Nonmodal Stability Theory

Schmid, Peter J.

doi:10.1146/annurev.fluid.38.050304.092139

Cited by 814 publications

(842 citation statements)

References 67 publications

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“…Schmid 2007, and the references contained therein). For sake of clarity, we sketch the iteration in the following, by using the ADA algorithm as an example.…”

Section: Implementation and Convergencementioning

confidence: 99%

Riccati-less approach for optimal control and estimation: an application to two-dimensional boundary layers

et al. 2013

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The control of Tollmien-Schlichting (TS) in a 2D boundary layer is analysed by using numerical simulation. Full-dimensional optimal controllers are used in combination with a set-up of spatially localised inputs (actuators and disturbance) and outputs (sensors). The Adjoint of the Direct-Adjoint (ADA) algorithm, recently proposed by Pralits & Luchini (2010), is used to efficiently compute the Linear Quadratic Regulator (LQR) controller; the method is iterative and allows to by-pass the solution of the corresponding Riccati equation, unfeasible for high-dimensional systems. We show that an analogous iteration can be cast for the estimation problem; the dual algorithm is referred to as Adjoint of the Adjoint-Direct (AAD). By combining the solutions of the estimation and control problem, a full dimensional, model-free, Linear Gaussian Quadratic (LQG) controllers are obtained and used for the attenuation of the disturbances arising in the boundary layer flow. Model-free, full dimensional controllers turn out to be an excellent benchmark for evaluating the performance of the optimal control/estimation design based on open-loop model reduction. We show the conditions under which the two strategies are in perfect agreement by focusing on the issues arising when feedback configurations are considered. An analysis of the finite amplitude cases is also carried out addressing the limitations of the optimal controllers, the role of the estimation and the robustness to the nonlinearities arising in the flow of the control design

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“…Schmid 2007, and the references contained therein). For sake of clarity, we sketch the iteration in the following, by using the ADA algorithm as an example.…”

Section: Implementation and Convergencementioning

confidence: 99%

Riccati-less approach for optimal control and estimation: an application to two-dimensional boundary layers

et al. 2013

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“…Furthermore, the tools from the 'non-modal' stability analysis (e.g. [8]) have been used to plausibly explain the large-scale structures observed in turbulent boundary layers (e.g. [9]), and also to model more detailed features of wall turbulence (e.g.…”

Section: Introductionmentioning

confidence: 99%

Statistical evidence of anasymptotic geometric structure to the momentum transporting motions in turbulent boundary layers

Morrill-Winter

Philip

Klewicki

2017

Phil. Trans. R. Soc. A.

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“…Ozdemir, Hsu & Balachandar (2014) have performed direct numerical simulations, and they confirm the observation of turbulent flows for Reynolds numbers above Re T = 900. A subcritical transition to turbulence is typical for wall-bounded shear flows, since this property is related to the non-normal nature of the linearised Navier-Stokes equations (Farrell 1988;Butler & Farrell 1992;Trefethen et al 1993;Schmid & Henningson 1999;Schmid 2007). Consequently, the idealised analytical flow has quite different stability properties from those seen in practice.…”

Section: Introductionmentioning

confidence: 99%

Transient growth of perturbations in Stokes oscillatory flows

Biau

2016

J. Fluid Mech.

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. Oscillatory Stokes flows, with zero mean, are subjected to subcritical transition to turbulence. The maximal energy growth of perturbations is computed in the subcritical regime through an optimisation method. The results show strong amplifications during half a period. The energy transfer from the base flow involves an Orr mechanism with two-dimensional vorticity waves, and the maximum energy scales exponentially with the Reynolds number. Nonlinear simulations show that low-energy perturbations are sufficient to trigger turbulent flow.

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Nonmodal Stability Theory

Cited by 814 publications

References 67 publications

Riccati-less approach for optimal control and estimation: an application to two-dimensional boundary layers

Riccati-less approach for optimal control and estimation: an application to two-dimensional boundary layers

Statistical evidence of anasymptotic geometric structure to the momentum transporting motions in turbulent boundary layers

Transient growth of perturbations in Stokes oscillatory flows

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