@article{rolandi_ribeiro_yeh_taira_2024, title={An invitation to resolvent analysis}, ISSN={["1432-2250"]}, DOI={10.1007/s00162-024-00717-x}, abstractNote={Abstract Resolvent analysis is a powerful tool that can reveal the linear amplification mechanisms between the forcing inputs and the response outputs about a base flow. These mechanisms can be revealed in terms of a pair of forcing and response modes and the associated energy gains (amplification magnitude) at a given frequency. The linear relationship that ties the forcing and the response is represented through the resolvent operator (transfer function), which is constructed through spatially discretizing the linearized Navier–Stokes operator. One of the unique strengths of resolvent analysis is its ability to analyze statistically stationary turbulent flows. In light of the increasing interest in using resolvent analysis to study a variety of flows, we offer this guide in hopes of removing the hurdle for students and researchers to initiate the development of a resolvent analysis code and its applications to their problems of interest. To achieve this goal, we discuss various aspects of resolvent analysis and its role in identifying dominant flow structures about the base flow. The discussion in this paper revolves around the compressible Navier–Stokes equations in the most general manner. We cover essential considerations ranging from selecting the base flow and appropriate energy norms to the intricacies of constructing the linear operator and performing eigenvalue and singular value decompositions. Throughout the paper, we offer details and know-how that may not be available to readers in a collective manner elsewhere. Towards the end of this paper, examples are offered to demonstrate the practical applicability of resolvent analysis, aiming to guide readers through its implementation and inspire further extensions. We invite readers to consider resolvent analysis as a companion for their research endeavors.}, journal={THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS}, author={Rolandi, Laura Victoria and Ribeiro, Jean Helder Marques and Yeh, Chi-An and Taira, Kunihiko}, year={2024}, month={Aug} } @article{towne_dawson_bres_lozano-duran_saxton-fox_parthasarathy_jones_biler_yeh_patel_et al._2023, title={A Database for Reduced-Complexity Modeling of Fluid Flows}, ISSN={["1533-385X"]}, DOI={10.2514/1.J062203}, abstractNote={ We present a publicly accessible database specifically designed to aid in the conception, training, demonstration, evaluation, and comparison of reduced-complexity models for fluid mechanics. Availability of high-quality flow data is essential for all of these aspects of model development for both data-driven and physics-based methods. The current database is unique in that it has been curated with this need in mind. The database contains time-resolved data for six distinct datasets: a large eddy simulation of a turbulent jet, direct numerical simulations of a zero-pressure-gradient turbulent boundary layer, particle-image-velocimetry measurements for the same boundary layer at several Reynolds numbers, direct numerical simulations of laminar stationary and pitching flat-plate airfoils, particle-image-velocimetry and force measurements of an airfoil encountering a gust, and a large eddy simulation of the separated, turbulent flow over an airfoil. These six cases span several key flow categories: laminar and turbulent, statistically stationary and transient, tonal and broadband spectral content, canonical and application-oriented, wall-bounded and free-shear flow, and simulation and experimental measurements. For each dataset, we describe the flow setup and computational/experimental methods, catalog the data available in the database, and provide examples of how these data can be used for reduced-complexity modeling. All data can be downloaded using a browser interface or Globus. Our vision is that the common testbed provided by this database will aid the fluid mechanics community in clarifying the distinct capabilities of new and existing methods. }, journal={AIAA JOURNAL}, author={Towne, Aaron and Dawson, Scott T. M. and Bres, Guillaume A. and Lozano-Duran, Adrian and Saxton-Fox, Theresa and Parthasarathy, Aadhy and Jones, Anya R. and Biler, Hulya and Yeh, Chi-An and Patel, Het D. and et al.}, year={2023}, month={May} } @article{iwatani_asada_yeh_taira_kawai_2023, title={Identifying the Self-Sustaining Mechanisms of Transonic Airfoil Buffet with Resolvent Analysis}, ISSN={["1533-385X"]}, DOI={10.2514/1.J062294}, abstractNote={ The self-sustaining mechanisms of shock oscillations in transonic airfoil buffet are studied by wall-resolved large-eddy simulation (LES) and resolvent analysis. The LES successfully reproduces the large-scale shock oscillations over a transonic OAT15A airfoil, and the resolvent analysis using the high-fidelity LES data reveals the input–output relations in the self-sustained shock oscillations. Based on the input–output relations revealed by the resolvent analysis, this study identifies two mechanisms of the self-sustained shock oscillations. The first mechanism is closely tied to the periodic variations of the shock-induced separation height, whereas the second mechanism is related to the pressure dynamics around the shock wave. The mechanisms of the self-sustained shock oscillations identified by the input–output relations are examined in detail along with the high-fidelity LES data