Turbulent-turbulent Spot across the Buffer Layer of the Turbulent Zero-pressure-gradient Flat-plate Boundary Layer

We define turbulent-turbulent spot as a local concentration of vortices with high level of swirling strength originating from hairpin packet in a turbulent boundary layer. We also define bypass transition in the narrow sense as the breakdown of the Blasius boundary layer beneath freestream homogeneous isotropic turbulence with an initial amplitude of 1 to 4 percent. We present evidence for the existence and plurality of turbulent-turbulent spots across the buffer layer within the first 100 wall units. Infant/young turbulent-turbulent spot is a hairpin packet, more matured ones are a mixture of hairpin vortices and random vortex filaments. Although structurally analogous to the transitional-turbulent spots, these turbulent-turbulent spots are nevertheless generated locally in the chaotic fully-turbulent environment instead of being transported from the far-upstream transition, and they are robust with the variation of detection threshold. Viscous sublayer streaks are strongly indented, segmented and often terminated by the turbulent-turbulent spots. Evidence is extracted from our spatiallydeveloping direct simulation, which carries the inlet Blasius boundary layer through a bypass transition (in the narrow sense) arriving at the canonical turbulent boundary layer state over a moderate Reynolds number range. The present results seem to be at odds with the widely-held belief that the buffer layer is dominated by random quasi-streamwise vortices. Accuracy of the direct simulation statistics is demonstrated by comparing with established turbulent boundary layer measurements. For the present bypass transition in the narrow sense at 3 percent inlet freestream turbulence intensity, we also found that the transitional turbulent spot inception mechanism and laminar boundary layer breakdown process is analogous to the secondary instability of boundary layer natural transition. Long streak meandering does occur, but in our flow it mostly happens when a streak is in the vicinity of an existing transitional-turbulent spot. Streak meandering and breakdown is therefore not the mechanism for the inception of transitional turbulent spot, but only facilitates the growth and spreading of existing transitional-turbulent spots. INTRODUCTION One of the corner-stones of modern fluid mechanical science is the incompressible flow over a smooth flat-plate at zero pressuregradient (canonical boundary layer), which forms the limiting case and calibration benchmark of many practical aeronautical engineering flows. Starting from a Blasius boundary layer, there are numerous ways of generating the downstream transitional and turbulent boundary layers. The most fundamental route, natural transition, is that the layer being subjected to infinitesimal disturbances in the sense of Schubauer & Skramstad [1], who verified through experiments the existence of TollmienSchlichting wave predicted by linear stability theory. The second most fundamental route, bypass transition in the narrow sense, is a superposition of the canonical boundary layer, in its freestream, with the simplest possible turbulent flow – initially homogeneous isotropic turbulence of (mildly) finite amplitude. There is a pronounced plurality of this case compared to the case of natural transition since the length-scale and intensity of the isotropic grid turbulence participating in the superposition are the extra independent variables. Westin et al. [2] pointed out the need for creating “standard” conditions in transition experiments, and mentioned that if the freestream turbulence intensity (FST) level is larger than 5% transition will be rapid and occurs at the minimum Reynolds number for self-sustained boundary layer turbulence to exist. It is also obvious that for boundary layers with very high FST level, e.g., 5%, the superposition will severely distort the basic boundary layer profile right at the inlet. For purposes of investigating mechanisms of bypass transition in the narrow sense, it has been accepted to only consider a narrow FST window between approximately 1% and 4% at the leading edge. The lower threshold 1% is chosen so that the Tollmien-Schlichting wave will not be the dominant mechanism. One important piece of experimental result from Westin et al. is confirming, for bypass transitional flows in the narrow sense, a quasi-linear dependence of squared peak streamwise turbulence intensity with streamwise distance. This linearity is an important result of the “algebraic/transient growth” theory, see Anderson et al [3]. Matsubara and Alfredsson [4] extended the experiments of Westin et al. [2] by varying leading edge freestream turbulent intensity