Helicity distributions and transfer in turbulent channel flows with streamwise rotation

Abstract

Helicity is a quadratic inviscid conservative quantity in three-dimensional turbulent flows and is crucial for turbulent system evolution. Helicity effects have mainly been highlighted over the past few decades to explore the intrinsic mechanism of turbulent flows, while the statistical characteristics of helicity itself are nearly absent in general anisotropic turbulent flows. In this paper, we investigate the helicity statistics in turbulent channel flows with streamwise rotation at moderate rotation numbers ( $Ro_{\tau }=7.5,15$ and 30) and Reynolds numbers ( $Re_{\tau }=180$ and 395), including their spatial and scale distributions, anisotropy and cross-scale transfer. The appearance of a mean secondary flow in the spanwise direction corresponds to a mean streamwise vorticity, which indicates the presence of a high-helicity distribution. Numerical results reveal a regular helicity profile along the wall-normal direction, and a new peak is found in the near-wall region around $y^+=6$ of the streamwise or spanwise helicity profiles. The inter-scale helicity transfer is analysed by the filtering method, and the numerical consequences reveal that the second channel of the helicity cascade we proposed previously is dominant in contrast to the first channel. The rotation effects are explored by comparing the numerical results obtained under different rotation numbers. With increasing rotation number, more helical structures in the near-wall regions are present, with peaks of helicity profiles and fluxes coming closer to the wall. With a higher Reynolds number, their amplitudes are larger and scale-space transfer is strengthened. These systematic numerical analyses uncover the helicity distributions and transfer in wall-bounded turbulent flows.

Multiscale dynamics in streamwise-rotating channel turbulence

“…Our DNS data include five cases, in which Ro τ ranges from 0 to 60 and Re τ = 180 or 395. Except for ST30S and ST60S, the computational domains of the cases are selected based on the third criterion of , which has been verified by Yu et al (2022). Cases ST30S and ST60S have relatively small streamwise sizes.…”

“…Except for ST30S and ST60S, the computational domains of the cases are selected based on the third criterion of Yang & Wang (2018), which has been verified by Yu et al. (2022). Cases ST30S and ST60S have relatively small streamwise sizes.…”

“…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.…”

Effects of streamwise rotation on helicity and vortex in channel turbulence

“…introduced the HWD in this flow and investigated the transfer process in the whole domain. 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).…”

New exact Betchov-like relation for the helicity flux in homogeneous turbulence

“…In a rotationally invariant ensemble, it is connected to the breaking of the symmetry under inversion of all axes. Inspired by its relevance to turbulence in atmospheric flows (Lilly 1986), dynamical and statistical effects connected with helicity have been studied in the atmospheric boundary layer (Deusebio & Lindborg 2014) and in rotating turbulence (Mininni & Pouquet 2010a,b), and more generally in homogeneous and isotropic turbulence (Chen, Chen & Eyink 2003a;Chen et al 2003b;Gledzer & Chkhetiani 2015;Kessar et al 2015;Sahoo, Bonaccorso & Biferale 2015;Stepanov et al 2015;Alexakis 2017;Sahoo, Alexakis & Biferale 2017;Yan et al 2020;Milanese, Loureiro & Boldyrev 2021), as well as shear flows (Yan et al 2020;Yu et al 2022) and in laboratory experiments (Scheeler et al 2017).…”