The turbulent/non-turbulent interface and entrainment in a boundary layer

Abstract

AbstractThe turbulent/non-turbulent interface in a zero-pressure-gradient turbulent boundary layer at high Reynolds number ($\mathit{Re}_\tau =14\, 500$) is examined using particle image velocimetry. An experimental set-up is utilized that employs multiple high-resolution cameras to capture a large field of view that extends $2\delta \times 1.1\delta $ in the streamwise/wall-normal plane with an unprecedented dynamic range. The interface is detected using a criteria of local turbulent kinetic energy and proves to be an effective method for boundary layers. The presence of a turbulent/non-turbulent superlayer is corroborated by the presence of a jump for the conditionally averaged streamwise velocity across the interface. The steep change in velocity is accompanied by a discontinuity in vorticity and a sharp rise in the Reynolds shear stress. The conditional statistics at the interface are in quantitative agreement with the superlayer equations outlined by Reynolds (J. Fluid Mech., vol. 54, 1972, pp. 481–488). Further analysis introduces the mass flux as a physically relevant parameter that provides a direct quantitative insight into the entrainment. Consistency of this approach is first established via the equality of mean entrainment calculations obtained using three different methods, namely, conditional, instantaneous and mean equations of motion. By means of ‘mass-flux spectra’ it is shown that the boundary-layer entrainment is characterized by two distinctive length scales which appear to be associated with a two-stage entrainment process and have a substantial scale separation.