HODMD Analysis in a Forced Flow over a Backward-Facing Step by Harmonic Perturbations

Abstract

This work studies in detail the energy amplification produced by inflow excitation of a steady flow over a backward-facing step. The disturbances introduced in the inflow are composed of a convergent series of sine functions with different wavenumbers, but the same temporal frequency. The evolution of the perturbations in time is solved using a linear integrator of the Navier-Stokes equations. This information is stored in a group of snapshots and then is analyzed using a data-driven method, higher order dynamic mode decomposition. The method provides a modal decomposition of the data that is used to solve an optimization problem, which identifies the inflow condition giving the maximum energy growth. The results obtained using this novel technique are in qualitatively good agreement with the theory. This is the first step on a new method that could be used for the analysis of numerical and experimental data, without the technical restrictions given by the classical methods. It is possible to identify maximum energy growths without the need of previous knowledge of the adjoint operator or without imposing Dirichlet boundary conditions, generally used in non-modal analyses.