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ON THE DISSIPATION RATE COEFFICIENT IN HOMOGENEOUS ISOTROPIC DECAYING AND FORCED TURBULENCE

Philip Schaefer
Department of Combustion Technology RWTH Aachen University Templergraben 64, 52056 Aachen, Germany

Markus Gampert
Department of Combustion Technology RWTH Aachen University Templergraben 64, 52056 Aachen, Germany

Norbert Peters
Department of Combustion Technology RWTH Aachen University Templergraben 64, 52056 Aachen, Germany

Abstract

The normalized non-dimensional von Karman-Howarth equation for isotropic homogeneous decaying and forced steady turbulence is integrated to obtain expressions for the dissipation rate coefficient Cε = (Lε)/〈u23/2, where L denotes the longitudinal integral length scale, e the mean dissipation rate and 〈u2〉 the mean variance of the longitudinal velocity fluctuations. For decaying turbulence the final exact expressions for Cε for the low and high Reynolds number limit depend on the decay exponent n, which is known to depend on the initial velocity structure at the turbulence production. The dependence on n leads to a non-universal coefficient. The expressions for the steady forced case depend on the forcing mechanism and thus are not universal either. Nonetheless, a lower value and considerably less scatter as compared to the decaying turbulence case should be expected when similiar forcing algorithms are employed.