Coherent structure generation in near-wall turbulence

Abstract

We present a new mechanism for generation of near-wall streamwise vortices -which dominate turbulence phenomena in boundary layers -using linear perturbation analysis and direct numerical simulations of turbulent channel flow. The base flow, consisting of the mean velocity profile and low-speed streaks (free from any initial vortices), is shown to be linearly unstable to sinuous normal modes only for relatively strong streaks, i.e. for wall inclination angles of streak vortex lines exceeding 50• . Analysis of streaks extracted from fully developed near-wall turbulence indicates that about 20% of streak regions in the buffer layer exceed the strength threshold for instability. More importantly, these unstable streaks exhibit only moderate (twofold) normalmode amplification, the growth being arrested by self-annihilation of streak-flank normal vorticity due to viscous cross-diffusion. We present here an alternative, streak transient growth (STG) mechanism, capable of producing much larger (tenfold) linear amplification of x-dependent disturbances. Note the distinction of STG -responsible for perturbation growth on a streak velocity distribution U(y, z) -from prior transient growth analyses of the (streakless) mean velocity U(y). We reveal that streamwise vortices are generated from the more numerous normal-mode-stable streaks, via a new STG-based scenario: (i) transient growth of perturbations leading to formation of a sheet of streamwise vorticity ω x (by a 'shearing' mechanism of vorticity generation), (ii) growth of sinuous streak waviness and hence ∂u/∂x as STG reaches nonlinear amplitude, and (iii) the ω x sheet's collapse via stretching by ∂u/∂x (rather than rollup) into streamwise vortices. Significantly, the three-dimensional features of the (instantaneous) streamwise vortices of x-alternating sign generated by STG agree well with the (ensemble-averaged) coherent structures educed from fully turbulent flow. The STGinduced formation of internal shear layers, along with quadrant Reynolds stresses and other turbulence measures, also agree well with fully developed turbulence. Results indicate the prominent -possibly dominant -role of this new, transient-growth-based vortex generation scenario, and suggest interesting possibilities for robust control of drag and heat transfer.

Opposition control within the resolvent analysis framework

“…Of particular importance has been the recognition that linear mechanisms play a key role in controlling the transition to turbulence at low Reynolds number (Trefethen et al 1993;Henningson & Reddy 1994), as well as generating and sustaining the dynamically important coherent structures that characterize wall turbulence (e.g. Butler & Farrell 1993;Schoppa & Hussain 2002;Kim 2011). As a result, the application of concepts from control theory has led to the design of many successful control strategies that delay the onset of turbulence (Joshi, Speyer & Kim 1997), relaminarize turbulent flows (Högberg, Bewley & Henningson 2003;Sharma et al 2011), or reduce turbulent kinetic energy (Lim & Kim 2004).…”

Wave-induced coherent turbulence structures and sediment resuspension in the nearshore of a prototype-scale sandy barrier beach

“…This is evident in the turbulent "bursting" process (Kline et al, 1967; Kline, 1974, 1975), which is a critical mechanism for production of turbulent kinetic energy (Dey et al, 2012;Schoppa and Hussain, 2002). Turbulent bursting may be explained by the advection of spatially distributed vortices and structural features past a fixed point of measurement (Robinson, 1991), although this may not detect how such vortices evolve in time (Schoppa and Hussain, 2002).…”

“…Besides the "conventional" bursting events which describe the intermittent, energetic process resulting from the passage of near-wall vortices as perceived by passive markers and/or visualisation studies (Schoppa and Hussain, 2002); one may identify vortices induced by wave breaking (Aagaard and Hughes, 2010), or by flow separation from vortex ripples upon reversal in an oscillatory flow, i.e. vortex entrainment/shedding (Amoudry et al, 2013).…”

Coherent structures in statistically stationary homogeneous shear turbulence

“…On average, Q2s and Q4s in channels form spanwise pairs located at the interface between high-and low-velocity streaks. The flow field conditioned to these pairs includes a central longitudinal large-scale roller (LFJ12; Jiménez 2013b), reminiscent of the average arrangement of streaks and quasi-streamwise vortices in the buffer layer (Robinson 1991;Jiménez & Pinelli 1999;Schoppa & Hussain 2002). Vortex clusters are also located on average between the two Qs, closer to the Q2.…”

“…This is reasonable, since they have to draw their energy from the local velocity difference, and has been mentioned often in the context of vortical structures (see, for example, Adrian 2007). These high-shear regions can be interpreted as the sharp interfaces between relatively uniform streamwise-velocity streaks, which are known to be layers of high activity both in the buffer region (Kim, Moin & Moser 1987;Jiménez & Pinelli 1999;Schoppa & Hussain 2002) and in the logarithmic layer (Meinhart & Adrian 1995;Flores & Jiménez 2006). In the buffer layer, the high shear close to the wall substitutes the horizontal segment of the arch in figure 10, and the attached Qs are only concentrated in the lateral boundaries between low-and high-velocity streaks (although see the enveloping high-velocity streak in figure 12d of LFJ12, and the conditional flow fields in the next section).…”