Large-eddy simulation (LES) and dynamic mode decomposition (DMD) are used to study an underexpanded sonic jet injected into a supersonic crossflow and an overexpanded supersonic jet injected into a subsonic crossflow, where the flow conditions are based on the experiments of Santiago & Dutton (J. Propul. Power, vol. 13 (2), 1997, pp. 264–273) and Beresh et al. (AIAA J., vol. 43, 2005a, pp. 379–389), respectively. The simulations successfully reproduce experimentally observed shock systems and vortical structures. The time averaged flow fields are compared to the experimental results, and good agreement is observed. The behaviour of the flow is discussed, and the similarities and differences between the two regimes are studied. The trajectory of the transverse jet is investigated. A modification to Schetz et al.’s theory is proposed (Schetz & Billig, J. Spacecr. Rockets, vol. 3, 1996, pp. 1658–1665), which yields good prediction of the jet trajectories in the current simulations in the near field. Point spectra taken at various locations in the flowfield indicate a global oscillation for the sonic jet flow, wherein different regions in the flow oscillate with a frequency of
. For supersonic jet flow, no such global frequency is observed. Dynamic mode decomposition of the three-dimensional pressure field obtained from LES is performed and shows the same behaviour. The DMD results indicate that the
mode is dominant between the upstream barrel shock and the bow shock for the sonic jet, while the roll up of the upstream shear layer is dominant for the supersonic jet.