Large-Scale Flow Structure in Turbulent Poiseuille Flows at Low-Reynolds Numbers

Abstract

Direct numerical simulations of a spectral method are performed to study the turbulent channel flow at the low-Reynolds numbers, where the quasi-laminar and turbulent regions simultaneously appear and form the stripe pattern, which is floated downstream with a constant bulk mean velocity. In the turbulent region, many quasi-streamwise vortical structures are followed by low-speed streaks upstream. In the quasi-laminar region, however, quasi-streamwise vortices are rarely observed, though vortex roll with weak streamwise vorticity is regularly found around the channel centre. The turbulent regions are fixed by subtracting their advection velocity from the mean flow. After being temporarily averaged, turbulence statistics are further averaged over the string direction. As a result, turbulent regions are found to be an interface between upwind high-speed fluids and downwind low-speed fluids, where the flow is redirected into the spanwise direction. We investigate the detailed flow structure of the striped turbulent region using the linear vorticity equations.

Flow Statistics in the Transitional Regime of Plane Channel Flow

“…Below the stripe pattern eventually breaks up to form independent turbulent bands of finite length, all parallel to each other [ 34 ], as shown in Figure 2 e for . The new resulting pattern as a whole shows negligible spanwise advection, while it propagates in x with a velocity close to [ 42 ]. The independent turbulent bands show enhanced motility in both directions x and z .…”

Statistical transition to turbulence in plane channel flow

“…In flow geometries with one confined and two extended directions, turbulent-laminar intermittency takes a more complex form that is dominated by turbulent bands which are oriented obliquely to the flow direction. Examples of such flows are Taylor-Couette flow [14][15][16][17][18][19][20], plane Couette flow [20,21], plane channel flow [22][23][24], and a free-slip version of plane Couette flow called Waleffe flow [25,26]. In terms of large-scale phenomena, one views these systems as two dimensional (2D).…”

Experimental measurements in plane Couette–Poiseuille flow: dynamics of the large- and small-scale flow

“…The second and third rows correspond to the small-and large-scale flows calculated by filtering instantaneous spatial two-dimensional FFT spectra, in the same way as in figures 8 and 9. In addition, in the second and third rows we superpose the vector fields of the large-scale flow to better illustrate its direction, similar to Barkley & Tuckerman (2007), Fukudome & Iida (2012) and Duguet & Schlatter (2013). The structure of the large-scale flow for a self-sustained spot in figure 18(e, f ) is similar to Re = 520 shown in figure 9.…”

“…In fact, oblique bands have been observed for a large number of shear flow examples, such as plane Couette (Prigent et al 2002(Prigent et al , 2003Barkley & Tuckerman 2005Duguet, Schlatter & Henningson 2010;Philip & Manneville 2011;Tuckerman & Barkley 2011;Lu et al 2019), plane Poiseuille (Tsukahara et al 2005;Hashimoto et al 2009;Fukudome, Iida & Nagano 2010;Fukudome & Iida 2012;Tuckerman et al 2014;Xiong et al 2015;Horii et al 2017;Tao, Eckhardt & Xiong 2018;Shimizu & Manneville 2019;Gomé, Tuckerman & Barkley 2020;Xiao & Song 2020), plane Couette-Poiseuille , Taylor-Couette (Coles 1965;Hegseth et al 1989), Taylor-Dean (Mutabazi et al 1990) and annular Poiseuille (Ishida, Duguet & Tsukahara 2016, 2017b flows. The same organization persists if the system is subjected to rotation (Tsukahara, Tillmark & Alfredsson 2010), rotation combined with stratification (Deusebio et al 2014), wall roughness (Ishida et al 2017a) and other effects as well (Brethouwer, Duguet & Schlatter 2012).…”