Stability and sensitivity of the low-speed jet in cross-flow

The tri-global stability and sensitivity of the jet in cross-flow (JICF) is studied at $Re=2000$, and two jet-to-cross-flow ratios: $R=2$ and $R=4$. A novel capability is developed on unstructured grids and parallel platforms for this purpose. Linear stability analysis reveals that upstream shear-layer modes have frequencies that match simulation (Iyer & Mahesh, 2016) and experiment (Megerian et al., 2007). Asymmetric modes are more important to the overall dynamics at $R=4$. Low-frequency modes show a connection to wake vortices. For $R=4$ a downstream shear-layer mode is the most unstable. Adjoint modes show that the upstream shear-layer is most sensitive along the upstream side of the jet nozzle. Lower frequency downstream modes are sensitive in the cross-flow boundary layer. For $R=2$, optimal perturbations reveal that for short-time horizons, asymmetric perturbations dominate and grow along the counter-rotating vortex pair. However, as the time horizon increases, growth is optimal along the upstream shear-layer. When $R=4$, the optimal perturbations for short-time scales grow along the downstream shear-layer. For long-time horizons, they become hybrid modes that grow along both the upstream and downstream shear-layers.