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Direct numerical simulation (DNS) and dynamic mode decomposition (DMD) are used to study the shear layer characteristics of a jet in a crossflow. Experimental observations by Megerian et al. (J. Fluid Mech., vol. 593, 2007, pp. 93-129) at velocity ratios (R = v j /u ∞ ) of 2 and 4 and Reynolds number (Re = v j D/ν) of 2000 on the transition from absolute to convective instability of the upstream shear layer are reproduced. Point velocity spectra at different points along the shear layer show excellent agreement with experiments. The same frequency (St = 0.65) is dominant along the length of the shear layer for R = 2, whereas the dominant frequencies change along the shear layer for R = 4. DMD of the full three-dimensional flow field is able to reproduce the dominant frequencies observed from DNS and shows that the shear layer modes are dominant for both the conditions simulated. The spatial modes obtained from DMD are used to study the nature of the shear layer instability. It is found that a counter-current mixing layer is obtained in the upstream shear layer. The corresponding mixing velocity ratio is obtained, and seen to delineate the two regimes of absolute or convective instability. The effect of the nozzle is evaluated by performing simulations without the nozzle while requiring the jet to have the same inlet velocity profile as that obtained at the nozzle exit in the simulations including the nozzle. The shear layer spectra show good agreement with the simulations including the nozzle. The effect of shear layer thickness is studied at a velocity ratio of 2 based on peak and mean jet velocity. The dominant frequencies and spatial shear layer modes from DNS/DMD are significantly altered by the jet exit velocity profile.

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. 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, 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 St = fD/u ∞ = 0.3. 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 St = 0.3 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.

Direct numerical simulation (DNS) is used to study laminar to turbulent transition induced by a discrete hemispherical roughness element in a high-speed laminar boundary layer. The simulations are performed under conditions matching the experiments of Danehy et al. (AIAA Paper 2009–394, 2009) for free-stream Mach numbers of 3.37, 5.26 and 8.23. It is observed that the Mach 8.23 flow remains laminar downstream of the roughness, while the lower Mach numbers undergo transition. The Mach 3.37 flow undergoes transition closer to the bump when compared with Mach 5.26, in agreement with experimental observations. Transition is accompanied by an increase in ${C}_{f} $ and ${C}_{h} $ (Stanton number). Even for the case that did not undergo transition (Mach 8.23), streamwise vortices induced by the roughness cause a significant rise in ${C}_{f} $ until 20$D$ downstream. The mean van Driest transformed velocity and Reynolds stress for Mach 3.37 and 5.26 show good agreement with available data. Temporal spectra of pressure for Mach 3.37 show that frequencies in the range of 10–1000 kHz are dominant. The transition process involves the following key elements: upon interaction with the roughness element, the boundary layer separates to form a series of spanwise vortices upstream of the roughness and a separation shear layer. The system of spanwise vortices wrap around the roughness element in the form of horseshoe/necklace vortices to yield a system of counter-rotating streamwise vortices downstream of the element. These vortices are located beneath the separation shear layer and perturb it, which results in the formation of trains of hairpin-shaped vortices further downstream of the roughness for the cases that undergo transition. These hairpins spread in the span with increasing downstream distance and the flow increasingly resembles a fully developed turbulent boundary layer. A local Reynolds number based on the wall properties is seen to correlate with the onset of transition for the cases considered.

Roughness elements in a laminar boundary layer can cause the flow to transition. The effects of discrete and distributed roughness are explored using direct numerical simulation on unstructured grids. Velocity profiles for Mach 8.12 flow past a cylindrical roughness element are compared to experiment. 1 Flow features produced by an isolated hemispherical bump are studied for three Mach numbers [3.37, 5.26, 8.23] whose simulation parameters are chosen to match the experiments performed by Danehyet al. 2 at NASA Langley. The vortices formed upstream of the roughness due to boundary layer separation wrap around the hemisphere generating coherent streamwise vortices. A significant increase in wall skin friction coefficient along with the presence of unsteady structures far downstream of the bump for the lower Mach number cases indicated the transitional/turbulent nature of the flow while M∞=8.23 remained laminar. These observations are consistent with those in experiment. The effect of a sinusoidally varying distributed roughness was also investigated at M∞=2.9. The flow transitioned to a fully developed turbulent boundary layer that shows good quantitative agreement with experimental data. The cumulative effect of multiple roughness elements is to decelerate the near wall fluid, and setup inflexional velocity profiles. For both types of roughness it was seen that: (1) coherent streamwise vortices were produced which broke down far downstream, (2) prominent hairpin shaped structures were observed as the flow transitioned and (3) wall normal and spanwise inflexion points in streamwise velocity are observed.