On Using the Finescale Parameterization and Thorpe Scales to Estimate Turbulence from Glider Data

Tara Howatt aDepartment of Earth, Ocean and Atmospheric Sciences, The University of British Columbia, Vancouver, British Columbia, Canada

Search for other papers by Tara Howatt in
Current site
Google Scholar
PubMed
Close
,
Stephanie Waterman aDepartment of Earth, Ocean and Atmospheric Sciences, The University of British Columbia, Vancouver, British Columbia, Canada

Search for other papers by Stephanie Waterman in
Current site
Google Scholar
PubMed
Close
, and
Tetjana Ross bInstitute of Ocean Sciences, Fisheries and Oceans Canada, Sidney, British Columbia, Canada

Search for other papers by Tetjana Ross in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Turbulence plays a key role in many oceanic processes, but a shortage of turbulence observations impedes its exploration. Parameterizations of turbulence applied to readily available CTD data can be useful in expanding our understanding of the space–time variability of turbulence. Typically tested and applied to shipboard data, these parameterizations have not been rigorously tested on data collected by underwater gliders, which show potential to observe turbulence in conditions that ships cannot. Using data from a 10-day glider survey in a coastal shelf environment, we compare estimates of turbulent dissipation from the finescale parameterization and Thorpe scale method to those estimated from microstructure observations collected on the same glider platform. We find that the finescale parameterization captures the magnitude and statistical distribution of dissipation, but cannot resolve spatiotemporal features in this relatively shallow water depth. In contrast, the Thorpe scale method more successfully characterizes the spatiotemporal distribution of turbulence; however, the magnitude of dissipation is overestimated, largely due to limitations on the detectable density overturn size imposed by the typical glider CTD sampling frequency of 0.5 Hz and CTD noise. Despite these limitations, turbulence parameterizations provide a viable opportunity to use CTD data collected by the multitude of gliders sampling the ocean to develop greater insight into the space–time variability of ocean turbulence and the role of turbulence in oceanic processes.

© 2021 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: Tara Howatt, thowatt@eoas.ubc.ca

Abstract

Turbulence plays a key role in many oceanic processes, but a shortage of turbulence observations impedes its exploration. Parameterizations of turbulence applied to readily available CTD data can be useful in expanding our understanding of the space–time variability of turbulence. Typically tested and applied to shipboard data, these parameterizations have not been rigorously tested on data collected by underwater gliders, which show potential to observe turbulence in conditions that ships cannot. Using data from a 10-day glider survey in a coastal shelf environment, we compare estimates of turbulent dissipation from the finescale parameterization and Thorpe scale method to those estimated from microstructure observations collected on the same glider platform. We find that the finescale parameterization captures the magnitude and statistical distribution of dissipation, but cannot resolve spatiotemporal features in this relatively shallow water depth. In contrast, the Thorpe scale method more successfully characterizes the spatiotemporal distribution of turbulence; however, the magnitude of dissipation is overestimated, largely due to limitations on the detectable density overturn size imposed by the typical glider CTD sampling frequency of 0.5 Hz and CTD noise. Despite these limitations, turbulence parameterizations provide a viable opportunity to use CTD data collected by the multitude of gliders sampling the ocean to develop greater insight into the space–time variability of ocean turbulence and the role of turbulence in oceanic processes.

© 2021 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: Tara Howatt, thowatt@eoas.ubc.ca
Save
  • Alford, M. H., and Coauthors, 2011: Energy flux and dissipation in Luzon Strait: Two tales of two ridges. J. Phys. Oceanogr., 41, 22112222, https://doi.org/10.1175/JPO-D-11-073.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Alford, M. H., and Coauthors, 2015: The formation and fate of internal waves in the South China Sea. Nature, 521, 6569, https://doi.org/10.1038/nature14399.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Batchelor, G. K., 1959: Small-scale variation of convected quantities like temperature in turbulent fluid: Part 1. General discussion and the case of small conductivity. J. Fluid Mech., 5, 113133, https://doi.org/10.1017/S002211205900009X.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Baumgartner, M. F., T. V. N. Cole, P. J. Clapham, and B. R. Mate, 2003: North Atlantic right whale habitat in the lower Bay of Fundy and on the SW Scotian Shelf during 1999-2001. Mar. Ecol. Prog. Ser., 264, 137154, https://doi.org/10.3354/meps264137.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bluteau, C. E., R. G. Lueck, G. N. Ivy, N. L. Jones, J. W. Book, and A. E. Rice, 2017: Determining mixing rates from concurrent temperature and velocity measurements. J. Atmos. Oceanic Technol., 34, 22832293, https://doi.org/10.1175/JTECH-D-16-0250.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brown, M. W., D. Fenton, K. Smedbol, C. Merriman, K. Robichaud-Leblanc, and J. D. Conway, 2009: Recovery strategy for the North Atlantic right whale (Eubalaena glacialis) in Atlantic Canadian waters. Fisheries and Oceans Canada Species at Risk Act Recovery Strategy Series Rep., 66 pp.

