The stability of low-speed jets in cross-flow (JICF) is studied using tri-global linear stability analysis (GLSA). Simulations are performed at a Reynolds number of 2000, based on the jet exit diameter and the average velocity. A time stepper method is used in conjunction with the implicitly restarted Arnoldi iteration method. GLSA results are shown to capture the complex upstream shear-layer instabilities. The Strouhal numbers from GLSA match upstream shear-layer vertical velocity spectra and dynamic mode decomposition from simulation (Iyer & Mahesh, J. Fluid Mech., vol. 790, 2016, pp. 275-307) and experiment (Megerian et al., J. Fluid Mech., vol. 593, 2007, pp. 93-129). Additionally, the GLSA results are shown to be consistent with the transition from absolute to convective instability that the upstream shear layer of JICFs undergoes between R = 2 to R = 4 observed by Megerian et al. (J. Fluid Mech., vol. 593, 2007, pp. 93-129), where R = vjet/u∞ is the jet to cross-flow velocity ratio. The upstream shear-layer instability is shown to dominate when R = 2, whereas downstream shear-layer instabilities are shown to dominate when R = 4.
Bibliographical noteFunding Information:
This work was supported by AFOSR grant FA9550-15-1-0261. Simulations were performed using computer time provided by the Texas Advanced Computing Center (TACC) through the Extreme Science and Engineering Discovery Environment (XSEDE) allocation, and the Minnesota Supercomputing Institute (MSI). We thank Dr P. S. Iyer for discussions and performing preliminary simulations.
- absolute/convective instability
- turbulent flows