Estimating Turbulence Kinetic Energy Dissipation Rates in the Numerically Simulated Stratocumulus Cloud-Top Mixing Layer: Evaluation of Different Methods

Emmanuel O. Akinlabi Institute of Geophysics, Faculty of Physics, University of Warsaw, Warsaw, Poland

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Marta Wacławczyk Institute of Geophysics, Faculty of Physics, University of Warsaw, Warsaw, Poland

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Juan Pedro Mellado Max Planck Institute for Meteorology, Hamburg, Germany

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Szymon P. Malinowski Institute of Geophysics, Faculty of Physics, University of Warsaw, Warsaw, Poland

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Abstract

In this work, direct numerical simulation (DNS) of the stratocumulus cloud-top mixing layer is used to test various approaches to estimate the turbulence kinetic energy (TKE) dissipation rate ε from one-dimensional (1D) intersections that resemble experimental series. Results of these estimates are compared with “true” (DNS) values of ε in buoyant and inhomogeneous atmospheric flows. We focus on recently proposed methods of the TKE dissipation-rate retrievals based on zero crossings and recovering the missing part of the spectrum. These methods are tested on fully resolved turbulence fields and compared to standard retrievals from power spectra and structure functions. Anisotropy of turbulence due to buoyancy is shown to influence retrievals based on the vertical velocity component. TKE dissipation-rate estimates from the number of crossings correspond well to spectral estimates. The method based on the recovery of the missing part of the spectrum works best for Pope’s model of the dissipation spectrum and is sensitive to external intermittency. This allows for characterization of external intermittency by the Taylor-to-Liepmann scale ratio. Further improvements of this method are possible when the variance of the velocity derivative is used instead of the number of zero crossings per unit length. In conclusion, the new methods of TKE dissipation-rate retrieval from 1D series provide a valuable complement to standard approaches.

© 2019 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: Marta Wacławczyk, marta.waclawczyk@igf.fuw.edu.pl

Abstract

In this work, direct numerical simulation (DNS) of the stratocumulus cloud-top mixing layer is used to test various approaches to estimate the turbulence kinetic energy (TKE) dissipation rate ε from one-dimensional (1D) intersections that resemble experimental series. Results of these estimates are compared with “true” (DNS) values of ε in buoyant and inhomogeneous atmospheric flows. We focus on recently proposed methods of the TKE dissipation-rate retrievals based on zero crossings and recovering the missing part of the spectrum. These methods are tested on fully resolved turbulence fields and compared to standard retrievals from power spectra and structure functions. Anisotropy of turbulence due to buoyancy is shown to influence retrievals based on the vertical velocity component. TKE dissipation-rate estimates from the number of crossings correspond well to spectral estimates. The method based on the recovery of the missing part of the spectrum works best for Pope’s model of the dissipation spectrum and is sensitive to external intermittency. This allows for characterization of external intermittency by the Taylor-to-Liepmann scale ratio. Further improvements of this method are possible when the variance of the velocity derivative is used instead of the number of zero crossings per unit length. In conclusion, the new methods of TKE dissipation-rate retrieval from 1D series provide a valuable complement to standard approaches.

© 2019 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: Marta Wacławczyk, marta.waclawczyk@igf.fuw.edu.pl
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  • Albertson, J. D., M. B. Parlange, G. Kiely, and W. E. Eichinger, 1997: The average dissipation rate of turbulent kinetic energy in the neutral and unstable atmospheric surface layer. J. Geophys. Res., 102, 13 42313 432, https://doi.org/10.1029/96JD03346.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ansorge, C., and J. P. Mellado, 2016: Analyses of external and global intermittency in the logarithmic layer of Ekman flow. J. Fluid Mech., 805, 611635, https://doi.org/10.1017/jfm.2016.534.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bolgiano, R., 1959: Turbulent spectra in a stably stratified atmosphere. J. Geophys. Res., 64, 22262229, https://doi.org/10.1029/JZ064i012p02226.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brost, R. A., J. C. Wyngaard, and D. H. Lenschow, 1982: Marine stratocumulus layers. Part II: Turbulence budgets. J. Atmos. Sci., 39, 818836, https://doi.org/10.1175/1520-0469(1982)039<0818:MSLPIT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chamecki, M., and N. L. Dias, 2004: The local isotropy hypothesis and the turbulent kinetic energy dissipation rate in the atmospheric surface layer. Quart. J. Roy. Meteor. Soc., 130, 27332752, https://doi.org/10.1256/qj.03.155.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Faloona, I., and Coauthors, 2005: Observations of entrainment in eastern Pacific marine stratocumulus using three conserved scalars. J. Atmos. Sci., 62, 32683284, https://doi.org/10.1175/JAS3541.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gerber, H., G. Frick, S. P. Malinowski, H. Jonsson, D. Khelif, and S. K. Krueger, 2013: Entrainment rates and microphysics in POST stratocumulus. J. Geophys. Res. Atmos., 118, 12 09412 109, https://doi.org/10.1002/jgrd.50878.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Heinze, R., D. Mironov, and S. Raasch, 2015: Second-moment budgets in cloud topped boundary layers: A large-eddy simulation study. J. Adv. Model. Earth Syst., 7, 510536, https://doi.org/10.1002/2014MS000376.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hou, T. Y., X. H. Wu, S. Chen, and Y. Zhou, 1998: Effect of finite computational domain on turbulence scaling law in both physical and spectral spaces. Phys. Rev., 58E, 58415844, https://doi.org/10.1103/PhysRevE.58.5841.

