View Video Presentation: https://doi.org/10.2514/6.2023-4483.vid
A reduced-order model (ROM) of a two-dimensional mixing layer is obtained through Galerkin projection of the full Navier-Stokes equations onto a finite set of basis functions, which are obtained as balanced modes of the associated linearised system. Besides the use of modes related to the linearised operator, a key feature of the derived ROM compared to earlier efforts is that the same boundary conditions, sponge zones and forcing functions of a corresponding direct numerical simulation (DNS) are considered in the Galerkin projection. The Galerkin system does not display numerical instabilities observed in similar models, possibly due to the use of techniques consistent with DNS. Good agreement is observed between ROM and DNS for various excitation frequencies. Stochastic excitation of the mixing layer is also possible, leading to fluctuations behaving as a jittering wavepacket. The reduced-order model accurately models vortex roll-up and pairing, thus representing an interesting framework to take modal dynamics, often performed with linearised systems, to the non-linear regime.
