DNS OF STRIPE PATTERN IN POISEUILLE FLOW AT VERY LOW REYNOLDS NUMBER

Direct numerical simulations (DNSs) of a spectral method were performed to study the turbulent structure in a transitional regime in Poiseuille flow. A computational domain tilted towards the streamwise direction was adopted at a high aspect ratio. Though the simulations, turbulent stripes consisting of turbulent and quasilaminar regions were obtained for various values of the angle θ of the stripe with respect to the streamwise direction. The flow rate in the streamwise direction attained a local minimum at θ = 20°, although the flow rate in the spanwise direction attained a maximum at this angle. Moreover, the stripe at θ = 20° became temporally steady for least t < 2800 without lateral spreading. Both the widths and intervals of the turbulent regions are well normalized by the streamwise distance at θ = 10–35°. Furthermore, the width of the turbulent region measured perpendicular to the stripe at θ = 20° is consistent with the highly dissipating region in the homogeneous flow at a very high Reynolds number. INTRODUCTION In the transitional regime, the flow is known to be spatially intermittent, consisting of turbulent and quasilaminar regions. A turbulent stripe is one of the intermittent flow structures in which the turbulent and quasilaminar regions are alternately arrayed in the streamwise and spanwise directions and form a stripe pattern. The turbulent stripe was firstly discovered in the experimental study of Taylor–Couette flow by Coles (1965, 1966). Then, stripes were experimentally observed in a Couette flow by Prigent et al. (2002) and studied numerically by Barkley (2005); similarly, stripes were numerically studied in a Poiseuille flow by Tsukahara et al. (2005, 2007) and experimentally observed (Tsukahara et al., 2010a, Seki et al., 2010, 2012). Additionally, a similar stripe was also found in a torsional Couette flow by Cros et al. (2002). Therefore, turbulent stripes are a common flow state in a flow bounded by parallel walls at the transitional Reynolds number. Further, the turbulent structures of the stripes in various shear flows are common; for instance, the turbulent region evolves many vortical structures, and highand low-speed fluids are distributed upwind and downwind in turbulent regions, respectively. In Poiseuille flow, Iida and Nagano (1998) carried out DNSs of Poiseuille flows in the transitional regime in a small computational domain and found temporal oscillations in the flow rates and friction coefficients. Although they could not capture the turbulent stripe because of their small computational domain, Tsukahara et al. (2005, 2006, 2007) carried out DNSs a large computational domain, captured the stripe structure, and studied the mean structure of the stripes inclined at 21° with respect to the streamwise direction in a very huge computational domain. Duguet et al. (2010) studied the appearance of turbulent stripes in Couette flows and concluded that a stripe was obtained from both a single point disturbance and a homogeneous disturbance, such that turbulent stripes appear naturally and generally. Philip and Manneville (2011) clarified that the turbulent stripes and the temporal evolution in Couette flows were affected by the computational domain. Manneville (2011, 2012) observed the development and decay of turbulent stripes in Couette flows by changing the Reynolds number by numerical simulation. Fukudome and Iida (2012) also clarified the turbulent stripe in Poiseuille flows and suggested the sustaining mechanism for which the tilting of the mean shear is important. Duguet et al. (2013) also suggested the maintaining mechanism and mathematical models for the stripe. On the other hand, a turbulent stripe was observed at much higher Reynolds numbers with the addition of a stable body force and confirmed by Tsukahara et al. (2010b) and Brethouwer et al. (2013). According to previous research, the turbulent stripes in various shear flows have a common feature in that the stripes incline towards the spanwise direction from the streamwise direction, and the turbulent regions are sandwiched by highand low-speed fluid on the upwind and downwind sides. In this study, we performed direct numerical simulations of the Poiseuille flow in the transitional regime to clarify the inclination angle and the space interval of the stripes.