Nonmodal Stability Theory

By Peter J. Schmid. 2007

1,041 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f49e2e9487c1ea34bd4d75dcfa9b52f5151efc35

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Citations in the corpus

Dynamics and Control of Global Instabilities in Open-Flows: A Linearized Approach (2010, background): “This eigenproblem may also be viewed as a largescale optimization problem [12, 21, 76] that may be solved thanks to direct-adjoint techniques.”
Sensitivity and Nonlinearity of Thermoacoustic Oscillations (2018, background): “They have since been extended to nonmodal stability theory and nonlinear time-dependent flows (Schmid 2007).”
Linear non-normal energy amplification of harmonic and stochastic forcing in the turbulent channel flow (2010, background): “For further details, the reader is referred to Farrell & Ioannou (1993a ,b), Zhou et al. (1996), Bamieh & Dahleh (2001), Jovanović & Bamieh (2005) and Schmid (2007).”
Amplification of coherent streaks in the turbulent Couette flow: an input–output analysis at low Reynolds number (2010, methodology): “…Ioannou (1993b) and Jovanović & Bamieh (2005) for the optimal stochastic response of laminar channel flows (see also e.g. Schmid & Henningson 2001; Schmid 2007, for a review), and the results of del Álamo & Jiménez (2006) and Pujals et al. (2009) for the optimal temporal response of the…”
Computational Methods for Linear Matrix Equations (2016, background): “Lyapunov equations are a theoretical and computational tool also in hydrodynamic stability theory of timedependent problems, which is emerging as an attractive alternative to classical modal spectral analysis, in the quantitative description of short-term disturbance behaviors [225].”
Perspectives on viscoelastic flow instabilities and elastic turbulence (2021, background): “It was shown that the maximum energy amplification that can be achieved through this mechanism in plane Couette and channel flows is O(Re(2)) [165].”
Coherent structures in wall-bounded turbulence (2017, background): “An appendix in Schmid & Henningson (2001) provides a practical computer code to optimise the amplification history of some chosen norm,”
The lift-up effect : The linear mechanism behind transition and turbulence in shear flows (2014, background): “If the state of the system has a strong projection on some of these highly non-orthogonal eigenmodes the energy of the flow can experience a significant transient growth (Schmid, 2007).”
Triggering in the horizontal Rijke tube: non-normality, transient growth and bypass transition (2010, methodology): “) Non-normal stability operators can cause very high transient growth, typically 10(4)–10(6) times the initial perturbation energy, even in situations that are linearly stable (Schmid & Henningson 2001). This transient growth is a key component of bypass transition in the first three flows. In flow ”
Convective instability and transient growth in flow over a backward-facing step (2007, background): “This brings us to a third area of hydrodynamic stability analysis known generally as non-modal stability analysis or transient growth analysis (Butler & Farrell 1992; Trefethen et al. 1993; Schmid & Henningson 2001; Schmid 2007).”
Cascades in Wall-Bounded Turbulence (2012, background): “Examples include the above-mentioned reviews by Panton (2001) and McKeon (2007) and papers by Jiménez & Moin (1991), Jiménez & Pinelli (1999), Schoppa & Hussain (2002), and Kawahara et al. (2012).”
The engine behind (wall) turbulence: perspectives on scale interactions (2017, background): “…identified above, the lack of orthogonality between (decaying) eigenvectors can lead to significant energy growth over a finite time horizon (as opposed to the infinite time horizon associated with linear instability) before the inevitable energy decay (see, for example, figure 2 of Schmid 2007).”