Dynamics of coherent structures and transition to turbulence in free square jets

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Abstract
We report results of time‐dependent numerical simulation of spatially developing free square jets initialized with a thin square vortex‐sheet with slightly rounded corner‐regions. The studies focus on the near field of jets with Mach number 0.3–0.6 and moderately high Reynolds numbers. A monotonically‐integrated large‐eddy‐simulation approach is used, based on the solution of the unfiltered inviscid equations and appropriate inflow/outflow open boundary conditions. The simulations show that the initial development of the square jet is characterized by the dynamics of vortex rings and braid vortices. Farther downstream, strong vortex interactions lead to the breakdown of the vortices, and to a more disorganized flow regime characterized by smaller scale elongated vortices and spectral content consistent with that of the Kolmogorov (K41) inertial subrange. Entrainment rates significantly larger than those for round jets are directly related to the enhanced fluid and momentum transport between jet and surroundings determined by the vortex dynamics underlying the axis‐rotation of the jet cross‐section. The first axis‐rotation of the jet cross‐section can be directly correlated with self‐induced vortex‐ring deformation. However, subsequent jet axis‐rotations are the result of strong interactions between ring and braid vortices, rather than being correlated with successive self‐induced vortex‐ring deformations, as previously conjectured based on laboratory observations. The interaction between braid and ring vortices has the effect of inhibiting the periodic self‐induced axis‐rotations observed in the case of isolated square vortex rings.