    • Search Google Scholar
    • Export Citation
  • Jen-La Plante, I., and Coauthors, 2016: Physics of Stratocumulus Top (POST): Turbulence characteristics. Atmos. Chem. Phys., 16, 97119725, https://doi.org/10.5194/acp-16-9711-2016.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kailasnath, P., and K. R. Sreenivasan, 1993: Zero crossings of velocity fluctuations in turbulent boundary layers. Phys. Fluids, 5A, 28792885, https://doi.org/10.1063/1.858697.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kaiser, R., and E. Fedorovich, 1998: Turbulence spectra and dissipation rates in a wind tunnel model of the atmospheric convective boundary layer. J. Atmos. Sci., 55, 580594, https://doi.org/10.1175/1520-0469(1998)055<0580:TSADRI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kimura, Y., and J. R. Herring, 2012: Energy spectra of stably stratified turbulence. J. Fluid Mech., 698, 1950, https://doi.org/10.1017/jfm.2011.546.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kolmogorov, A. N., 1941: Dissipation of energy in locally isotropic turbulence. Dokl. Akad. Nauk SSSR, 434, 1517.

  • Kopeć, J. M., K. Kwiatkowski, S. de Haan, and S. P. Malinowski, 2016a: Retrieving atmospheric turbulence information from regular commercial aircraft using Mode-S and ADS-B. Atmos. Meas. Tech., 9, 22532265, https://doi.org/10.5194/amt-9-2253-2016.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kopeć, M. K., S. P. Malinowski, and Z. P. Piotrowski, 2016b: Effects of wind shear and radiative cooling on the stratocumulus-topped boundary layer. Quart. J. Roy. Meteor. Soc., 142, 32223233, https://doi.org/10.1002/qj.2903.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kumar, A., A. G. Chatterjee, and M. K. Verma, 2014: Energy spectrum of buoyancy-driven turbulence. Phys. Rev., 90E, 023016, https://doi.org/10.1103/PhysRevE.90.023016.

    • Search Google Scholar
    • Export Citation
  • Kurowski, M. J., S. P. Malinowski, and W. W. Grabowski, 2009: A numerical investigation of entrainment and transport within a stratocumulus-topped boundary layer. Quart. J. Roy. Meteor. Soc., 135, 7792, https://doi.org/10.1002/qj.354.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lighthill, M. J., 1956: The structure of turbulent shear flow. J. Fluid Mech., 1, 554560, https://doi.org/10.1017/S0022112056210366.

  • Lindborg, E., 2006: The energy cascade in a strongly stratified fluid. J. Fluid Mech., 550, 207242, https://doi.org/10.1017/S0022112005008128.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lumley, J. L., 1964: The spectrum of nearly inertial turbulence in a stably stratified fluid. J. Atmos. Sci., 21, 99102, https://doi.org/10.1175/1520-0469(1964)021<0099:TSONIT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Malinowski, S. P., and Coauthors, 2013: Physics of Stratocumulus Top (POST): Turbulent mixing across capping inversion. Atmos. Chem. Phys., 13, 12 17112 186, https://doi.org/10.5194/acp-13-12171-2013.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mazellier, N., and J. C. Vassilicos, 2008: The turbulence dissipation constant is not universal because of its universal dependence on large-scale flow topology. Phys. Fluids, 20, 015101, https://doi.org/10.1063/1.2832778.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mellado, J. P., 2017: Cloud-top entrainment in stratocumulus clouds. Annu. Rev. Fluid Mech., 49, 145169, https://doi.org/10.1146/annurev-fluid-010816-060231.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mellado, J. P., B. Stevens, H. Schmidt, and N. Peters, 2010: Two-fluid formulation of the cloud-top mixing layer for direct numerical simulation. Theor. Comput. Fluid Dyn., 24, 511536, https://doi.org/10.1007/s00162-010-0182-x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mellado, J. P., C. S. Bretherton, B. Stevens, and M. C. Wyant, 2018: DNS and LES for simulating stratocumulus: Better together. J. Adv. Model. Earth Syst., 10, 14211438, https://doi.org/10.1029/2018MS001312.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Moeng, C. H., and P. P. Sullivan, 1994: A comparison of shear-driven and buoyancy-driven planetary boundary layer flows. J. Atmos. Sci., 51, 9991022, https://doi.org/10.1175/1520-0469(1994)051<0999:ACOSAB>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Obukhov, A., 1959: Effect of Archimedean forces on the structure of the temperature field in a turbulent flow. Dokl. Akad. Nauk SSSR, 125, 12461249.

