Global linear stability analysis of jets in cross-flow

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 = v_jet/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.