Abstract. We have produced a fluid dynamics video with data from Direct Numerical Simulation (DNS) of a jet in crossflow at several low values of the velocity inflow ratio R. We show that, as the velocity ratio R increases, the flow evolves from simple periodic vortex shedding (a limit cycle) to more complicated quasi periodic behavior, before finally exhibiting asymmetric chaotic motion. We also perform a stability analysis just above the first bifurcation, where R is the bifurcation parameter. Using the overlap of the direct and the adjoint eigenmodes, we confirm that the first instability arises in the shear layer downstream of the jet orifice on the boundary of the backflow region just behind the jet.

Abstract. We study direct numerical simulations (DNS) of a jet in crossflow at low values of the jet- to-crossflow velocity ratio R. We observe that, as the ratio R increases, the flow evolves from simple periodic vortex shedding (a limit cycle) to more complicated quasi-periodic behavior, before finally becoming turbulent, as seen in the simulation of Bagheri et al. (2009b). The first bifurcation is found to occur at R = 0.675, and the observed shedding of hairpin vortices is linked to a possible existence of a local absolute instability connected to the region of reversed flow immediately downstream of the jet. We focus on this first bifurcation, and find that a global linear stability analysis predicts well the frequency and initial growth rate of the nonlinear DNS simulation at R = 0.675, and that good qualitative predictions about the dynamics can still be made at slightly higher values of R where multiple unstable eigenmodes are present. In addition, we compute the adjoint global eigenmodes, and find that the overlap of the direct and the adjoint eigenmode, also known as a ‘wavemaker’, provides additional evidence that the source of the first instability indeed lies in the shear layer just downstream of the jet.

Abstract. The nonlinear stability of laminar sinuously bent streaks is studied for the plane Couette flow at Re = 500 in a nearly-minimal box and for the Blasius boundary layer at Reδ∗ = 700. The initial perturbations are nonlinearly saturated streamwise streaks of amplitude AU perturbed with sinuous perturbations of amplitude AW. The local boundary of the basin of attraction of the linearly stable laminar flow is computed by bisection in the AU − AW plane. When the streamwise uniform streaks (AW = 0) are locally unstable, typically for AU > 25−27% for the considered flows, sinuous perturbations of amplitude below AW ≈ 1−2% are sufficient to induce breakdown and counteract the streak viscous dissipation. The critical amplitude of the sinuous perturbations increases when the streamwise streak amplitude is decreased. With secondary perturbations amplitude AW ≈ 4%, breakdown is induced on stable streamwise streaks with AU ≈ 13%, following the secondary transient growth scenario first examined by Schoppa & Hussain (J. Fluid Mech. 453, 2002). A cross-over, where the critical amplitude of the sinuous perturbation become larger than the amplitude of streamwise streaks, is observed for streaks of small amplitude AU < 5 − 6%. In this case the transition is induced by an initial transient amplification of streamwise vortices, forced by the decaying sinuous mode. This is followed by the growth of the streaks and final breakdown. Our results show that the stability of streamwise streaks should always be assessed in terms of both the streak amplitude and the amplitude of spanwise velocity perturbations.