    • Search Google Scholar
    • Export Citation
  • Patton, E. G., M. J. Judd, and M. R. Raupach, 1998: Large eddy simulation of windbreak flow. Bound.-Layer Meteor., 87, 275306, https://doi.org/10.1023/A:1000945626163.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pedersen, J. G., Y. Ma, W. W. Grabowski, and S. P. Malinowski, 2018: Anisotropy turbulence and evolution of marine stratocumulus: Observations and large eddy simulations. J. Adv. Model. Earth Syst., 10, 500515, https://doi.org/10.1002/2017MS001140.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Poggi, D., and G. G. Katul, 2006: Two-dimensional scalar spectra in the deeper layers of a dense and uniform model canopy. Bound.-Layer Meteor., 121, 267281, https://doi.org/10.1007/s10546-006-9075-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Poggi, D., and G. G. Katul, 2009: Flume experiments on intermittency and zero-crossing properties of canopy turbulence. Phys. Fluids, 21, 065103, https://doi.org/10.1063/1.3140032.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Poggi, D., and G. G. Katul, 2010: Evaluation of the turbulent kinetic energy dissipation rate inside canopies by zero- and level-crossing density methods. Bound.-Layer Meteor., 136, 219233, https://doi.org/10.1007/s10546-010-9503-2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pope, S. B., 2000: Turbulent Flows. Cambridge University Press, 771 pp., https://doi.org/10.1017/CBO9780511840531.

    • Crossref
    • Export Citation
  • Rice, S. O., 1945: Mathematical analysis of random noise. Bell Syst. Tech. J., 24, 46156, https://doi.org/10.1002/j.1538-7305.1945.tb00453.x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schulz, B., and J. P. Mellado, 2018: Wind shear effects on radiatively and evaporatively driven stratocumulus tops. J. Atmos. Sci., 75, 32453263, https://doi.org/10.1175/JAS-D-18-0027.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sharman, R. D., L. B. Cornman, G. Meymaris, J. P. Pearson, and T. Farrar, 2014: Description and derived climatologies of automated in situ eddy-dissipation-rate reports of atmospheric turbulence. J. Appl. Meteor. Climatol., 53, 14161432, https://doi.org/10.1175/JAMC-D-13-0329.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sreenivasan, K., A. Prabhu, and R. Narasimha, 1983: Zero-crossings in turbulent signals. J. Fluid Mech., 137, 251272, https://doi.org/10.1017/S0022112083002396.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stevens, B., and Coauthors, 2003: Dynamics and Chemistry of Marine Stratocumulus—DYCOMS-II. Bull. Amer. Meteor. Soc., 84, 579594, https://doi.org/10.1175/BAMS-84-5-Stevens.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Verma, M. K., A. Kumar, and A. Pandey, 2017: Phenomenology of buoyancy-driven turbulence: Recent results. New J. Phys., 19, 025012, https://doi.org/10.1088/1367-2630/aa5d63.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wacławczyk, M., Y.-F. Ma, J. M. Kopeć, and S. P. Malinowski, 2017: Novel approaches to estimating turbulent kinetic energy dissipation rate from low and moderate resolution velocity fluctuation time series. Atmos. Meas. Tech., 10, 45734585, https://doi.org/10.5194/amt-10-4573-2017.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Waite, M. L., 2011: Stratified turbulence at the buoyancy scale. Phys. Fluids, 23, 066602, https://doi.org/10.1063/1.3599699.

  • Wilson, D. J., 1995: Concentration Fluctuations and Averaging Time in Vapor Clouds. American Institute of Chemical Engineers, 181 pp., https://doi.org/10.1002/9780470937976.

    • Crossref
    • Export Citation
  • Yee, E., P. R. Kosteniuk, G. M. Chandler, C. A. Biltoft, and J. F. Bowers, 1995: Measurements of level-crossing statistics of concentration fluctuations in plumes dispersing in the atmospheric surface layer. Bound.-Layer Meteor., 73, 5390, https://doi.org/10.1007/BF00708930.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, D. H., Y. T. Chew, and S. H. Winoto, 1996: Investigation of intermittency measurement methods for transitional boundary layer flows. Exp. Therm. Fluid Sci., 12, 433–433, https://doi.org/10.1016/0894-1777(95)00133-6.

    • Crossref
    • Search Google Scholar
    • Export Citation
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