Abstract
We demonstrate the use of the harmonic resolvent to study the physics of subharmonic flow structures in the proximity of time-periodic solutions of the Navier-Stokes equation. As an illustrative example, we study the vortex pairing phenomenon in a periodically forced axisymmetric jet. While it is well-known that vortex pairing in jets and mixing layers arises from the interaction between subharmonic perturbations and the fundamental vortex shedding mode, here we provide additional insight. In particular, we uncover the nature of the strong cross-frequency interactions in the flow, and we compute the spatiotemporal mode that drives the pairing mechanism.
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