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Turbulent Schmidt Number Measurements Over Three-Dimensional Cubic Arrays

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Abstract

We present turbulent Schmidt number (\( Sc_{\text{t}} \)) estimations above three-dimensional urban canopies, where \( Sc_{\text{t}} \) is a property of the flow defined as the ratio of the eddy diffusivity of momentum (\( K_{M} \)) to the eddy diffusivity of mass (\( D_{t} \)). Despite the fact that \( Sc_{t} \) modelling is of great interest, inter alia, for pollutant dispersion simulations conducted via computational fluid dynamics, no universal value is known. Simultaneous measurements of fluid velocity and mass concentration are carried out in a water channel for three staggered arrays of cubical obstacles corresponding to isolated flow, wake-interference, and skimming-flow regimes. A passive tracer is released from a continuous point source located at a height \( z = 1.67H \) where H is the obstacle height. The results show an increase of \( Sc_{\text{t}} \) with height above the canopy for all three arrays, with values at \( z = 2H \) (\( Sc_{t} \approx 0.6 \)) about double compared to that at \( z = H \). The observed \( Sc_{t} \) agrees well with that modelled by using a simple formulation for \( Sc_{t} \) based on expressions for \( K_{M} \) and \( D_{t} \) published in previous studies. Comparisons with other \( Sc_{t} \) models found in the literature are also presented and discussed.

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Acknowledgements

The assistance of Manuel Mastrangelo and Cristina Grossi (Master degree students of the University of Rome “La Sapienza”) to the measurements was greatly appreciated. This research was supported by the RG11715C7D43B2B6 fund from the University of Rome “La Sapienza”.

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Authors and Affiliations

  1. Dipartimento di Fisica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 2, 00185, Rome, Italy

    Annalisa Di Bernardino

  2. DICEA, Università di Roma “La Sapienza”, Via Eudossiana 18, 00184, Rome, Italy

    Paolo Monti & Giovanni Leuzzi

  3. DICAAR, Università degli Studi di Cagliari, Via Marengo 2, 09123, Cagliari, Italy

    Giorgio Querzoli

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  1. Annalisa Di Bernardino
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  2. Paolo Monti
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  3. Giovanni Leuzzi
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  4. Giorgio Querzoli
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Correspondence to Paolo Monti.

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Di Bernardino, A., Monti, P., Leuzzi, G. et al. Turbulent Schmidt Number Measurements Over Three-Dimensional Cubic Arrays. Boundary-Layer Meteorol 174, 231–250 (2020). https://doi.org/10.1007/s10546-019-00482-z

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