RESOLVENT OPTIMISATION VIA NONLINEAR VARIABLE TRANSFORMATION

Date

2023-06-30

Author

Karban, Uğur
Cavalieri, Andre V.G.
Jordan, Peter
Colonius, Tim

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

25
views

0
downloads

Cite This

In a previous study [1], we showed mean-flow-based linear analysis depends on the choice of dependentvariables. It was argued that this ambiguity could be used for optimization of resolvent-based models viaspecific 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 theresponse modes of the resolvent operator and the SPOD modes of the flow. SPOD modes correspondto 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 predictthe dynamic flow structures using RANS-type analyses. There is an ever expanding literature on theinvestigation of such a similarity in different turbulent flows. In Beneddine et al. (2016) [2], the similaritybetween the optimal response and SPOD modes was related to the high-gain separation observed in theresolvent operator. The underlying idea was that in case of very high-gain separation, the response wouldbe dominated by the optimal response mode regardless of the forcing color. In a later study by Symonet al. (2018) [3], the success of the resolvent analysis was shown to depend on the non-normality of themean-flow-based linear operator. One measure of non-normality involves the distance of the least stableeigenvalue to the imaginary axis. They state that for pseudo-resonant systems, where this distance issmall, 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 viavariable transformation, which causes change in the eigenvalues/singular values of the linear/resolventoperator. We will show using a model problem based on Ginzburg-Landau equation that maximization ofthe gain separation does not necessarily increase the alignment between the optimal response and SPODmodes. The alignment does increase on the other hand, if the least stable eigenvalue is brought closer tothe imaginary axis. Figure 1 shows for the model problem the improvement in the alignment betweenthe optimal response and SPOD modes thanks to a nonlinear transformation. In the full paper, we willapply this approach to a turbulent channel to test its applicability in a real flow case.

URI

https://www.ercoftac.org/downloads/sig33/bookofabstracts_15th_hr_withcover.pdf
https://hdl.handle.net/11511/118013

Collections

Department of Aerospace Engineering, Conference / Seminar