Physics of turbulence generation and sustenance in a boundary layer

Abstract

In this paper, a systematic report of our recent DNS study on physics of late boundary layer transition is presented. This includes mechanism of the large coherent vortex structure formation, small length scale generation and flow chaos. First, it is not appropriate to call the turbulent flow as a “random” motion since the conservation law of mass, momentum and energy must be satisfied. Turbulence is built up by organized “vortex packets” which can be accepted by Navier–Stokes equations. Second, the linearly unstable modes are important, but the role of these modes is only to trigger the vorticity rollup. They cannot form the vortex by themselves and cannot cause the flow transition directly. The flow transition is mainly an inherent property of fluid flow, which shows that fluids cannot tolerate shear and shear must transfer to rotation when Reynolds number is large. The commonly accepted concept that “Lambda vortex self-deforms to hairpin vortex” does not exist. Finally, the widely spread concept “vortex breakdown to turbulence”, which was considered as the last stage of flow transition, is not observed.We proposed a new mechanism about turbulence generation and sustenance, that all small length scales (turbulence) are generated by shear layer instability produced by large vortex structure with multiple level vortex rings, multiple level sweeps and ejections, and multiple level negative and positive spikes near the laminar sub-layers. Therefore, “turbulence” is not generated by “vortex breakdown” but rather positive and negative spikes and consequent high-shear layers. “Shear layer instability” is considered as the “mother of turbulence”. This new mechanism may give a universal mechanism for turbulence generation and sustenance – the energy is brought by large vortex structure through multiple level sweeps not by “vortex breakdown”. Fluid shear, which is dominant in laminar boundary layer, is conditionally unstable but fluid rotation, which is dominant in turbulent boundary layer, is stable. In other words, the laminar boundary layer is an unstable state, but the turbulent is a stable state, and thus transition from laminar to turbulent is doomed when the Reynolds number is large enough. We prefer to present new stages to describe the boundary layer transition with five steps, i.e. perturbation (may include receptivity and linear instability), vorticity rollup, large vortex formation, small length scale generation, loss of symmetry and becoming chaotic to turbulence.