Estimating Turbulent Dissipation from Microstructure Shear Measurements Using Maximum Likelihood Spectral Fitting over the Inertial and Viscous Subranges

Cynthia E. Bluteau School of Civil, Environmental and Mining Engineering, and Oceans Institute, University of Western Australia, Perth, Western Australia, Australia

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Nicole L. Jones School of Civil, Environmental and Mining Engineering, and Oceans Institute, University of Western Australia, Perth, Western Australia, Australia

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Gregory N. Ivey School of Civil, Environmental and Mining Engineering, and Oceans Institute, University of Western Australia, Perth, Western Australia, Australia

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Abstract

A technique is presented to derive the dissipation of turbulent kinetic energy ϵ by using the maximum likelihood estimator (MLE) to fit a theoretical or known empirical model to turbulence shear spectral observations. The commonly used integration method relies on integrating the shear spectra in the viscous range, thus requiring the resolution of the highest wavenumbers of the turbulence shear spectrum. With current technology, the viscous range is not resolved at sufficiently large wavenumbers to estimate high ϵ; however, long inertial subranges can be resolved, making spectral fitting over both this subrange and the resolved portion of the viscous range an attractive method for deriving ϵ. The MLE takes into account the chi-distributed properties of the spectral observations, and so it does not rely on the log-transformed spectral observations. This fitting technique can thus take advantage of both the inertial and viscous subranges, a portion of both, or simply one of the subranges. This flexibility allows a broad range of ϵ to be resolved. The estimated ϵ is insensitive to the range of wavenumbers fitted with the model, provided the noise-dominated portion of the spectra and the low wavenumbers impacted by the mean flow are avoided. For W kg−1, the MLE fitting estimates agree with those obtained by integrating the spectral observations. However, with increasing ϵ the viscous subrange is not fully resolved and the integration method progressively starts to underestimate ϵ compared with the values obtained from fitting the spectral observations.

Corresponding author address: Cynthia E. Bluteau, School of Civil, Environmental and Mining Engineering, University of Western Australia, MO15, 35 Stirling Highway, Crawley, Perth WA 6009, Australia. E-mail: cynthia.bluteau@uwa.edu.au

Abstract

A technique is presented to derive the dissipation of turbulent kinetic energy ϵ by using the maximum likelihood estimator (MLE) to fit a theoretical or known empirical model to turbulence shear spectral observations. The commonly used integration method relies on integrating the shear spectra in the viscous range, thus requiring the resolution of the highest wavenumbers of the turbulence shear spectrum. With current technology, the viscous range is not resolved at sufficiently large wavenumbers to estimate high ϵ; however, long inertial subranges can be resolved, making spectral fitting over both this subrange and the resolved portion of the viscous range an attractive method for deriving ϵ. The MLE takes into account the chi-distributed properties of the spectral observations, and so it does not rely on the log-transformed spectral observations. This fitting technique can thus take advantage of both the inertial and viscous subranges, a portion of both, or simply one of the subranges. This flexibility allows a broad range of ϵ to be resolved. The estimated ϵ is insensitive to the range of wavenumbers fitted with the model, provided the noise-dominated portion of the spectra and the low wavenumbers impacted by the mean flow are avoided. For W kg−1, the MLE fitting estimates agree with those obtained by integrating the spectral observations. However, with increasing ϵ the viscous subrange is not fully resolved and the integration method progressively starts to underestimate ϵ compared with the values obtained from fitting the spectral observations.

Corresponding author address: Cynthia E. Bluteau, School of Civil, Environmental and Mining Engineering, University of Western Australia, MO15, 35 Stirling Highway, Crawley, Perth WA 6009, Australia. E-mail: cynthia.bluteau@uwa.edu.au
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  • Baumert, H. Z., Simpson J. , and Sündermann J. , Eds., 2005: Marine Turbulence: Theories, Observations, and Models; Results of the CARTUM Project. Cambridge University Press, 630 pp.

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

    • Search Google Scholar
    • Export Citation
  • Doron, P., Bertuccioli L. , Katz J. , and Osborn T. R. , 2001: Turbulence characteristics and dissipation estimates in the coastal ocean bottom boundary layer from PIV data. J. Phys. Oceanogr., 31, 21082134, doi:10.1175/1520-0485(2001)031<2108:TCADEI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Emery, W. J., and Thomson R. E. , 2001: Data Analysis Methods in Physical Oceanography. 2nd ed. Elsevier Science, 638 pp.

