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Phase aligned ensemble averaging for environmental flow studies

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Abstract

The quantification of turbulent mixing in nature is predicated by inherent randomness of causal events, and obtaining relevant turbulence statistics requires ensemble averaging of identical realizations that are unachievable in field observations or onerous in laboratory situations. Laboratory modeling is often used to study nonstationary natural processes, but jitters due to intrinsic variability of events as well as experimental uncertainties introduce additional (spurious) fluctuations that affect ensemble averaging of individual realizations. In this paper, the phase-aligned ensemble averaging technique (PAET), which aligns the events based on information on flow structures, is introduced in the context of environmental fluid mechanics studies. The accuracy and computational efficiency of PAET are investigated systematically for two cases: (1) synthetic density field alignment and (2) laboratory flows involving collision of counter flowing gravity currents. The latter is a frequent phenomenon in the stable atmospheric boundary layer in mountainous areas. In the synthetic density field case, the PAET aligns the complex structures precisely within the allowable range of measurement accuracy. For the experimental gravity current case, the precisely aligned result is unknown, and the results of PAET are compared with those obtained with the Monte Carlo method, a simulated annealing algorithm, and the gradient descent method; the PAET was found to be the most efficient. This study broaches the PAET as a versatile method for obtaining accurate turbulence statistics in laboratory experiments designed to mimic environmental flows where spatial and temporal inhomogeneities abound.

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Acknowledgements

This research was funded by Office of Naval Research Award # N00014-11-1-0709, Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) Program (QZ and HJSF) and the NSF Grant # AGS-1565535, and the Melchor Chair Endowment (FH) at University of Notre Dame. The author (QZ) was supported by the Joint Fund of State Key Lab of Hydroscience and Institute of Internet of Waters Tsinghua-Ningxia Yinchuan (Grant No. sklhse-2020-Iow06) and the National Natural Science Foundation of China (Grant No. 51809268).

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Authors and Affiliations

  1. College of Water Resources and Civil Engineering, China Agricultural University, Beijing, 100083, China

    Qiang Zhong

  2. Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN, 46556, USA

    Qiang Zhong, Fazle Hussain & Harindra J. S. Fernando

  3. Department of Mechanical Engineering, Texas Tech University, Lubbock, TX, 79409-1021, USA

    Fazle Hussain

  4. Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA

    Harindra J. S. Fernando

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  1. Qiang Zhong
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  2. Fazle Hussain
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  3. Harindra J. S. Fernando
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Correspondence to Qiang Zhong.

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Zhong, Q., Hussain, F. & Fernando, H.J.S. Phase aligned ensemble averaging for environmental flow studies. Environ Fluid Mech 20, 1357–1377 (2020). https://doi.org/10.1007/s10652-020-09771-5

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  • DOI: https://doi.org/10.1007/s10652-020-09771-5

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