  • Crawford, W. R., 1986: A comparison of length scales and decay times of turbulence in stably stratified flows. J. Phys. Oceanogr., 16, 18471854, https://doi.org/10.1175/1520-0485(1986)016<1847:ACOLSA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Crawford, W. R., and R. K. Dewey, 1989: Turbulence and mixing: Sources of nutrients on the Vancouver Island continental shelf. Atmos.–Ocean, 27, 428442, https://doi.org/10.1080/07055900.1989.9649345.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • D’Asaro, E. A., and J. H. Morison, 1992: Internal waves and mixing in the Arctic Ocean. Deep-Sea Res., 39, S459S484, https://doi.org/10.1016/S0198-0149(06)80016-6.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Davies, K. T. A., T. Ross, and C. T. Taggart, 2013: Tidal and subtidal currents affect deep aggregations of right whale prey, Calanus spp., along a shelf-basin margin. Mar. Ecol. Prog. Ser., 479, 263282, https://doi.org/10.3354/meps10189.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dillon, T. M., 1982: Vertical overturns: A comparison of Thorpe and Ozmidov length scales. J. Geophys. Res., 87, 96019613, https://doi.org/10.1029/JC087iC12p09601.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Emery, W. J., and R. E. Thomson, 1997: Data Analysis Methods in Physical Oceanography. Pergamon Elsevier, 634 pp.