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

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

    • Search Google Scholar
    • Export Citation
  • Geyer, W. R., Scully M. E. , and Ralston D. K. , 2008: Quantifying vertical mixing in estuaries. Environ. Fluid Mech., 8, 495509, doi:10.1007/s10652-008-9107-2.

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

    • Search Google Scholar
    • Export Citation
  • Lucas, N., Simpson J. , Rippeth T. P. , and Old C. P. , 2014: Measuring turbulent dissipation using a tethered ADCP. J. Atmos. Oceanic Technol., 31, 18261837, doi:10.1175/JTECH-D-13-00198.1.

    • Search Google Scholar
    • Export Citation
  • Lueck, R. G., 2015: Calculating the rate of dissipation of turbulent kinetic energy. Rockland Scientific International Inc. Tech. Note TN-028, 18 pp. [Available online at http://rocklandscientific.com/?wpdmdl=1034.]

  • Lueck, R. G., Wolk F. , and Yamazaki H. , 2002: Oceanic velocity microstructure measurements in the 20th century. J. Oceanogr., 58, 153174, doi:10.1023/A:1015837020019.

    • Search Google Scholar
    • Export Citation
  • Lumley, J. L., 1965: Interpretation of time spectra measured in high-intensity shear flows. Phys. Fluids, 8, 10561062, doi:10.1063/1.1761355.

    • Search Google Scholar
    • Export Citation
  • Macoun, P., and Lueck R. , 2004: Modeling the spatial response of the airfoil shear probe using different sized probes. J. Atmos. Oceanic Technol., 21, 284297, doi:10.1175/1520-0426(2004)021<0284:MTSROT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Moum, J. N., Gregg M. C. , Lien R. C. , and Carr M. E. , 1995: Comparison of turbulence kinetic energy dissipation rate estimates from two ocean microstructure profilers. J. Atmos. Oceanic Technol., 12, 346366, doi:10.1175/1520-0426(1995)012<0346:COTKED>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Nasmyth, P. W., 1970: Oceanic turbulence. Ph.D. thesis, University of British Columbia, 71 pp., doi:10.14288/1.0084817.

  • 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, doi:10.1175/1520-0485(1982)012<0256:DOTROD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Osborn, T. R., 1974: Vertical profiling of velocity microstructure. J. Phys. Oceanogr., 4, 109115, doi:10.1175/1520-0485(1974)004<0109:VPOVM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Pope, S. B., 2000: Turbulent Flows. 1st ed. Cambridge University Press, 770 pp.

  • Price, J. F., and Coauthors, 1993: Mediterranean outflow mixing and dynamics. Science, 259, 12771282, doi:10.1126/science.259.5099.1277.

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

    • Search Google Scholar
    • Export Citation
  • Sreenivasan, K. R., 1995: On the universality of the Kolmogorov constant. Phys. Fluids, 7, 27782784, doi:10.1063/1.868656.

  • Steinbuck, J. V., and Coauthors, 2010: An autonomous open-ocean stereoscopic PIV profiler. J. Atmos. Oceanic Technol., 27, 13621380, doi:10.1175/2010JTECHO694.1.

    • Search Google Scholar
    • Export Citation
  • Voulgaris, G., and Trowbridge J. H. , 1998: Evaluation of the acoustic Doppler velocimeter (ADV) for turbulence measurements. J. Atmos. Oceanic Technol., 15, 272289, doi:10.1175/1520-0426(1998)015<0272:EOTADV>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Walter, R. K., Squibb M. E. , Woodson C. B. , Koseff J. R. , and Monismith S. G. , 2014: Stratified turbulence in the nearshore coastal ocean: Dynamics and evolution in the presence of internal bores. J. Geophys. Res. Oceans, 119, 87098730, doi:10.1002/2014JC010396.

    • Search Google Scholar
    • Export Citation
  • Wiles, P. J., Rippeth T. P. , Simpson J. H. , and Hendricks P. J. , 2006: A novel technique for measuring the rate of turbulent dissipation in the marine environment. Geophys. Res. Lett., 33, L21608, doi:10.1029/2006GL027050.

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

    • Search Google Scholar
    • Export Citation
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