Global stability and optimal perturbation for a jet in cross-flow

We study the stability of a jet in cross-flow at low values of the jet to cross-flow velocity ratio RR using direct numerical simulations (DNS) and global linear stability analysis adopting a time-stepper method. For the simplified setup without a meshed pipe in the simulations we compare results of a fully-spectral code SIMSON with a spectral-element code Nek5000. We find the use of periodic domains, even with the fringe method, unsuitable due to the large sensitivity of the eigenvalues and due to the large spatial growth of the corresponding eigenmodes. However, we observe a similar sensitivity to reflection from the outflow boundary in the inflow/outflow configuration, and therefore we use an extended domain where reflections are minimal. We apply in our studies both modal and non-modal linear analyses investigating transient effects and their asymptotic fate, and we find a transient wavepacket to develop almost identically in both the globally stable and unstable cases. The final results of the global stability analysis for our numerical setup show the critical value of RR, at which the first bifurcation occurs, to lie in the range between 1.5 and 1.6.