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Radiation, evaporation and the maintenance of turbulence under stable conditions in the lower atmosphere

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Abstract

An expression is derived relating the critical flux Richardson number with the critical (gradient) Richardson number. In contrast to an earlier analysis by Townsend (1958), which is restricted to the atmosphere well outside the earth's boundary layer, the present treatment is intended specifically for turbulent flow in the lower atmosphere and it takes account of the effect of evaporation on the stability. The effect of radiation on the rate of destruction of the mean square of the temperature fluctuations is obtained by considering the radiative flux divergence in a stratified atmosphere and by using a simple functional relationship to represent empirical emissivity data.

It was found that evaporation and radiation increase the critical Richardson number by a sensible amount depending on the atmospheric conditions, mainly temperature, humidity and the gradients. There is no definite critical Richardson number but rather a range between 0.25, below which turbulence is very likely, and somewhat higher than 0.5, above which turbulence is improbable. The value of the critical Richardson number can be expressed in terms of evaporation, radiation and the ratio (σ w /u *) which also appears not to have a definite critical value. Evaporation and radiation cause the ratio (σ w /u *) to be larger than unity under neutral conditions. These results, based on the assumption of Reynolds' analogy,K H =K M, are consistent with the available experimental evidence.

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  1. Cornell University, Ithaca, N.Y., USA

    Wilfried Brutsaert

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Brutsaert, W. Radiation, evaporation and the maintenance of turbulence under stable conditions in the lower atmosphere. Boundary-Layer Meteorol 2, 309–325 (1972). https://doi.org/10.1007/BF02184772

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