Entrainment and spreading of turbulent shear flows

Over the last decade there has been a renewed interest in understanding the entrainment process in turbulent shear flows [5]. Even though there are differences between the way different shear flows (such as jets, wakes, boundary layers and shearfree flows) develop [14], the origin of these differences is not clear. Here, employing experimental data from an axisymmetric turbulent jet and a turbulent boundary layer, we present conditional velocity profiles at the tubrbulent/non-turbulent interface (TNTI) and quantitatively reveal the differences encountered by the two different shear flows. In particular, we examine the role of radial velocity in the entrainment process which is present in jets and is absent for boundary layers (and wake flows). We consider the turbulent kinetic energy budget for the axisymmetric jet to illustrate the dominant role of ‘radial advection’ compared to ‘streamwise advection’, clarifying the important role of the radial velocity at the interface in jet entrainment which is absent in boundary layers. Subsequently, we classify the shearflows for entrainment based on the largeand small-scale mechanisms. Finally, a simplified approach by which the scaling of ‘small scale’ entrainment velocity can be used to derive the well known overall ‘large scale’ spreading of turbulent shear flows is presented. Introduction and objectives Research in the area of entrainment has undergone a dramatic increase over the past few years [5], primarily fuelled by large scale computations (e.g., [6, 19]) and particle image velocimetry (PIV) measurements (e.g., [20, 2, 15, 3]). The turbulent/nonturbulent interface (TNTI) is suggested to be dominated by small-scale, viscous, diffusive activity called ‘nibbling’ [20], where nibbling is the mechanism by which ‘non-turbulent fluid’ is converted into ‘turbulent fluid’[5]. Classically, however, entrainment has been attributed to large-scale mechanisms collectively referred to here as ‘engulfment’[18]. The main reason for considering large-scales is that the evolution of different canonical flows such as turbulent jets, wakes and boundary layers are different and this evolution can be described by the largescale mean properties of the flow. Furthermore, these turbulent flows have been observed to be dominated by large-scale coherent structures. A small-scale-only mechanism would suggest a development that is similar for different shear flows which is contrary to the observations. To reconcile this, Philip et.al [14] suggested a ‘multi-stage’ entrainment process which is different for different shear flows, in which the initial stages are largescale dominated and the final stage is always nibbling. Another way to accommodate the largeand small-scale process is by considering entrainment as a ‘multi-scale’ phenomenon, which can be evidenced by filtering the equations of motion at different length scales (where engulfment is defined with largest and nibbing by the smallest filter size, respectively)[15]. A fractal TNTI surface (e.g, [7]) following [16] and [13] would be consistent with such a multi-scale approach. As such, the first two objectives of this paper are: (i) to characterise differences between jets and boundary layer flows concerning entrainment across TNTI, thus testing the validity of the TURBULENT TURBULENT NON-TURBULENT