Vorticity formulation for an actuated jet in crossflow

The mixing properties of a transverse jet are important to a variety of engineering applications. This study seeks to develop actuation strategies that manipulate the geometry and rate of mixing between jet and crossflow, based on a mechanistic understanding of vorticity structure and evolution. Previous studies have shown that vorticity from both the jet boundary layer and the channel wall boundary layer may affect the evolution of the transverse jet. We present a new construction accounting for both sources of vorticity and derive an analytical description of vortex filament geometry in the near field of the jet, showing dependence on parameters that describe unsteady actuation at the jet nozzle. Three-dimensional vortex element simulations of the transverse jet using this construction reveal the mechanism by which a counter-rotating vortex pair forms in the transverse jet flow field, in a manner consistent with our earlier studies.7,16 We further demonstrate agreement between these simulation results and jet trajectories obtained from a recent scaling analysis.2