Taylor's hypothesis in turbulent channel flow considered using a transport equation analysis
Direct numerical simulations of turbulent channel flow at Re-tau = 205 and 932 have been carried out to examine Taylor's "frozen turbulence" hypothesis. The terms in Taylor's hypothesis appear in the transport equation for instantaneous momentum (Navier-Stokes) in this flow. The additional terms, i.e., the additional convective acceleration term and the pressure gradient and viscous force terms, act to diminish the validity of Taylor's hypothesis when they are relatively large compared to the Taylor's hypothesis terms and are not in balance. A similar analysis has been applied to the transport equation for instantaneous vorticity. The additional terms in this equation, namely, the additional convective rates of change of vorticity terms, the stretching/compression/rotation of vorticity terms, and the viscous diffusion of vorticity terms, similarly act to diminish the validity of Taylor's hypothesis when they are relatively large compared to the terms in the hypothesis and are not in balance. Where in the channel flow this diminishment occurs, and to what degree, and which of the non-Taylor's hypothesis terms in the momentum and vorticity equations contribute most to this diminishment are unraveled here.
This research was supported by the Institute of Mechanics of the Chinese Academy of Science during the visit of J.M.W. in October 2013, and by the Burgers Program for Fluid Dynamics of the University of Maryland. Support was also provided by the National Natural Science Foundation of China under Project Nos. 11232011 (Key project) and 11021262 (Innovative team) and by the National Basic Research Program of China (973 Program) under Project No. 2013CB834100 (Nonlinear science).
Geng, CH,He GW,Wang, YS,et al. Taylor's hypothesis in turbulent channel flow considered using a transport equation analysis[J]. PHYSICS OF FLUIDS,2015-02,27(2):25111.