Non-universal scaling transition of momentum cascade in wall turbulence. (24th May 2019)

• Record Type: Journal Article
• Authors: Chen, Xi; Hussain, Fazle; She, Zhen-Su
• Is Part Of: Journal of fluid mechanics. Volume 871(2019)
• Publication Date: 2019-05-24
• Subjects: turbulence theory; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2019.309
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract : As a counterpart of energy cascade, turbulent momentum cascade (TMC) in the wall-normal direction is important for understanding wall turbulence. Here, we report an analytic prediction of non-universal Reynolds number ( $Re_{\unicode[STIX]{x1D70F}}$ ) scaling transition of the maximum TMC located at $y_{p}$ . We show that in viscous units, $y_{p}^{+}$ (and $1+\overline{u^{\prime }v^{\prime }}_{p}^{+}$ ) displays a scaling transition from $Re_{\unicode[STIX]{x1D70F}}^{3/7}$ ( $Re_{\unicode[STIX]{x1D70F}}^{-6/7}$ ) to $Re_{\unicode[STIX]{x1D70F}}^{3/5}$ ( $Re_{\unicode[STIX]{x1D70F}}^{-3/5}$ ) in turbulent boundary layer, in sharp contrast to that from $Re_{\unicode[STIX]{x1D70F}}^{1/3}$ ( $Re_{\unicode[STIX]{x1D70F}}^{-2/3}$ ) to $Re_{\unicode[STIX]{x1D70F}}^{1/2}$ ( $Re_{\unicode[STIX]{x1D70F}}^{-1/2}$ ) in a channel/pipe, countering the prevailing view of a single universal near-wall scaling. This scaling transition reflects different near-wall motions in the buffer layer for small $Re_{\unicode[STIX]{x1D70F}}$ and log layer for large $Re_{\unicode[STIX]{x1D70F}}$, with the non-universality being ascribed to the presence/absence of mean wall-normal velocity $V$ . Our predictions are validated by a large set of data, and a probable flow state with a full coupling between momentum and energy cascades beyond a critical $Re_{\unicode[STIX]{x1D70F}}$ is envisaged.