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COMPOSITE EXPANSION OF ACTIVE AND INACTIVE MOTIONS OF THE STREAMWISE REYNOLDS STRESS

Ronald L. Panton
Mechanical Engineering Department University of Texas Austin, TX 78712

Abstract

Fluctuations of the streamwise velocity are considered as a sum of active and inactive parts. The active and inactive components of the streamwise Reynolds stress are assumed to scale differently. Because the active motions produce Reynolds shear stress, the active component is further assumed to be proportional to the Reynolds shear stress. This allows DNS data can be used to compute the inactive component. A model of the inactive motion in the inner and outer layers is proposed and a composite expansion formulated. The composite expansion of the inactive component, together with a previous composite expansion of the Reynolds shear stress, allows the streamwise Reynolds stress to be predicted as a function of wall distance and Reynolds number. According to the model the streamwise Reynolds stress is dominated by the inactive component. This domination increases as the Reynolds number increases.