are the energy-containing eddies of turbulence in shallow coastal seas during conditions driven predominantly by a wave-induced Langmuir vortex force (Gargett and Grosch 2014). Well-resolved (Gargett et al. 2008, 2009) observations of the large-eddy structure of this particular form of turbulence show that , where H is the water column depth and the factor of 2 accounts for the pair of large-scale counterrotating vortices (“large eddies”) that make up a complete Langmuir cell of horizontal scale . In this case , a bias that cannot be considered small. Moreover, this is the bias that would be obtained with a measurement path normal to the roughly wind-aligned long axis of the vortex pair; hence, this is very much a best-case estimate. Because Langmuir circulations are much larger in the downwind direction than the crosswind direction, any measurement path other than crosswind would result in even larger horizontal scale, hence even smaller estimates.

What evidence do we have for applicability of a large-eddy model for dissipation rate in this case (apart from the fact that it is unreasonable to assume that the method works for some large eddies but not others)? Profiler-based dissipation measurements are not available for comparison. Even if profiler operations were possible in the wind and sea-state conditions under which supercells exist, impacts of sediment particles that are resuspended and distributed throughout the water column during these events would most likely irreversibly contaminate shear probe measurements. Available evidence comes instead from a large-eddy simulation (LES) model (Tejada-Martínez and Grosch 2007) that, when run with forcing parameters matched to observational conditions, produces results closely resembling all available observational features of Langmuir supercells (Gargett and Wells 2007). Figure 1 shows profiles of three dissipation rate estimates (normalized with water depth H and the surface stress velocity used to force the LES). The “direct” estimate is the sum of the viscous dissipation rate of the part of the flow resolved by the LES and the dissipation rate associated with the subgrid-scale closure: results are insensitive to the exact form used for this closure (Tejada-Martínez and Grosch 2007). Both large-eddy estimates use the value of = 1.0 determined by Gargett (1999). The light line is a large-eddy estimate made with characteristic length scale equal to the vertical length scale of the cells and characteristic velocity , where angle brackets denote an average of fluctuating vertical velocity over horizontal dimensions and time. This estimate would not differ greatly if averaging were performed over the vertical extent of individual cells, as in Gargett (1999), because is relatively uniform over . These two estimates are seen to agree well, save in near-boundary layers where the effects of the smaller Reynolds number of the LES are observed. The large-eddy estimate that would result from use of measured in the crosswind direction (dashed line) is noticeably inferior, and it would be even more so if the value of = 0.35 suggested by Greene et al. (2015) were used. Finally, as remarked above, any other path angle would result in larger values of , hence even smaller values of .

Fig. 1.
Fig. 1.

Profiles as a function of scaled height above the bottom of , the natural logarithm of turbulent kinetic energy dissipation rate normalized with H and the surface stress velocity used to force an LES of Langmuir supercells. Estimates are determined both directly from LES results (heavy line) and as large-eddy estimates and made with the same rms vertical velocity (averaged over both horizontal dimensions) but different length scales, (light line) and (dashed line), respectively: both estimates use calibration constant = 1 (Gargett 1999). The dashed line is a best-case scenario for the estimate, obtained when the horizontal transect is normal to the long axis of the supercells: because of the substantial anisotropy of Langmuir circulations, any other path would yield larger , hence even smaller εh.

Citation: Journal of Atmospheric and Oceanic Technology 34, 6; 10.1175/JTECH-D-16-0091.1

Although the example of Langmuir supercells was useful because of the complete information available from an observationally validated LES, the degree of anisotropy of the large eddies and consequent effects on resulting large-eddy computations of dissipation rate are not unique. In Kelvin–Helmholtz instability (KHI), the most likely mechanism producing turbulence in stratified shear flows, the direct numerical simulations (DNS) of Smyth et al. (2001) exhibit primary instabilities (billows) with , where is the horizontal length scale of the billows in direction of the mean sheared current and is the vertical scale of the billows: this ratio is roughly maintained during vortex pairing. Moreover, the resolution required to approach oceanographically relevant Reynolds numbers requires DNS computations of KHI to severely restrict the horizontal spanwise (cross current) scale [Smyth et al. (2001) explore the spanwise scale to a maximum of ~, while higher Reynolds numbers restrict Salehipour et al. (2015) to ]; thus, these computations cannot address the question of large-eddy scale in the spanwise direction. However, in nature, as dramatically evidenced by roll clouds in the atmosphere (e.g., Holt 1998, his Fig. 1), the spanwise scale can be much larger than . Reviewing both laboratory measurements and field evidence, Thorpe (2002) finds that during KHI, the minimum average length of the billow crests in the spanwise direction is about 4 times , hence about 10 times . Thus, as with Langmuir circulations, the (observationally unknown) direction of travel across a field of KHI structures may influence the value determined for the horizontal length scale.

2. Discussion and conclusions

The main purpose of this comment is a general warning against using a horizontal length scale together with a characteristic vertical velocity scale in a large-eddy estimate of the turbulent dissipation rate without supplying an independent calibration by concurrent microprofiler measurements. This necessity for accompanying microscale measurements when using as a decay time scale unfortunately negates one of the main reasons for the original proposal of the large-eddy technique, which was to eventually eliminate the costs and labor that are (still) involved in operating microscale profilers.

Returning to use of , hence , automatically ensures against an unknown degree of anisotropy of the energy-containing eddies. For use in calculating , can be determined by a zero-crossing algorithm (Gargett 1999), by a correlation method similar to that used by Greene et al. (2015) for , or in stratified conditions as (Moum 1996). Use of also eliminates two additional constraints inherent to the use of , namely, that the turbulence must fulfill the frozen field condition necessary to convert temporal measurements to length scales and that ship speed must remain effectively constant for the length of time used to calculate : both conditions are unnecessary when using (nearly instantaneous) measurements of .

