Variational formulation of resolvent analysis

Barthel, Benedikt; Gomez, Salvador; McKeon, Beverley

doi:10.1103/physrevfluids.7.013905

Cited by 10 publications

(4 citation statements)

References 53 publications

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“…Similar considerations impact the development of numerical methods (Bazilevs et al. 2007), self-consistent mean flow modelling (Meliga 2017) and resolvent analysis (Padovan, Otto & Rowley 2020; Rigas, Sipp & Colonius 2021; Barthel, Zhu & McKeon 2021; Barthel, Gomez & McKeon 2022).…”

Section: Introductionmentioning

confidence: 93%

Multiscale model reduction for incompressible flows

Callaham,

Loiseau,

Brunton

2023

J. Fluid Mech.

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We introduce a projection-based model reduction method that systematically accounts for nonlinear interactions between the resolved and unresolved scales of the flow in a low-dimensional dynamical systems model. The proposed method uses a separation of time scales between the resolved and subscale variables to derive a reduced-order model with cubic closure terms for the truncated modes, generalizing the classic Stuart–Landau equation. The leading-order cubic terms are determined by averaging out fast variables through a perturbation series approximation of the action of a stochastic Koopman operator. We show analytically that this multiscale closure model can capture both the effects of mean-flow deformation and the energy cascade before demonstrating improved stability and accuracy in models of chaotic lid-driven cavity flow and vortex pairing in a mixing layer. This approach to closure modelling establishes a general theory for the origin and role of cubic nonlinearities in low-dimensional models of incompressible flows.

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Section: Introductionmentioning

confidence: 93%

Multiscale model reduction for incompressible flows

Callaham,

Loiseau,

Brunton

2023

J. Fluid Mech.

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“…Using CPU computing, a 70 by 70 grid requires multiple hours to compute the inverse using MATLAB's inversion routine. Alternative resolvent methods exist such as the variational formulation [33] and randomized resolvent analysis [34]. Rather than implementing these more complex alternatives, we instead performed the simpler method described earlier using graphics-processing-unit (GPU) computing.…”

Section: Numerical Implementationmentioning

confidence: 99%

Prediction of Streaks in Rectangular Jets

Marshall,

Edgington-Mitchell,

Nogueira

2024

Preprint

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Streaks in rectangular-jet flows are modeled using resolvent analysis, providing insight into the underlying physics of coherent structures. Two-dimensional, cross-plane resolvent analysis is used to evaluate the most-amplified coherent structures at very low frequencies. The highest-gain mode exhibits a large dipole-like structure, featuring a high-speed streak on one major-axis edge of the jet and a low-speed streak on the other, while the second-highest gain mode is the minor-axis-aligned counterpart. Higher-order modes exhibit finer streak spacing, resembling boundary layer modes. Varying the curvature of the jet corners has minimal impact on the gains and mode shapes, suggesting corner vortices in real rectangular-jet flows may not be primarily caused by free-shear streak formation, at least under the modeling hypothesis. Increasing shear thickness typically decreases gains and disperses mode shapes but sensitivity to the forcing weighting method is evident. Increasing the aspect ratio increases the gains for all modes except for the leading dipole-type modes which exhibit a monotonic decrease. The position of streaks relative to the corners changes with aspect ratio causing some complicated gain dependence.

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“…The bottleneck is related to the time and memory requirements of the linear system solvers within the SVD. Building an optimal basis to avoid linear system solvers is possible (Barthel, Gomez & McKeon 2022), although a generalization for complex geometries is still challenging. It is possible, however, to obtain accurate resolvent modes with time-stepping instead of direct solvers.…”

Section: Problem Set-upmentioning

confidence: 99%

Triglobal resolvent analysis of swept-wing wakes

2023

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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.

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Variational formulation of resolvent analysis

Cited by 10 publications

References 53 publications

Multiscale model reduction for incompressible flows

Multiscale model reduction for incompressible flows

Prediction of Streaks in Rectangular Jets

Triglobal resolvent analysis of swept-wing wakes

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