An alternative method to study cross-flow instabilities based on high order dynamic mode decomposition

We present a novel method for the determination of N-factors in cross-flow transition scenarios. The method considers numerical simulations, in which a turbulent model is applied downstream from a predetermined point and solves a laminar flow upstream from this point. The solution is postprocessed using higher order dynamic mode decomposition to extract the leading spatial mode in several small sections along the streamwise direction. The spatial evolution of the amplitude of this mode will determine the N-factor. The results presented are compared with experimental measurements and linear stability theory, showing the good performance of this novel method, which does not assume parallel flow assumptions, is automatic and computationally efficient.