  • Fer, I., R. Skogseth, and F. Geyer, 2010: Internal waves and mixing in the marginal ice zone near Yermak Plateau. J. Phys. Oceanogr., 40, 16131630, https://doi.org/10.1175/2010JPO4371.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fer, I., A. K. Peterson, and J. E. Ullgren, 2014: Microstructure measurements from an underwater glider in the turbulent Faroe Bank Channel overflow. J. Atmos. Oceanic Technol., 31, 11281150, https://doi.org/10.1175/JTECH-D-13-00221.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ferron, B., H. Mercier, K. Speer, A. Gargett, and K. Polzin, 1998: Mixing in the Romanche fracture zone. J. Phys. Oceanogr., 28, 19291945, https://doi.org/10.1175/1520-0485(1998)028<1929:MITRFZ>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Frants, M., G. M. Damerell, S. T. Gille, K. J. Heywood, J. MacKinnon, and J. Sprintall, 2013: An assessment of density-based finescale methods for estimating diapycnal diffusivity in the Southern Ocean. J. Atmos. Oceanic Technol., 30, 26472661, https://doi.org/10.1175/JTECH-D-12-00241.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fuchs, H. L., and G. P. Gerbi, 2016: Seascape-level variation in turbulence- and wave-generated hydrodynamic signals experienced by plankton. Prog. Oceanogr., 141, 109129, https://doi.org/10.1016/j.pocean.2015.12.010.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Galbraith, P. S., and D. E. Kelley, 1996: Identifying overturns in CTD profiles. J. Atmos. Oceanic Technol., 13, 688702, https://doi.org/10.1175/1520-0426(1996)013<0688:IOICP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gargett, A., and T. Garner, 2008: Determining Thorpe scales from ship-lowered CTD density profiles. J. Atmos. Oceanic Technol., 25, 16571670, https://doi.org/10.1175/2008JTECHO541.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Garrett, C. J. R., and W. H. Munk, 1979: Internal waves in the ocean. Annu. Rev. Fluid Mech., 11, 339369, https://doi.org/10.1146/annurev.fl.11.010179.002011.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Goodman, L., E. R. Levine, and R. G. Lueck, 2006: On measuring the terms of the turbulent kinetic energy budget from an AUV. J. Atmos. Oceanic Technol., 23, 977990, https://doi.org/10.1175/JTECH1889.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gregg, M. C., 1989: Scaling turbulent dissipation in the thermocline. J. Geophys. Res., 94, 96869698, https://doi.org/10.1029/JC094iC07p09686.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gregg, M. C., 1999: Uncertainties and limitations in measuring ϵ and χT. J. Atmos. Oceanic Technol., 16, 14831490, https://doi.org/10.1175/1520-0426(1999)016<1483:UALIMA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gregg, M. C., T. B. Sanford, and D. P. Winkel, 2003: Reduced mixing from the breaking of internal waves in equatorial waters. Nature, 422, 513515, https://doi.org/10.1038/nature01507.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hamme, R. C., and S. R. Emerson, 2006: Constraining bubble dynamics and mixing with dissolved gases: Implications for productivity measurements by oxygen bass balance. J. Mar. Res., 64, 7395, https://doi.org/10.1357/002224006776412322.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Han, G., C. G. Hannah, J. W. Loder, and P. C. Smith, 1997: Seasonal variation of the three-dimensional mean circulation over the Scotian Shelf. J. Geophys. Res., 102, 10111025, https://doi.org/10.1029/96JC03285.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hannah, C. G., J. A. Shore, J. W. Loder, and C. E. Naimie, 2001: Seasonal circulation on the western and central Scotian shelf. J. Phys. Oceanogr., 31, 591615, https://doi.org/10.1175/1520-0485(2001)031<0591:SCOTWA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Henyey, F. S., J. Wright, and S. M. Flatté, 1986: Energy and action flow through the internal wave field: An eikonal approach. J. Geophys. Res., 91, 84878495, https://doi.org/10.1029/JC091iC07p08487.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hughes, G. O., A. M. Hogg, and R. W. Griffiths, 2009: Available potential energy and irreversible mixing in the meridional overturning circulation. J. Phys. Oceanogr., 39, 31303146, https://doi.org/10.1175/2009JPO4162.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jackett, D. R., and T. J. McDougall, 1997: A neutral density variable for the world’s oceans. J. Phys. Oceanogr., 27, 237263, https://doi.org/10.1175/1520-0485(1997)027<0237:ANDVFT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Johnston, T. M. S., and D. L. Rudnick, 2015: Trapped diurnal internal tides, propagating semidiurnal internal tides, and mixing estimates in the California Current System from sustained glider observations, 2006–2012. Deep-Sea Res. II, 112, 6178, https://doi.org/10.1016/j.dsr2.2014.03.009.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Klymak, J. M., R. Pinkel, and L. Rainville, 2008: Direct breaking of the internal tide near topography: Kaena Ridge, Hawaii. J. Phys. Oceanogr., 38, 380399, https://doi.org/10.1175/2007JPO3728.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kunze, E., 2017: Internal-wave-driven mixing: Global geography and budgets. J. Phys. Oceanogr., 47, 13251345, https://doi.org/10.1175/JPO-D-16-0141.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kunze, E., J. F. Dower, I. Beveridge, R. Dewey, and K. P. Bartlett, 2006a: Observations of biologically generated turbulence in a coastal inlet. Science, 313, 17681770, https://doi.org/10.1126/science.1129378.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kunze, E., E. Firing, J. M. Hummon, T. K. Chereskin, and A. M. Thurnherr, 2006b: Global abyssal mixing inferred from lowered ADCP shear and CTD strain profiles. J. Phys. Oceanogr., 36, 15531576, https://doi.org/10.1175/JPO2926.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lueck, R., 2016: Calculating the rate of dissipation of turbulent kinetic energy. Rockland Scientific Tech. Note 028, 18 pp., http://rocklandscientific.com/.

  • Lueck, R., and D. Huang, 1999: Dissipation measurement with a moored instrument in a swift tidal channel. J. Atmos. Oceanic Technol., 16, 14991505, https://doi.org/10.1175/1520-0426(1999)016<1499:DMWAMI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lueck, R., F. Wolk, and H. Yamazaki, 2002: Oceanic velocity microstructure measurements in the 20th century. J. Oceanogr., 58, 153174, https://doi.org/10.1023/A:1015837020019.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Luketina, D. A., and J. Imberger, 2001: Determining turbulent kinetic energy dissipation from Batchelor curve fitting. J. Atmos. Oceanic Technol., 18, 100113, https://doi.org/10.1175/1520-0426(2001)018<0100:DTKEDF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • MacKinnon, J., L. St. Laurent, and A. C. Naveira Garabato, 2013: Diapycnal mixing processes in the ocean interior. Ocean Circulation and Climate, G. Siedler et al., Eds., International Geophysics Series, Vol. 103, Academic Press, 159–177, https://doi.org/10.1016/B978-0-12-391851-2.00007-6.

    • Crossref
    • Export Citation
  • Mater, B. D., S. M. Schaad, and S. K. Venayagamoorthy, 2013: Relevance of the Thorpe length scale in stably stratified turbulence. Phys. Fluids, 25, 076604, https://doi.org/10.1063/1.4813809.

