Phase-locking flows between orthogonally stretching parallel plates

In this paper, we explore the stability and dynamical relevance of a wide variety steady, time-periodic, quasiperiodic, chaotic flows arising between orthogonally stretching parallel plates. We first all steady flow solution families formerly identified by Ayats et al. [“Flows plates,” Phys. Fluids 33, 024103 (2021)], concluding that only one originates from Stokesian approximation is actually stable. When both plates are shrinking at identical or nearly same deceleration rates, exhibits Hopf bifurcation leads to stable time-periodic regimes. The resulting orbits tracked for different Reynolds numbers rates while monitoring their Floquet exponents identify secondary instabilities. It found these also exhibit Neimark–Sacker bifurcations, generating quasiperiodic (tori) may sometimes give rise dynamics through Ruelle–Takens–Newhouse scenario. However, unusually observed, as generally become phase-locked resonance mechanism before strange attractor arise, thus restoring time-periodicity flow. work, have four regions, known Arnold tongues horns. particular, 1 : 4 strong region explored in great detail, where scenarios very good agreement with normal form theory.