Abstract
The aim of this work is to study the nonlinear temporal evolution of an alternating swirling streaming jet. According to laboratory observations, the viscous dissipation is simulated by means of a phenomenological damping coefficient included in the equation of motion (Jiang et al. in J Fluid Mech 369:273–299, 1998; Wright et al. in J Fluid Mech 402:1–32, 2000) and added to the Bernoulli equation or to the evolution equation. The multiple scales are used for finding out the evolution equations. The fixed points of the solutions have been determined. Really, the modulation concept is exploited in order to analyze the stability criteria in the possible cases of resonance. While in the non-resonant case, the nontrivial solutions are obtained numerically. Different numerical applications have been considered. The studied cases have showed that the Weber number, the phenomenological number and the streamwise circulation play a significant role in determining the dynamics of the developing interfacial patterns.
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