Finally, as part of a discussion of estimation of via a large-eddy technique, it is interesting to consider the origin of the present use of as a measure of turbulence in the ocean. For more than three decades, sea-state constraints meant that ocean turbulence was measured via freely falling profilers divorced from the motion of the sea surface. The response of profilers to internal flows on scales similar to their own meant that only the very smallest scales of turbulence, the dissipation scales, could be reliably observed. The lack of alternatives has allowed measurements of these smallest scales to become enshrined as the measurement of ocean turbulence. However, direct information about the connection between turbulence and the processes generating it is lost during the inertial cascade of energy to dissipation scales. As a result, we generally have only inferred properties of these forcing processes, limiting our ability to understand the connections between forcing and mixing in the ocean. As reported in the paper under discussion, advances in Doppler technology over the past 15–20 years have indeed allowed large-eddy estimates of to be made at levels much lower than the original ones of Gargett (1994, 1999). It seems even more important, however, that these technological advances in acoustic measurements and in deployment strategies are beginning to allow us to measure the large eddies of turbulence directly and thus observe, rather than infer, the connections between forcings and features of the resulting turbulent structures (Gargett and Grosch 2014). These connections are essential to understanding the properties and the influence of turbulence in the ocean, as well as potential changes in them, as large-scale parameters such as forcings, buoyancy, and shear evolve under climate change.

Acknowledgments

The LES results of Fig. 1 were supported by NSF Grant 0927724 to C. E. Grosch and A. E. Tejada-Martínez and kindly provided by G. Martinat.

REFERENCES

  • Gargett, A. E., 1994: Observing turbulence with a modified acoustic Doppler current profiler. J. Atmos. Oceanic Technol., 11, 15921610, doi:10.1175/1520-0426(1994)011<1592:OTWAMA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gargett, A. E., 1999: Velcro measurement of turbulence kinetic energy dissipation rate ε. J. Atmos. Oceanic Technol., 16, 19731993, doi:10.1175/1520-0426(1999)016<1973:VMOTKE>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gargett, A. E., and J. R. Wells, 2007: Langmuir turbulence in shallow water. Part 1. Observations. J. Fluid Mech., 576, 2761, doi:10.1017/S0022112006004575.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gargett, A. E., and C. E. Grosch, 2014: Turbulence process domination under the combined forcings of wind stress, the Langmuir vortex force, and surface cooling. J. Phys. Oceanogr., 44, 4467, doi:10.1175/JPO-D-13-021.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gargett, A. E., T. R. Osborn, and P. W. Nasmyth, 1984: Local isotropy and the decay of turbulence in a stratified fluid. J. Fluid Mech., 144, 231280, doi:10.1017/S0022112084001592.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gargett, A. E., J. R. Wells, A. E. Tejada-Martínez, and C. E. Grosch, 2004: Langmuir supercells: A mechanism for sediment resuspension and transport in shallow seas. Science, 306, 19251928, doi:10.1126/science.1100849.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gargett, A. E., A. E. Tejada-Martínez, and C. E. Grosch, 2008: Measuring turbulent large-eddy structures with an ADCP. 1. Vertical velocity variance. J. Mar. Res., 66, 157189, doi:10.1357/002224008785837149.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gargett, A. E., A. E. Tejada-Martínez, and C. E. Grosch, 2009: Measuring turbulent large-eddy structures with an ADCP. 2. Horizontal velocity variance. J. Mar. Res., 67, 569595, doi:10.1357/002224009791218823.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Greene, A. D., P. J. Hendricks, and M. C. Gregg, 2015: Using an ADCP to estimate turbulent kinetic energy dissipation rate in sheltered coastal waters. J. Atmos. Oceanic Technol., 32, 318333, doi:10.1175/JTECH-D-13-00207.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Holt, J. T., 1998: Experiments on Kelvin-Helmholtz billows influenced by boundaries. Geophys. Astrophys. Fluid Dyn., 89, 205233, doi:10.1080/03091929808203686.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kolmogoroff, A. N., 1941: The local structure of turbulence in an incompressible viscous fluid for very large Reynolds number. Dokl. Akad. Nauk SSSR, 30, 301–305.

  • Moum, J. N., 1996: Energy-containing scales of turbulence in the ocean thermocline. J. Geophys. Res., 101, 14 09514 109, doi:10.1029/96JC00507.

  • Pope, S. B., 2000: Turbulent Flows. Cambridge University Press, 771 pp.

    • Crossref
    • Export Citation
  • Salehipour, H., W. Peltier, and A. Mashayek, 2015: Turbulent diapycnal mixing in stratified shear flows: The influence of Prandtl number on mixing efficiency and transition at high Reynolds number. J. Fluid Mech., 773, 178223, doi:10.1017/jfm.2015.225.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smyth, W. D., J. N. Moum, and D. R. Caldwell, 2001: The efficiency of mixing in turbulent patches: Inferences from direct simulations and microstructure observations. J. Phys. Oceanogr., 31, 19691992, doi:10.1175/1520-0485(2001)031<1969:TEOMIT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tejada-Martínez, A. E., and C. E. Grosch, 2007: Langmuir turbulence in shallow water. Part 2. Large-eddy simulation. J. Fluid Mech., 576, 63108, doi:10.1017/S0022112006004587.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., 2002: The axial coherence of Kelvin–Helmholtz billows. Quart. J. Roy. Meteor. Soc., 128, 15291542, doi:10.1002/qj.200212858307.

    • Crossref
    • Search Google Scholar
    • Export Citation
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