Quantifying Flow Speeds by Using Microstructure Shear and Temperature Spectral Analysis

Shuang-Xi Guo State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou, China
Southern Marine Science and Engineering Guangdong Laboratory, Guangzhou, China

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Xian-Rong Cen State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou, China
Southern Marine Science and Engineering Guangdong Laboratory, Guangzhou, China

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Ling Qu State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou, China
Southern Marine Science and Engineering Guangdong Laboratory, Guangzhou, China

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Yuan-Zheng Lu State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou, China
Southern Marine Science and Engineering Guangdong Laboratory, Guangzhou, China

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Peng-Qi Huang State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou, China
China University of the Chinese Academy of Sciences, Beijing, China

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Sheng-Qi Zhou State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou, China
Southern Marine Science and Engineering Guangdong Laboratory, Guangzhou, China
Institution of South China Sea Ecology and Environmental Engineering, Chinese Academy of Sciences, Guangzhou, China

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Abstract

Flow speed past the measuring probe is definitely needed for the estimation of the turbulent kinetic energy dissipation rates ε and temperature dissipation rates χ based on the Taylor frozen hypothesis. This speed is usually measured with current instruments. Occasional failed work of these instruments may lead to unsuccessful speed measurement. For example, low concentration of suspended particles in water could make the observed speed invalid when using acoustic measuring instruments. In this study, we propose an alternative approach for quantifying the flow speeds by only using the microstructure shear or temperature data, according to the spectral theories of the inertial and dissipation subranges. A dataset of the microstructure profiler, vertical microstructure profiler (VMP), collected in the South China Sea (SCS) during 2017, is used to describe this approach, and the inferred speeds are compared with the actual passing-probe speeds, i.e., the falling speeds of the VMP. Probability density functions (PDFs) of the speed ratios, i.e., the ratios of the speeds respectively inferred from the inertial and dissipation subranges of the shear and temperature spectra to the actual speeds, follow the lognormal distribution, with corresponding mean values of 1.32, 1.03, 1.56, and 1.43, respectively. This result indicates that the present approach for quantifying the flow speeds is valid, and the speeds inferred from the dissipation subrange of shear spectrum agree much better with the actual ones than those from the inertial subrange of shear spectrum and the inertial and dissipation subranges of temperature spectrum. The present approach may be complementary and useful in the evaluation of turbulent mixing when the directly observed speeds are unavailable.

© 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: Sheng-Qi Zhou, sqzhou@scsio.ac.cn

Abstract

Flow speed past the measuring probe is definitely needed for the estimation of the turbulent kinetic energy dissipation rates ε and temperature dissipation rates χ based on the Taylor frozen hypothesis. This speed is usually measured with current instruments. Occasional failed work of these instruments may lead to unsuccessful speed measurement. For example, low concentration of suspended particles in water could make the observed speed invalid when using acoustic measuring instruments. In this study, we propose an alternative approach for quantifying the flow speeds by only using the microstructure shear or temperature data, according to the spectral theories of the inertial and dissipation subranges. A dataset of the microstructure profiler, vertical microstructure profiler (VMP), collected in the South China Sea (SCS) during 2017, is used to describe this approach, and the inferred speeds are compared with the actual passing-probe speeds, i.e., the falling speeds of the VMP. Probability density functions (PDFs) of the speed ratios, i.e., the ratios of the speeds respectively inferred from the inertial and dissipation subranges of the shear and temperature spectra to the actual speeds, follow the lognormal distribution, with corresponding mean values of 1.32, 1.03, 1.56, and 1.43, respectively. This result indicates that the present approach for quantifying the flow speeds is valid, and the speeds inferred from the dissipation subrange of shear spectrum agree much better with the actual ones than those from the inertial subrange of shear spectrum and the inertial and dissipation subranges of temperature spectrum. The present approach may be complementary and useful in the evaluation of turbulent mixing when the directly observed speeds are unavailable.

© 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: Sheng-Qi Zhou, sqzhou@scsio.ac.cn
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  • Antonia, R., and P. Orlandi, 2003: On the Batchelor constant in decaying isotropic turbulence. Phys. Fluids, 15, 20842086, https://doi.org/10.1063/1.1577346.

    • 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
  • Baumert, H. Z., J. Simpson, J. H. Simpson, J. Sundermann, and J. Sündermann, 2005: Marine Turbulence: Theories, Observations, and Models. Cambridge University Press, 630 pp.

