Energy transport in the spectral space is analyzed to study the mechanism underlying the Taylor-Görtler-like (TGL) vortices that appear as two layers of streamwise-elongated roll cells in a turbulent channel flow subjected to fast streamwise system rotation. The transport equation of the velocity-spectrum tensor in a rotating frame is derived to study the budget balance of energy spectra at different length scales. Two new terms, namely, the rotation-induced redistribution term and rotation-induced wall-normal diffusion term, are defined to reflect the effect of the imposed system rotation on the energy transport process. By analyzing the data obtained from direct numerical simulation, it is discovered that four key processes are responsible for sustaining the motion of the TGL vortices. The first process corresponds to the energy production at the characteristic length scales of the TGL vortices that drains energy from the mean flow to the TGL vortices. The second process is the rotation-induced energy redistribution from the streamwise velocity fluctuations to the wall-normal and spanwise velocity fluctuations that form the vortex structures on a cross-stream plane. The third process is the energy diffusion from the near-wall region to the channel center, which is enhanced due to the occurrence of the TGL vortices and, in turn, feeds energy to the vortices. The last process is the inverse interscale energy transfer, through which the large-scale TGL vortices absorb energy from small-scale eddies.
Bibliographical noteFunding Information:
This research was supported by NSFC Basic Science Center Program for “Multiscale Problems in Nonlinear Mechanics” (Grant No. 11988102). Z.Y. would like to thank the LiXing research funding of the Institute of Mechanics, Chinese Academy of Sciences. Research funding from the Natural Sciences and Engineering Research Council (NSERC) of Canada to B.-C.W. is gratefully acknowledged. The National Supercomputer Center in Tianjin is acknowledged for access to supercomputing and storage facilities.
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