Spatio-temporal coherent structures in complex flows using DMD-based methods

Abstract The deep study and understanding of complex flow behavior, such as transitional or turbulent flows, is a research topic of high interest. The main reason is that these type of flows are not only found in nature, but also cover a wide range of industrial applications. Although these flows have been studied for decades, due to their high complexity, to elucidate their spatio-temporal structure is still considered an open topic in a large quantity of relevant cases. The main goal of this talk is to present a method suitable to predict spatio-temporal structures in complex flows (laminar to turbulent regimes). This method, called as, higher order dynamic mode decomposition (HODMD), combines singular value decomposition with dynamic mode decomposition and Takens' delay embedding theorem to approximate flow dynamics. The performance of the method will be tested in a wide range of applications, including the analysis of noisy experimental data (i.e.: synthetic jets in transitional-turbulent regime), to predict aerodynamic flutter in flight test or its usage as a reduced order model to reduce the computational cost in numerical simulations. Finally, in the second part of the talk, Spatio Temporal Koopman Decomposition (STKD) will also be introduced, which is a method suitable to calculate flow structures, defined as traveling waves. Some examples such as the analysis of the wake of a wind turbine or the coherent structures in a rotating spherical shell will also be presented.