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Gradient-Based Similarity in the Stable Atmospheric Boundary Layer

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Achievements, History and Challenges in Geophysics

Part of the book series: GeoPlanet: Earth and Planetary Sciences ((GEPS))

Abstract

A structure of the stably-stratified atmospheric boundary layer is examined in terms of a novel gradient-based similarity theory. The presented approach introduces similarity scales based on the vertical gradient of the potential temperature, contrary to the traditional method, which is based on momentum and temperature fluxes. The length scale, defined using the semi-empirical form of the mixing length, is demonstrated to be effective in the entire stable boundary layer. In more complex cases, an alternative formulation of the mixing length, based on vertical velocity or temperature variances, can be employed. The empirical similarity functions of the Richardson number are expressed in analytical form, valid in the entire stable boundary layer. The introduced similarity approach allows for evaluating the minimum values of the dimensionless turbulent heat flux and the temperature standard deviation as functions of the Richardson number. It can also be used as a closure scheme for a single column model.

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Acknowledgements

The work has been supported by the US National Science Foundation grant ATM-0938293, and by the Polish National Science Centre grant 0572/B/P01/2011/40.

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Authors and Affiliations

  1. Institute of Geophysics, Polish Academy of Sciences, Warsaw, Poland

    Zbigniew Sorbjan

  2. Department of Physics, Marquette University, Milwaukee, USA

    Zbigniew Sorbjan

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  1. Zbigniew Sorbjan
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Correspondence to Zbigniew Sorbjan .

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Editors and Affiliations

  1. Department of Hydrology and Hydrodynamics, Institute of Geophysics, Polish Academy of Sciences, Warszawa, Mazowieckie, Poland

    Robert Bialik

  2. Department of the Lithospheric Research, Institute of Geophysics, Polish Academy of Sciences, Warsaw, Mazowieckie, Poland

    Mariusz Majdański

  3. Department of Polar Research, Institute of Geophysics, Polish Academy of Sciences, Warsaw, Mazowieckie, Poland

    Mateusz Moskalik

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Sorbjan, Z. (2014). Gradient-Based Similarity in the Stable Atmospheric Boundary Layer. In: Bialik, R., Majdański, M., Moskalik, M. (eds) Achievements, History and Challenges in Geophysics. GeoPlanet: Earth and Planetary Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-07599-0_20

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