    • Crossref
    • Export Citation
  • Mater, B. D., S. K. Venayagamoorthy, L. St. Laurent, and J. Moum, 2015: Biases in Thorpe-scale estimates of turbulence dissipation. Part I: Assessments from large-scale overturns in oceanographic data. J. Phys. Oceanogr., 45, 24972521, https://doi.org/10.1175/JPO-D-14-0128.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mauritzen, C., K. L. Polzin, M. S. McCartney, R. C. Millard, and D. E. West-Mack, 2002: Evidence in hydrography and density fine structure for enhanced vertical mixing over the Mid-Atlantic Ridge in the western Atlantic. J. Geophys. Res., 107, 3147, https://doi.org/10.1029/2001JC001114.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Merckelbach, L., D. Smeed, and G. Griffiths, 2010: Vertical water velocities from underwater gliders. J. Atmos. Oceanic Technol., 27, 547563, https://doi.org/10.1175/2009JTECHO710.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Munk, W. H., 1966: Abyssal recipes. Deep-Sea Res. Oceanogr. Abstr., 13, 707730, https://doi.org/10.1016/0011-7471(66)90602-4.

  • Munk, W. H., and C. Wunsch, 1998: Abyssal recipes II: Energetics of tidal and wind mixing. Deep-Sea Res. I, 45, 19772010, https://doi.org/10.1016/S0967-0637(98)00070-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nasmyth, P. W., 1970: Oceanic turbulence. Ph.D. thesis, The University of British Columbia, 106 pp., https://doi.org/10.14288/1.0302459.

    • Crossref
    • Export Citation
  • Naveira Garabato, A. C., K. L. Polzin, B. A. King, K. J. Heywood, and M. Visbeck, 2004: Widespread intense turbulent mixing in the Southern Ocean. Science, 303, 210213, https://doi.org/10.1126/science.1090929.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Osborn, T. R., 1980: Estimates of the local rate of vertical diffusion from dissipation measurements. J. Phys. Oceanogr., 10, 8389, https://doi.org/10.1175/1520-0485(1980)010<0083:EOTLRO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Osborn, T. R., and C. S. Cox, 1972: Oceanic fine structure. Geophys. Fluid Dyn., 3, 321345, https://doi.org/10.1080/03091927208236085.

  • Ott, M. W., J. A. Barth, and A. Y. Erofeev, 2004: Microstructure measurements from a towed undulating platform. J. Atmos. Oceanic Technol., 21, 16211632, https://doi.org/10.1175/1520-0426(2004)021<1621:MMFATU>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Palmer, M. R., G. R. Stephenson, M. E. Inall, C. Balfour, A. Düsterhus, and J. A. M. Green, 2015: Turbulence and mixing by internal waves in the Celtic Sea determined from ocean glider microstructure measurements. J. Mar. Syst., 144, 5769, https://doi.org/10.1016/j.jmarsys.2014.11.005.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Park, Y. H., and Coauthors, 2014: Validation of Thorpe-scale-derived vertical diffusivities against microstructure measurements in the Kerguelen region. Biogeosciences, 11, 69276937, https://doi.org/10.5194/bg-11-6927-2014.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Peterson, A. K., and I. Fer, 2014: Dissipation measurements using temperature microstructure from an underwater glider. Methods Oceanogr., 10, 4469, https://doi.org/10.1016/j.mio.2014.05.002.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Polzin, K. L., J. M. Toole, and R. W. Schmitt, 1995: Finescale parameterizations of turbulent dissipation. J. Phys. Oceanogr., 25, 306328, https://doi.org/10.1175/1520-0485(1995)025<0306:FPOTD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Polzin, K. L., A. C. N. Garabato, T. N. Huussen, B. M. Sloyan, and S. Waterman, 2014: Finescale parameterizations of turbulent dissipation. J. Geophys. Res. Oceans, 119, 13831419, https://doi.org/10.1002/2013JC008979.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rothschild, B. J., and T. R. Osborn, 1988: Small-scale turbulence and plankton contact rates. J. Plankton Res., 10, 465474, https://doi.org/10.1093/plankt/10.3.465.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ruddick, B., A. Anis, and K. Thompson, 2000: Maximum likelihood spectral fitting: The Batchelor spectrum. J. Atmos. Oceanic Technol., 17, 15411555, https://doi.org/10.1175/1520-0426(2000)017<1541:MLSFTB>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Scheifele, B., S. Waterman, L. Merckelbach, and J. R. Carpenter, 2018: Measuring the dissipation rate of turbulent kinetic energy in strongly stratified, low energy environments: A case study from the Arctic Ocean. J. Geophys. Res. Oceans, 123, 54595480, https://doi.org/10.1029/2017JC013731.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schultze, L. K. P., L. M. Merckelbach, and J. R. Carpenter, 2017: Turbulence and mixing in a shallow shelf sea from underwater gliders. J. Geophys. Res. Oceans, 122, 90929109, https://doi.org/10.1002/2017JC012872.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schultze, L. K. P., L. M. Merckelbach, and J. R. Carpenter, 2020: Storm-induced turbulence alters shelf sea vertical fluxes. Limnol. Oceanogr. Lett., 5, 264270, https://doi.org/10.1002/lol2.10139.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Scotti, A., 2015: Biases in Thorpe-scale estimates of turbulence dissipation. Part II: Energetics arguments and turbulence simulations. J. Phys. Oceanogr., 45, 25222543, https://doi.org/10.1175/JPO-D-14-0092.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Seim, H. E., and M. C. Gregg, 1994: Detailed observations of a naturally occurring shear instability. J. Geophys. Res., 99, 10 04910 073, https://doi.org/10.1029/94JC00168.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sloyan, B. M., 2005: Spatial variability of mixing in the Southern Ocean. Geophys. Res. Lett., 32, L18603, https://doi.org/10.1029/2005GL023568.