    • Search Google Scholar
    • Export Citation
  • Becherer, J., and J. N. Moum, 2017: An efficient scheme for onboard reduction of moored χpod data. J. Atmos. Oceanic Technol., 34, 25332546, https://doi.org/10.1175/JTECH-D-17-0118.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bluteau, C. E., N. L. Jones, and G. Ivey, 2011: Estimating turbulent kinetic energy dissipation using the inertial subrange method in environmental flows. Limnol. Oceanogr. Methods, 9, 302321, https://doi.org/10.4319/lom.2011.9.302.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bluteau, C. E., N. L. Jones, and G. Ivey, 2016a: Estimating turbulent dissipation from microstructure shear measurements using maximum likelihood spectral fitting over the inertial and viscous subranges. J. Atmos. Oceanic Technol., 33, 713722, https://doi.org/10.1175/JTECH-D-15-0218.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bluteau, C. E., N. L. Jones, and G. Ivey, 2016b: Acquiring long-term turbulence measurements from moored platforms impacted by motion. J. Atmos. Oceanic Technol., 33, 25352551, https://doi.org/10.1175/JTECH-D-16-0041.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bogucki, D. J., H. Luo, and J. A. Domaradzki, 2012: Experimental evidence of the Kraichnan scalar spectrum at high Reynolds numbers. J. Phys. Oceanogr., 42, 17171728, https://doi.org/10.1175/JPO-D-11-0214.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bouruet-Aubertot, P., H. Van Haren, and M. P. Lelong, 2010: Stratified inertial subrange inferred from in situ measurements in the bottom boundary layer of the Rockall Channel. J. Phys. Oceanogr., 40, 24012417, https://doi.org/10.1175/2010JPO3957.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Caulfield, S. P., 2021: Instabilities, and mixing in turbulent stratified flow. Annu. Rev. Fluid Mech., 53, 113145, https://doi.org/10.1146/annurev-fluid-042320-100458.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dillon, T. M., and D. R. Caldwell, 1980: The Batchelor spectrum and dissipation in the upper ocean. J. Geophys. Res., 85, 19101916, https://doi.org/10.1029/JC085iC04p01910.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fer, I., and M. B. Paskyabi, 2014: Autonomous ocean turbulence measurements using shear probes on a moored instrument. J. Atmos. Oceanic Technol., 31, 474490, https://doi.org/10.1175/JTECH-D-13-00096.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gibson, C. H., and W. H. Schwarz, 1963: The universal equilibrium spectra of turbulent velocity and scalar fields. J. Fluid Mech., 16, 365384, https://doi.org/10.1017/S0022112063000835.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Goto, Y., I. Yasuda, and M. Nagasawa, 2016: Turbulence estimation using fast-response thermistors attached to a free-fall vertical microstructure profiler. J. Atmos. Oceanic Technol., 33, 20652078, https://doi.org/10.1175/JTECH-D-15-0220.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Goto, Y., I. Yasuda, and M. Nagasawa, 2018: Comparison of turbulence intensity from CTD-attached and free-fall microstructure profilers. J. Atmos. Oceanic Technol., 35, 147162, https://doi.org/10.1175/JTECH-D-17-0069.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gregg, M. C., and T. B. Meagher, 1980: The dynamic response of glass rod thermistors. J. Geophys. Res., 85, 27792786, https://doi.org/10.1029/JC085iC05p02779.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gregg, M. C., E. A. D’Asaro, J. J. Riley, and E. Kunze, 2018: Mixing efficiency in the ocean. Annu. Rev. Mar. Sci., 10, 443473, https://doi.org/10.1146/annurev-marine-121916-063643.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Habersack, H., H. Piegay, and M. Rinaldi, 2011: Gravel Bed Rivers 6: From Process Understanding to River Restoration. Vol. 11, Elsevier, 836 pp.

    • Search Google Scholar
    • Export Citation
  • Ijichi, T., and T. Hibiya, 2018: Observed variations in turbulent mixing efficiency in the deep ocean. J. Phys. Oceanogr., 48, 18151830, https://doi.org/10.1175/JPO-D-17-0275.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Khani, S., 2018: Mixing efficiency in large-eddy simulations of stratified turbulence. J. Fluid Mech., 849, 373394, https://doi.org/10.1017/jfm.2018.417.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kocsis, O., H. Prandke, A. Stips, A. Simon, and A. Wuest, 1999: Comparison of dissipation of turbulent kinetic energy determined from shear and temperature microstructure. J. Mar. Syst., 21, 6784, https://doi.org/10.1016/S0924-7963(99)00006-8.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kraichnan, R. H., 1968: Small-scale structure of a scalar field convected by turbulence. Phys. Fluids, 11, 945953, https://doi.org/10.1063/1.1692063.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lueck, R., O. Hertzman, and T. R. Osborn, 1977: The spectral response of thermistors. Deep-Sea Res., 24, 951970, https://doi.org/10.1016/0146-6291(77)90565-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lueck, R., D. Huang, and D. Newman, 1997: Turbulence measurement with a moored instrument. J. Atmos. Oceanic Technol., 14, 143161, https://doi.org/10.1175/1520-0426(1997)014<0143:TMWAMI>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., 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
  • Macoun, P., and R. G. Lueck, 2004: Modeling the spatial response of the airfoil shear probe using different sized probes. J. Atmos. Oceanic Technol., 21, 284297, https://doi.org/10.1175/1520-0426(2004)021<0284:MTSROT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Monismith, S. G., J. R. Koseff, and B. L. White, 2018: Mixing efficiency in the presence of stratification: When is it constant? Geophys. Res. Lett., 45, 56275634, https://doi.org/10.1029/2018GL077229.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Moum, J. N., 2015: Ocean speed and turbulence measurements using pitot-static tubes on moorings. J. Atmos. Oceanic Technol., 32, 14001413, https://doi.org/10.1175/JTECH-D-14-00158.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Moum, J. N., and J. D. Nash, 2009: Mixing measurements on an equatorial ocean mooring. J. Atmos. Oceanic Technol., 26, 317336, https://doi.org/10.1175/2008JTECHO617.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nasmyth, P. W., 1970: Oceanic turbulence. Ph.D. dissertation, University of British Columbia, 106 pp.

