Propagating Structures in Wall-Bounded Turbulent Flows

Abstract

The Karhunen-Loeve (K-L) procedure for generating the empirical eigenfunctions is used to analyze two turbulent channel flow simulations of different geometry and origins. In one instance the Reynolds number Re_T based on wall shear velocity, u _r, and channel halfwidth, δ, is 80 and in the second instance Re_T = 125. The latter case showed a well defined log-layer, while this was absent in the former case. According to accepted convention, the turbulence is said to be continuous when Re_r = 80, and fully developed when Re_r = 125. In both instances the empirical eigenfunctions reveal the presence of propagating plane wave structures. Thus the contrasts in the two cases is of some importance since they virtually eliminate the possibility that the waves are artifacts.

In addition to the propagating structures the K-L analysis reveals a complimentary set of modes (non-propagating) which can be identified with the streaks that are found in wall bounded turbulence. The energy contained in the propagating structures is relatively small compared to that contained in the remaining streaky modes. Nevertheless the waves are shown to play an essential role in the local production of turbulence via bursting and sweeping.

The full text of this paper is to appear inTheoretical & Computational Fluid Dynamics