Statistical Equilibria of Uniformly Forced Advection Condensation

Jai Sukhatme; Raymond T. Pierrehumbert

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Statistical Equilibria of Uniformly Forced Advection Condensation

Jai Sukhatme·Raymond T. Pierrehumbert

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Abstract

We examine the state of statistical equilibrium attained by a uniformly forced condensable substance subjected to advection in a periodic domain. In particular, we examine the probability density function (\pdf{}) of the condensable substance in the limit of rapid condensation. The constraints imposed by this limit are pointed out and are shown to result in a \pdf{} -- whenever the advecting velocity field admits a diffusive representation -- that features a peak at small values, decays exponentially and terminates in a rapid "roll-off" near saturation. Possible physical implications of this feature as compared to a \pdf{} which continues to decay slowly are pointed out. A set of simple numerical exercises which employ lattice maps for purposes of advection are performed to test these features. Despite the simplicity of the model, the derived \pdf{} is seen to compare favourably with \pdf{}'s constructed from isentropic specific humidity data. Further, structure functions associated with the condensable field are seen to scale anomalously with near saturation of the scaling exponents for high moments -- a feature which agrees with studies of high resolution aircraft data.

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Jai Sukhatme, Raymond T. Pierrehumbert. 2006-06-30. Statistical Equilibria of Uniformly Forced Advection Condensation. https://arxiv.org/abs/nlin/0512039

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