to aid the understanding of the feedback formulations in transonic airfoil buffet. }, journal={AIAA JOURNAL}, author={Iwatani, Yuta and Asada, Hiroyuki and Yeh, Chi-An and Taira, Kunihiko and Kawai, Soshi}, year={2023}, month={Mar} } @article{ribeiro_yeh_taira_2023, title={Triglobal resolvent analysis of swept-wing wakes}, volume={954}, ISSN={["1469-7645"]}, DOI={10.1017/jfm.2022.1033}, abstractNote={Through triglobal resolvent analysis, we reveal the effects of wing tip and sweep angle on laminar separated wakes over swept wings. For the present study, we consider wings with semi-aspect ratios from $1$ to $4$ , sweep angles from $0^\circ$ to $45^\circ$ and angles of attack of $20^\circ$ and $30^\circ$ at a chord-based Reynolds number of $400$ and a Mach number of $0.1$ . Using direct numerical simulations, we observe that unswept wings develop vortex shedding near the wing root with a quasi-steady tip vortex. For swept wings, vortex shedding is seen near the wing tip for low sweep angles, while the wakes are steady for wings with high sweep angles. To gain further insights into the mechanisms of flow unsteadiness, triglobal resolvent analysis is used to identify the optimal spatial input–output mode pairs and the associated gains over a range of frequencies. The three-dimensional forcing and response modes reveal that harmonic fluctuations are directed towards the root for unswept wings and towards the wing tip for swept wings. The overlapping region of the forcing–response mode pairs uncovers triglobal resolvent wavemakers associated with self-sustained unsteady wakes of swept wings. Furthermore, we show that for low-aspect-ratio wings optimal perturbations develop globally over the entire wingspan. The present study uncovers physical insights on the effects of tip and sweep on the growth of optimal harmonic perturbations and the wake dynamics of separated flows over swept wings.}, journal={JOURNAL OF FLUID MECHANICS}, author={Ribeiro, J. H. Marques and Yeh, Chi-An and Taira, Kunihiko}, year={2023}, month={Jan} } @article{skene_yeh_schmid_taira_2022, title={Sparsifying the resolvent forcing mode via gradient-based optimisation}, volume={944}, ISSN={["1469-7645"]}, DOI={10.1017/jfm.2022.519}, abstractNote={We consider the use of sparsity-promoting norms in obtaining localised forcing structures from resolvent analysis. By formulating the optimal forcing problem as a Riemannian optimisation, we are able to maximise cost functionals whilst maintaining a unit-energy forcing. Taking the cost functional to be the energy norm of the driven response results in a traditional resolvent analysis and is solvable by a singular value decomposition (SVD). By modifying this cost functional with the $L_1$ -norm, we target spatially localised structures that provide an efficient amplification in the energy of the response. We showcase this optimisation procedure on two flows: plane Poiseuille flow at Reynolds number $Re=4000$ , and turbulent flow past a NACA 0012 aerofoil at $Re=23\,000$ . In both cases, the optimisation yields sparse forcing modes that maintain important features of the structures arising from an SVD in order to provide a gain in energy. These results showcase the benefits of utilising a sparsity-promoting resolvent formulation to uncover sparse forcings, specifically with a view to using them as actuation locations for flow control.}, journal={JOURNAL OF FLUID MECHANICS}, author={Skene, Calum S. and Yeh, Chi-An and Schmid, Peter J. and Taira, Kunihiko}, year={2022}, month={Jul} } @article{ribeiro_yeh_zhang_taira_2022, title={Wing sweep effects on laminar separated flows}, volume={950}, ISSN={["1469-7645"]}, DOI={10.1017/jfm.2022.612}, abstractNote={We reveal the effects of sweep on the wake dynamics around NACA 0015 wings at high angles of attack using direct numerical simulations and resolvent analysis. The influence of sweep on the wake dynamics is considered for sweep angles from $0^\circ$ to $45^\circ$ and angles of attack from $16^\circ$ to $30^\circ$ for a spanwise periodic wing at a chord-based Reynolds number of $400$ and a Mach number of $0.1$ . Wing sweep affects the wake dynamics, especially in terms of stability and spanwise fluctuations with implications on the development of three-dimensional (3-D) wakes. We observe that wing sweep attenuates spanwise fluctuations. Even as the sweep angle influences the wake, force and pressure coefficients can be collapsed for low angles of attack when examined in wall-normal and wingspan-normal independent flow components. Some small deviations at high sweep and incidence angles are attributed to vortical wake structures that impose secondary aerodynamic loads, revealed through the force element analysis. Furthermore, we conduct global resolvent analysis to uncover oblique modes with high disturbance amplification. The resolvent analysis also reveals the presence of wavemakers in the shear-dominated region associated with the emergence of 3-D wakes at high angles of attack. For flows at high sweep angles, the optimal convection speed of the response modes is shown to be faster than the optimal wavemakers speed suggesting a mechanism for the attenuation of perturbations. The present findings serve as a fundamental stepping stone to understanding separated flows at higher Reynolds numbers.}, journal={JOURNAL OF FLUID MECHANICS}, author={Ribeiro, Jean Helder Marques and Yeh, Chi-An and Zhang, Kai and Taira, Kunihiko}, year={2022}, month={Oct} }