Helicity budget in turbulent channel flows with streamwise rotation

Abstract

The streamwise rotation effects in turbulent channel flows are reflected not only in the appearance of the secondary flows, but also the weakened streamwise velocity and spanwise vorticity. In this paper, we investigate the secondary flows from three perspectives: the mean spanwise velocity, the mean streamwise vorticity, and combined mean and fluctuating helicity. We found that the combined helicity is also an alternative perspective to characterize the streamwise rotation effect, especially for the secondary flows. The budget equations of the mean and fluctuating helicity in physical space are derived theoretically and analyzed numerically. The streamwise rotation effects on the secondary flows are directly reflected on the pressure and Coriolis terms, which provides an essential source for helicity within the near-wall regions. The production term could be decomposed into two terms, which originate from the momentum and vorticity equations, respectively. The helical stress (velocity-vorticity correlation) originating from the vorticity equation shows a simple profile distribution, and is dominant for the production for the helicity within the near-wall regions. The high helical structures in the core regions can be explained as an intense wall-normal transportation, which transfers produced helicity within the near-wall regions into the core regions.

Effects of streamwise rotation on helicity and vortex in channel turbulence

“…Furthermore, the secondary mean flow is reversed around the channel centre, which has been verified through the stability analysis (Masuda, Fukuda & Nagata 2008) and various direct numerical simulation (DNS) (Yang, Su & Wu 2010; Yang & Wang 2018; Yang et al. 2018; Dai, Huang & Xu 2019; Yan, Li & Yu 2022). Yang et al.…”

“…The streaks, streamwise vortices and hairpin vortices in the non-rotating channel turbulence have been studied by various researchers (Jiménez & Pinelli 1999;Wang, Huang & Xu 2015). In streamwise-rotating channel turbulence, previous studies mainly cared about the large-scale TG vortices Yan et al 2022) and the inclined structures (Dai et al 2019;Hu et al 2023). In this study, the vortices are examined from a relatively microscopic perspective.…”

“…Yu et al (2022) studied the helicity distribution in such a flow and performed simple multiscale analysis related to the dual channel of the helicity cascades. The dual channel process was first found in homogeneous turbulence (Yan et al 2022) and then generalized to the streamwise-rotating channel turbulence by Yu et al (2022). Nevertheless, in streamwise-rotating channel turbulence, the interscale helicity dynamics and their relations with vortices have not been thoroughly studied.…”

“…The dual channel process was first found in homogeneous turbulence (Yan et al. 2022) and then generalized to the streamwise-rotating channel turbulence by Yu et al. (2022).…”

Multiscale dynamics in streamwise-rotating channel turbulence

“…Recently, Yu et al. (2022) and Yan, Li & Yu (2022) discussed the distribution and budget balance of the helicity in streamwise-rotating channel turbulence. In terms of coherent structures, Yang et al.…”