Transitional–turbulent spots and turbulent–turbulent spots in boundary layers

Abstract

Two observations drawn from a thoroughly validated direct numerical simulation of the canonical spatially developing, zero-pressure gradient, smooth, flat-plate boundary layer are presented here. The first is that, for bypass transition in the narrow sense defined herein, we found that the transitional-turbulent spot inception mechanism is analogous to the secondary instability of boundary-layer natural transition, namely a spanwise vortex filament becomes a Λ vortex and then, a hairpin packet. Long streak meandering does occur but usually when a streak is infected by a nearby existing transitionalturbulent spot. Streak waviness and breakdown are, therefore, not the mechanisms for the inception of transitional-turbulent spots found here. Rather, they only facilitate the growth and spreading of existing transitional-turbulent spots. The second observation is the discovery, in the inner layer of the developed turbulent boundary layer, of what we call turbulent-turbulent spots. These turbulent-turbulent spots are dense concentrations of small-scale vortices with high swirling strength originating from hairpin packets. Although structurally quite similar to the transitional-turbulent spots, these turbulent-turbulent spots are generated locally in the fully turbulent environment, and they are persistent with a systematic variation of detection threshold level. They exert indentation, segmentation, and termination on the viscous sublayer streaks, and they coincide with local concentrations of high levels of Reynolds shear stress, enstrophy, and temperature fluctuations. The sublayer streaks seem to be passive and are often simply the rims of the indentation pockets arising from the turbulent-turbulent spots.boundary layer | transition | turbulence | direct numerical simulation T he zero-pressure gradient, smooth, flat-plate boundary layer (ZPGSFPBL) is the simplest viscous external flow. It serves as the idealized limiting case and calibration benchmark of atmospheric and oceanic planetary boundary layers as well as aeronautical, maritime, and automotive boundary-layer flows. For over 60 y since the work by Theodorsen (1), a central theme in fundamental fluid mechanics research has been the search for the constitutive coherent structure in the turbulent ZPGSFPBL, particularly inside the near-wall/inner layer less than ∼100 viscous units away from the plate where the production and dissipation of turbulence kinetic energy reach their peaks (2-6). When the nature of the inner-layer structure and dynamics is thoroughly understood, this understanding can be incorporated in turbulence theory and predictive modeling.Decades of research have produced an apparent consensus view (7-9) that the inner layer, which consists of the buffer layer and the viscous sublayer, of a turbulent ZPGSFPBL is populated by randomly distributed quasistreamwise vortices as well as elongated high-and low-momentum streaks. Streaks are thought to actively participate in a self-sustaining bursting cycle that includes streak generation, lift up, oscil...

The coherent structure of the kinetic energy transfer in shear turbulence

“…Both forward and backward cascades coexist, as seen from the positive and negative regions of Π, although the forward cascade prevails. The spatial distribution of the fluxes is strongly inhomogeneous, with regions of intense energy transfer organised into intermittent spots (Piomelli et al 1991;Domaradzki et al 1993;Cerutti & Meneveau 1998;Aoyama et al 2005;Ishihara et al 2009;Wu et al 2017;Yang & Lozano-Durán 2017). The probability density function (p.d.f.)…”

Turbulence in intermittent transitional boundary layers and in turbulence spots

“…The results from linear theory focus on the early stages of instability, but breakdown is itself nonlinear. Using direct numerical simulations, Wu et al (2017) showed that the formation of turbulence spots involves the deformation of spanwise vorticity filaments into Λ-structures and ultimately hairpin packets. This process bears qualitative similarity with the late stages of breakdown of Tollmien-Schlichting waves in orderly transition, where the formation of Λ-structures and hairpin packets are well established, although the presence of streaks may alter the sizes of these structures (Liu, Zaki & Durbin 2008).…”

Robust features of a turbulent boundary layer subjected to high-intensity free-stream turbulence

“…For instance, free-stream turbulence intensity (u ∞ /U ∞ ) is a dominant factor in promoting laminar-to-turbulent transition of a developing boundary layer, influencing both the start of the transition region and its length (Fransson et al 2005). With direct numerical simulations (DNS), it has been demonstrated that FST also influences streak instabilities (Hack & Zaki 2014) and turbulent spots in bypass transition (Kreilos et al 2016;Wu et al 2017). Furthermore, the DNS of Brandt et al (2004) showed that if u ∞ /U ∞ = 4.7% was fixed, then transition occurred earlier for larger values of the integral length scale in the free-stream (L ∞ ).…”