Akademik Veri Yönetim Sistemi
ERCOFTAC SIG33 15th Workshop on Progress in Flow Instability, Transition and Control, Sassari, İtalya, 28 - 30 Haziran 2023, ss.19, (Özet Bildiri)
In a previous study [1], we showed mean-flow-based linear analysis depends on the choice of dependent variables. It was argued that this ambiguity could be used for optimization of resolvent-based models via specific choice of variables. In this study, we will present a methodology to achieve this goal. A key parameter to measure the performance of resolvent-based models is the alignment between the response modes of the resolvent operator and the SPOD modes of the flow. SPOD modes correspond to the most-energetic coherent structures that exist in the flow. Similarity between the response modes, which depends only on the mean-flow quantities, and the SPOD modes indicates a potential to predict the dynamic flow structures using RANS-type analyses. There is an ever expanding literature on the investigation of such a similarity in different turbulent flows. In Beneddine et al. (2016) [2], the similarity between the optimal response and SPOD modes was related to the high-gain separation observed in the resolvent operator. The underlying idea was that in case of very high-gain separation, the response would be dominated by the optimal response mode regardless of the forcing color. In a later study by Symon et al. (2018) [3], the success of the resolvent analysis was shown to depend on the non-normality of the mean-flow-based linear operator. One measure of non-normality involves the distance of the least stable eigenvalue to the imaginary axis. They state that for pseudo-resonant systems, where this distance is small, resolvent analysis is more likely to provide information about the coherent structures of the flow. We will test in our study if these two criteria can be used for optimization of resolvent analysis via variable transformation, which causes change in the eigenvalues/singular values of the linear/resolvent operator. We will show using a model problem based on Ginzburg-Landau equation that maximization of the gain separation does not necessarily increase the alignment between the optimal response and SPOD modes. The alignment does increase on the other hand, if the least stable eigenvalue is brought closer to the imaginary axis. Figure 1 shows for the model problem the improvement in the alignment between the optimal response and SPOD modes thanks to a nonlinear transformation. In the full paper, we will
apply this approach to a turbulent channel to test its applicability in a real flow case.