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    Forecasting Reynolds and Nusselt numbers in turbulent thermal convection using modified Grossmann-Lohse model

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    Type
    Preprint
    Authors
    Bhattacharya, Shashwat
    Verma, Mahendra K.
    Samtaney, Ravi cc
    KAUST Department
    Fluid and Plasma Simulation Group (FPS)
    Mechanical Engineering Program
    Physical Science and Engineering (PSE) Division
    Date
    2020-07-19
    Permanent link to this record
    http://hdl.handle.net/10754/664436
    
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    Abstract
    In this paper, we revise Grossmann and Lohse's model [Phys. Rev. Lett. 86, 3316 (2001)] for the predictions of Reynolds number (Re) and Nusselt number (Nu) in turbulent Rayleigh-B\'{e}nard convection (RBC). The revision incorporates two anomalies observed in thermal convection: the viscous and thermal dissipation rates in the bulk are suppressed compared to free turbulence, and the viscous boundary layer profile deviates from Prandtl-Blasius theory. We perform 60 numerical runs on a three-dimensional unit box for range of Rayleigh numbers (Ra) and Prandtl numbers (Pr) and construct the revised model using four free constants (more appropriately, functions) that are determined using machine learning. The predictions of the revised model are in good agreement with the past numerical and experimental results, and they are sometimes better than those of Grossmann and Lohse's model.
    Sponsors
    The authors thank Arnab Bhattacharya, K. R. Sreenivasan, J¨org Schumacher, and Ambrish Pandey for useful discussions. The authors acknowledge Roshan Samuel, Ali Asad, Soumyadeep Chatterjee, and Syed Fahad Anwer for their contributions to the development of the finite-difference solver SARAS. Our numerical simulations were performed on Shaheen II of Kaust supercomputing laboratory, Saudi Arabia (under the project k1416) and on HPC2013 of IIT Kanpur, India.
    Publisher
    arXiv
    arXiv
    2007.09583
    Additional Links
    https://arxiv.org/pdf/2007.09583
    Collections
    Preprints; Physical Science and Engineering (PSE) Division; Mechanical Engineering Program

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