Experimental Investigation of Momentum Transport Associated with the Interaction of Concentrated and Distributed Vorticity

The flow field associated with a vortex ring advecting towards a moving wall is investigated. These physical simulations represent aspects of instantaneous flow field interactions known to exist in turbulent wall bounded flows. To allow for an explicit study of these interactions and avoid background turbulence, unsteady, laminar, vortex ring experiments are conducted with reproducible initial conditions. The experiments are conducted in a large water tank. The shear layer is validated and the basic parameters associated with the vortex ring are quantified. Opposite sign vorticity interactions between the vortex ring and shear layer vorticity results in a lifting of the near wall fluid. This gives rise to the formation of a primary hairpin vortex with the same sign vorticity as the top core of the vortex ring. The evolution of the hairpin is consistent with observations noted in a turbulent boundary layer. Introduction Turbulent flows are of ubiquitous technological importance due to their wide variety of applications. The action of vortical motions plays a vital role in turbulence production, dissipation, and time-averaged turbulence statistics. Therefore, it is important to understand what flow features are responsible for the inertial mechanisms of turbulence and ultimately the mean distribution of momentum. A variety of experimental and numerical studies suggests the presence of distinct coherent regions existing within the vorticity field of the wall-bounded turbulent flows, which are commonly termed “hairpins,” hp [1]. These coherent motions are thought to be the building block of wall-bounded turbulence and serve as a basis for modelling the turbulent boundary layer, e.g., see Smith et al. [9]. By convecting a vortex ring (Falco’s typical eddies) towards or away from a moving wall, Chu and Falco [4] were able to investigate features that have been observed in the turbulent boundary layer using flow visualization. They have broadly classified these interactions (vortex ring/moving wall) based upon stability considerations into four types (see therein for details). Dupont et al. [5] used a similar experimental set-up to [4] but used advanced measurement techniques, e.g., particle image velocimetry (PIV), for detailed characterization of type II interactions. Their findings indicated that the vortex ring acted as an external perturbation, which resulted in the lift up of the shear-layer, thereby, producing a hairpin. The studies by Haidari and Smith [6] provide important clarity regarding asymmetries inherent in the generation and regeneration of hairpins e.g., vortices and their contribution towards turbulent inertia. They validated this by examining vortex dynamics near a wall in a well-controlled environment and established an extension of the results to the dynamics of a turbulent boundary layer. Their experimental studies described that the lasting contribution to the mean Reynolds stress (turbulent inertia) are made during events causing surface layer eruptions followed by roll up of sheets of vorticity and these events continue to occur repeatedly. Another important conclusion drawn from their analysis is that in high shear flows, a small amount of local asymmetry can give rise to much larger asymmetry for a single vortex or combination of vortices. This motivates the fact that those interactions that leave a signature on the mean dynamics must contain asymmetries associated with their geometry or kinematics. Bernard [3] numerically examined the vorticity field in a transitional boundary layer. The results suggests that shearing of spanwise vorticity beyond the viscous sublayer creates wall-normal vorticity away from the boundary. This e↵ect causes the appearance of streamwise vorticity shaping into a hairpin. Herein, we report on experiments investigating velocityvorticity interactions that underlie the dynamical mechanisms by which turbulent motions distribute momentum. The scope of this study is to examine the growth and evolution of the resulting hairpin relative to an advecting vortex ring. It is an extension of the Dupont et al. [5] study since they were not able to characterize the properties of the hairpin. The aim of the study is to clarify specific properties of the hairpin, e.g., spanwise vorticity, trajectory, and circulation in the hairpin core. It is thought that by understanding the details of this interaction, further insight can be gained into the generic mechanisms operative in wall-bounded turbulent flows and vorticity dynamics in general. Experimental Facility Vortex rings are generated using a 127 mm piston-cylinder device and a 34.8 mm seamless stainless steel tube. The cylinder and tube are connected using flexible tubing. The piston-cylinder motion is precisely controlled using LabView and a stepper motor. A vortex ring is produced at the exit of the tube by converting rotational motion from the stepper motor to translation using a threaded rod. The outer contour at the exit plane of the tube is machined to form a wedge with a 10 tip angle and length of 6 mm. A Stokes layer, also referred to as the Rayleigh problem, i.e., a time developing shear-layer, is generated using a conveyor belt that is 305 mm wide and 1.83 m long. The conveyor belt rides on a nominally flat acrylic plate and is driven by a servo motor/timing belt system. Trapezoidal velocity versus time profiles are implemented in LabView with an impulse configuration, i.e., acceleration time is much less than the overall time interval, T. Since