“Turbulent/non-turbulent interface” in a low-Reynolds-number transitional boundary layer over a multi-element airfoil

Abstract

Akin to the turbulent/non-turbulent interface, which envelops a fully developed turbulence, the iso-vorticity interface that separates the irrotational fluids from the free stream is investigated in a transitional boundary layer over a multi-element airfoil. Geometrically, the interface is steady and flat at the initial transitional stage. With the progress of transition, the interface fluctuates more and more violently. Statistically, the evolution of interface properties, including the fluctuation of interface height σI, the fractal dimension Df, and the thickness of interface δI, are tracked along the streamwise direction. It is revealed that all the three quantities grow with transition. Both σI and δI become invariant at the latter half part of the airfoil where the transition is completed. Counter-intuitively, the growth of Df stops at a more upstream location, indicating the fractal property of turbulence is already existing during transition. Instantaneously, the above-mentioned quantities are found to be related to the periodical vortices inside the boundary layer. The vortex will elevate/sink the above interface by the induced ejection/sweep flow and increases Df at slightly downstream of the vortex. Furthermore, it is highlighted that the variations of interface properties will greatly influence the entrainment by two opposite effects: the length of interface LI and the vorticity gradient across the interface; and it is found that the entrainment flux is mainly controlled by LI. This suggests that the recently reported dominance of LI on entrainment for wall-bounded turbulence could be a universal phenomenon in boundary layers, despite the flow states and wall configurations.