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Generalized Non-dimensional Wind and Temperature Gradients in the Surface Layer

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Abstract

We propose a single generalized function for dimensionless wind and temperature gradients in stable and unstable conditions based on Monin–Obukhov similarity theory. The proposed function may be matched with the currently accepted universal functions for the dimensionless wind-speed and temperature gradients using the empirical coefficients a and b to yield differences within ± 14% for both wind and temperature gradients in the interval of \(-2\) < z/L < 0.5 (z is height and L is the Obukhov length). In neutral conditions, wind and temperature profiles are the same as the standard log-law profile. Under unstable conditions, the differences are smaller than 1.5%; conversely, under stable conditions, the differences reach up to \(-~5.2\)%. The coefficients a and b are analyzed here to evaluate the limits of this proposed semi-empirical function and possible physical characteristics are discussed. Although we use the same theoretical assumptions and limitations of Monin–Obukhov similarity theory in the surface layer, the proposed function has the flexibility of adjusting the wind and temperature gradients for specific sites using the empirical coefficients a and b within the range 0–1, with stable and unstable conditions able to be described by a single general function.

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Acknowledgements

The authors wish to acknowledge the support of the Brazilian Electricity Regulatory Agency (ANEEL) under the project 0403-0020/2011, funded by ENGIE Brasil Energia Company. Particular thanks to Frederico F. Taves for his collaborations in this project and Pedro Santos for reviewing the manuscript and the deep discussions that contributed to improve this paper. Furthermore, we thank the many colleagues who gave us many suggestions by email, and the three anonymous reviewers for their valuable time and wise comments that significantly improved the manuscript.

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Authors and Affiliations

  1. Department of Health and Service, Federal Institute of Santa Catarina, Florianópolis, Brazil

    Yoshiaki Sakagami

  2. Department of Physics, Federal University of Santa Catarina, Florianópolis, Brazil

    Reinaldo Haas

  3. Department of Mechanical Engineering, Federal University of Santa Catarina, Florianópolis, Brazil

    Júlio César Passos

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  1. Yoshiaki Sakagami
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  2. Reinaldo Haas
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  3. Júlio César Passos
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Correspondence to Yoshiaki Sakagami.

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Sakagami, Y., Haas, R. & Passos, J.C. Generalized Non-dimensional Wind and Temperature Gradients in the Surface Layer. Boundary-Layer Meteorol 175, 441–451 (2020). https://doi.org/10.1007/s10546-020-00510-3

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