On the modelling of the dissipation rate of turbulent kinetic energy

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Abstract

We consider a relaxation equation for turbulence wavenumber for use in semi-empirical turbulence closures. It is shown that the well-known phenomenological equation for the dissipation rate of turbulent kinetic energy can be related to this relaxation equation as a close approximation of the latter for stably stratified quasi-stationary flows. The proposed approach allows for more physically found definition of the empirical constants and improvement of atmospheric and oceanic boundary layer turbulence closures by using direct numerical and large eddy simulation data to define equilibrium states and relaxation mechanisms.

About the authors

E. V. Mortikov

Lomonosov Moscow State University; Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences

Author for correspondence.
Email: evgeny.mortikov@gmail.com
Russian Federation, 1, Leninskie gory, Moscow, 119991; 8, Gubkina street, Moscow, 119991

A. V. Glazunov

Lomonosov Moscow State University; Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences

Email: evgeny.mortikov@gmail.com
Russian Federation, 1, Leninskie gory, Moscow, 119991; 8, Gubkina street, Moscow, 119991

A. V. Debolskiy

Lomonosov Moscow State University; Obukhov Institute of Atmospheric Physics of the Russian Academy of Sciences

Email: evgeny.mortikov@gmail.com
Russian Federation, 1, Leninskie gory, Moscow, 119991; 3, Pizevsky, Moscow, 119017

V. N. Lykosov

Lomonosov Moscow State University; Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences

Email: evgeny.mortikov@gmail.com

Corresponding Member of the Russian Academy of Sciences

Russian Federation, 1, Leninskie gory, Moscow, 119991; 8, Gubkina street, Moscow, 119991

S. S. Zilitinkevich

Lomonosov Moscow State University; Finnish Meteorological Institute, University of Helsinki; Institute of Applied Physics of the Russian Academy of Sciences

Email: evgeny.mortikov@gmail.com
Russian Federation, 1, Leninskie gory, Moscow, 119991; 1, Erik Palménin square, Helsinki, Finland, FI-00560; 46, Ulyanov street, Nizhny Novgorod, 603950

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