Article Type:
Research Article

A Refinement of the Millionshchikov Quasi-Normality Hypothesis for Convective Boundary Layer Turbulence

Vladimir M. Gryanik Alfred Wegener Institute for Polar and Marine Research, Bremerhaven, Germany, and A. M. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Moscow, Russia

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Jörg Hartmann Alfred Wegener Institute for Polar and Marine Research, Bremerhaven, Germany

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Siegfried Raasch University of Hannover, Hannover, Germany

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Michael Schröter University of Hannover, Hannover, Germany

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Print Publication:
01 Jul 2005
DOI:
https://doi.org/10.1175/JAS3457.1
Page(s):
2632–2638
Restricted access

Abstract

The Millionshchikov hypothesis of quasi-normal distribution of fourth-order moments fails for convective conditions where the probability density functions of temperature and vertical velocity fluctuations are skewed. This is shown for aircraft and large-eddy simulation (LES) data, and new closures for fourth-order moments that take the skewness into account are suggested. These new closures are in very good agreement with the data.

Corresponding author address: Dr. Jörg Hartmann, Alfred Wegener Institute for Polar and Marine Research, Postfach 12 0161, Bremerhaven 27515, Germany. Email: jhartmann@awi-bremerhaven.de

Abstract

The Millionshchikov hypothesis of quasi-normal distribution of fourth-order moments fails for convective conditions where the probability density functions of temperature and vertical velocity fluctuations are skewed. This is shown for aircraft and large-eddy simulation (LES) data, and new closures for fourth-order moments that take the skewness into account are suggested. These new closures are in very good agreement with the data.

Corresponding author address: Dr. Jörg Hartmann, Alfred Wegener Institute for Polar and Marine Research, Postfach 12 0161, Bremerhaven 27515, Germany. Email: jhartmann@awi-bremerhaven.de

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