    • Crossref
    • Export Citation
  • Smyth, W. D., J. 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, https://doi.org/10.1175/1520-0485(2001)031<1969:TEOMIT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sommer, T., J. R. Carpenter, M. Schmid, R. G. Lueck, and A. Wüest, 2013: Revisiting microstructure sensor response with implications for double-diffusive fluxes. J. Atmos. Oceanic Technol., 30, 19071923, https://doi.org/10.1175/JTECH-D-12-00272.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Steinbuck, J. V., M. T. Stacey, and S. G. Monismith, 2009: An evaluation of χT. J. Atmos. Oceanic Technol., 26, 16521662, https://doi.org/10.1175/2009JTECHO611.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., 1977: Turbulence and mixing in a Scottish loch. Philos. Trans. Roy. Soc. London, 286A, 125181, https://doi.org/10.1098/rsta.1977.0112.

    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., 1978: On the shape and breaking of finite amplitude internal gravity waves in a shear flow. J. Fluid Mech., 85, 731, https://doi.org/10.1017/S0022112078000518.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., 2012: Measuring overturns with gliders. J. Mar. Res., 70, 93117, https://doi.org/10.1357/002224012800502417.

  • Ullman, D. S., A. C. Dale, D. Herbert, and J. A. Barth, 2003: The front on the northern flank of Georges Bank in spring: 2. Cross-frontal fluxed and mixing. J. Geophys. Res., 108, 8010, https://doi.org/10.1029/2002JC001328.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Visser, A. W., H. Saito, E. Saiz, and T. Kiørboe, 2001: Observations of copepod feeding and vertical distribution under natural turbulent conditions in the North Sea. Mar. Biol., 138, 10111019, https://doi.org/10.1007/s002270000520.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Waterhouse, A. F., and Coauthors, 2014: Global patterns of diapycnal mixing from measurements of the turbulent dissipation rate. J. Phys. Oceanogr., 44, 18541872, https://doi.org/10.1175/JPO-D-13-0104.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Waterman, S., K. L. Polzin, A. C. Naveira Garabato, K. L. Sheen, and A. Forryan, 2014: Suppression of internal wave breaking in the Antarctic Circumpolar Current near topography. J. Phys. Oceanogr., 44, 14661492, https://doi.org/10.1175/JPO-D-12-0154.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Whalen, C. B., 2021: Best practices for comparing ocean turbulence measurements across spatiotemporal scales. J. Atmos. Oceanic Technol., 38, 837841, https://doi.org/10.1175/JTECH-D-20-0175.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Whalen, C. B., L. D. Talley, and J. A. MacKinnon, 2012: Spatial and temporal variability of global ocean mixing inferred from Argo profiles. Geophys. Res. Lett., 39, L18612, https://doi.org/10.1029/2012GL053196.

    • Crossref
    • Export Citation
  • Whalen, C. B., J. A. MacKinnon, L. D. Talley, and A. F. Waterhouse, 2015: Estimating the mean diapycnal mixing using a finescale strain parameterization. J. Phys. Oceanogr., 45, 11741188, https://doi.org/10.1175/JPO-D-14-0167.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wolk, F., R. G. Lueck, and L. St. Laurent, 2009: Turbulence measurements from a glider. Oceans 2009, Biloxi, MS, IEEE, https://doi.org/10.23919/OCEANS.2009.5422413.

    • Crossref
    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 257 0 0
Full Text Views 2273 1754 143
PDF Downloads 810 198 14