Streak instability in near-wall turbulence revisited

Abstract

The regeneration cycle of streaks and streamwise vortices plays a central role in the sustainment of near-wall turbulence. In particular, the streak breakdown phase in the regeneration cycle is the core process in the formation of the streamwise vortices, but its current understanding is limited particularly in a real turbulent environment. This study is aimed at gaining fundamental insight into the underlying physical mechanism of the streak breakdown in the presence of background turbulent fluctuation. We perform a numerical experiment based on direct numerical simulation, in which streaks are artificially generated by a body forcing computed from previous linear theory. Upon increasing the forcing amplitude, the artificially driven streaks are found to generate an intense fluctuation of the wall-normal and spanwise velocities in a fairly large range of amplitudes. This cross-streamwise velocity fluctuation shows its maximum at λ + x ≈ 200 − 300 (λ + x is the inner-scaled streamwise wavelength), but it only appears for λ + x 3000 − 4000. Further examination with dynamic mode decomposition reveals that the related flow field is composed of sinuous meandering motion of the driven streaks and alternating cross-streamwise velocity structures, clearly reminiscent of sinuousmode streak instability found in previous studies. Finally, it is shown that these structures are reasonably well aligned along the critical layer of the secondary instability, indicating that the surrounding turbulence does not significantly modify the inviscid inflectional mechanism of the streak breakdown via streak instability and/or streak transient growth.

Spectral energetics of a quasilinear approximation in uniform shear turbulence

“…i.e. λ x /λ z = 1 ∼ 3, where λ z is the spanwise length of the streaks observed in a wall-bounded shear flow (Schoppa & Hussain 2002;Park, Hwang & Cossu 2011;Cassinelli, de Giovanetti & Hwang 2017;de Giovanetti, Sung & Hwang 2017). This is also consistent with the work by Sekimoto & Jiménez (2017), where a set of invariant solutions of homogeneous shear turbulence were shown to emerge for A xz = 1.6 − 3.3.…”

“…Hamilton et al 1995;Schoppa & Hussain 2002;Hwang & Bengana 2016), the predominant dynamics at the integral length scale. It has been understood that the self-sustaining process is composed of three substeps: (i) amplification of streamwise elongated streaks by streamwise vortices (Farrell & Ioannou 1993a;Kim & Lim 2000;del Alamo & Jiménez 2006;Cossu et al 2009;Hwang & Cossu 2010a); (ii) instability or transient growth of the amplified streaks (Hamilton et al 1995;Schoppa & Hussain 2002;Cassinelli et al 2017;de Giovanetti et al 2017); and (iii) nonlinear regeneration of streamwise vortices (Hamilton et al 1995;Schoppa & Hussain 2002;Hwang & Bengana 2016). In the QL model the first and second substeps would well be described by (2.8a) and (2.8b), respectively, but the absence of the last term in (2.8b) (or, equivalently, in (3.7b)) would damage the third substep.…”

Causality of energy-containing eddies in wall turbulence

“…The most notable inter-scale causal links arise from |û 1,1 | 2 → |ŵ 1,0 | 2 , and |ŵ 1,0 | 2 → |v 1,1 | 2 . The former is reminiscent of the spanwise flow motions induced by the loss of stability of the streaks, while the latter is consistent with the subsequent meander and breakdown (Swearingen & Blackwelder 1987;Waleffe 1995Waleffe , 1997Kawahara et al 2003;Park et al 2011;Alizard 2015;Cassinelli et al 2017). In contrast with previous studies, our results stem directly from the non-intrusive analysis of the fully non-linear signals and do not rely on a particular linearisation of the equations of motion.…”

Exact coherent states of attached eddies in channel flow

“…(2.2b) corresponds to the socalled 'shift-reflect' symmetry, which is imposed in order to seek an exact coherent state featured with 'sinuous-mode' streak instability. We note that the sinuous-mode streak instability has recently been found as the dominant breakdown mechanism of streaks in the self-sustaining process (Cassinelli et al 2017;de Giovanetti et al 2017). Furthermore, performing a numerical simulation in the minimal flow unit subject to this symmetry was previously found not to yield any significant difference in turbulence statistics from those without this symmetry .…”

“…The self-sustaining process has been firmly understood as the turbulence generation mechanism, which involves a two-way interaction between streaks and quasi-streamwise vortices (Hamilton et al 1995;Waleffe 1997): quasi-streamwise vortices significantly amplify streaks via the 'lift-up' effect (Butler & Farrell 1993;Cossu et al 2009;Pujals et al 2009;Hwang & Cossu 2010a;Willis et al 2010;McKeon & Sharma 2010), and the amplified streaks subsequently regenerate new quasistreamwise vortices via streak instability/transient growth and the following nonlinear mechanisms (Hamilton et al 1995;Schoppa & Hussain 2002;Park et al 2011;Alizard 2015;Cassinelli et al 2017;de Giovanetti et al 2017). Based on this observation, Waleffe (1998Waleffe ( , 2001Waleffe ( , 2003 computed a set of non-trivial (relative) equilibrium solutions of the Navier-Stokes equations by cleverly imposing the exact mathematical balance in the two-way interactions between streaks and quasi-streamwise vortices.…”