  • Oakey, N. S., 1982: Determination of the rate of dissipation of turbulent energy from simultaneous temperature and velocity shear microstructure measurements. J. Phys. Oceanogr., 12, 256271, https://doi.org/10.1175/1520-0485(1982)012<0256:DOTROD>2.0.CO;2.

    • 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. Astrophys. Fluid Dyn., 3, 321345, https://doi.org/10.1080/03091927208236085.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Perlin, A., and J. Moum, 2012: Comparison of thermal variance dissipation rates from moored and profiling instruments at the equator. J. Atmos. Oceanic Technol., 29, 13471362, https://doi.org/10.1175/JTECH-D-12-00019.1.

    • 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, J. R. Ledwell, and R. W. Schmitt, 1997: Spatial variability of turbulent mixing in the abyssal ocean. Science, 276, 9396, https://doi.org/10.1126/science.276.5309.93.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ribner, H. S., and T. E. Siddon, 1965: An aerofoil probe for measuring the transverse component of turbulence. AIAA J., 3, 747749, https://doi.org/10.2514/3.2963.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Roget, E., I. Lozovatsky, X. Sanchez, and M. Figueroa, 2006: Microstructure measurements in natural waters: Methodology and applications. Prog. Oceanogr., 70, 126148, https://doi.org/10.1016/j.pocean.2006.07.003.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ruddick, B., A. Anis, and K. R. 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
  • Sanchez, X., E. Roget, J. Planella, and F. Forcat, 2011: Small-scale spectrum of a scalar field in water: The Batchelor and Kraichnan models. J. Phys. Oceanogr., 41, 21552167, https://doi.org/10.1175/JPO-D-11-025.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schmitt, R. W., J. R. Ledwell, E. T. Montgomery, K. L. Polzin, and J. M. Toole, 2005: Enhanced diapycnal mixing by salt fingers in the thermocline of the tropical Atlantic. Science, 308, 685688, https://doi.org/10.1126/science.1108678.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Siddon, T. E., 1971: A miniature turbulence gauge utilizing aerodynamic lift. Rev. Sci. Instrum., 42, 653656, https://doi.org/10.1063/1.1685193.

  • Smyth, W. D., 2020: Marginal instability and the efficiency of ocean mixing. J. Phys. Oceanogr., 50, 21412150, https://doi.org/10.1175/JPO-D-20-0083.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Song, D., J. Sun, B. Xue, Q. Jiang, and B. Wu, 2013: Mooring system of ocean turbulence observation based on submerged buoy. China Ocean Eng., 27, 369378, https://doi.org/10.1007/s13344-013-0032-x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sreenivasan, K. R., 1996: The passive scalar spectrum and the Obukhov–Corrsin constant. Phys. Fluids, 8, 189196, https://doi.org/10.1063/1.868826.

  • Tian, C., S. Wang, S. Guan, Q. Yang, and X. Xu, 2014: Test and evaluation of a moored microstructure recorder. Chin. J. Oceanol. Limnol., 32, 201209, https://doi.org/10.1007/s00343-014-2078-x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wolk, F., H. Yamazaki, L. Seuront, and R. G. Lueck, 2002: A new free-fall profiler for measuring biophysical microstructure. J. Atmos. Oceanic Technol., 19, 780793, https://doi.org/10.1175/1520-0426(2002)019<0780:ANFFPF>2.0.CO;2.

    • 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
    • Export Citation
  • Wunsch, C., and R. Ferrari, 2004: Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech., 36, 281314, https://doi.org/10.1146/annurev.fluid.36.050802.122121.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, Y., and J. N. Moum, 2010: Inertial-convective subrange estimates of thermal variance dissipation rate from moored temperature measurements. J. Atmos. Oceanic Technol., 27, 19501959, https://doi.org/10.1175/2010JTECHO746.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, Y., K. Streitlien, J. G. Bellingham, and A. B. Baggeroer, 2001: Acoustic Doppler velocimeter flow measurement from an autonomous underwater vehicle with applications to deep ocean convection. J. Atmos. Oceanic Technol., 18, 20382051, https://doi.org/10.1175/1520-0426(2001)018<2038:ADVFMF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
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