A hierarchy of low-dimensional models for the transient and post-transient cylinder wake

By Bernd R. Noack, K. Afanasiev, Marek Morzynski, Gilead Tadmor, Frank Thiele. 2003

1,111 citations recorded by the source corpus.

Subfields: Computational Mechanics, Environmental Engineering

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Environmental Engineering

Citations in the corpus

Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems (2018, background): “An additional mode, called the shift mode, is included to capture the transient dynamics connecting the unstable steady state with the mean of the limit cycle [28].”
Discovering governing equations from data by sparse identification of nonlinear dynamical systems (2015, methodology): “g is a limit cycle in these coordinates. An additional mode, called the shift mode, is included to capture the transient dynamics connecting the unstable steady state with the mean of the limit cycle [31] (i.e., the direction connecting point ‘C’ to point ‘B’ in Fig. 7). In the three-dimensional coo”
Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators (2009, methodology): “Alternately, the balanced models, which accurately capture the transient dynamics, could be combined with the POD-based models using shift modes of Noack et al. (2005) which accurately capture vortex shedding and some of the transient dynamics.”
Three-dimensional coherent structures in a swirling jet undergoing vortex breakdown: stability analysis and empirical mode construction (2011, background): “However, weakly nonlinear stability approaches explicitly assume that instability modes and most energetic (POD) modes are the same, at least near the onset of a supercritical Hopf bifurcation (Stuart 1958; Noack et al. 2003).”
On dynamic mode decomposition: Theory and applications (2013, background): “For instance, the main features of the laminar flow past a two-dimensional cylinder can be described using as few as three ordinary differential equations [1].”
Feedback shear layer control for bluff body drag reduction (2008, background): “the cylinder wake (Bergmann, Cordier, & Brancher 2005; Gerhard et al. 2003; King et al. 2005; Noack et al. 2003; Noack, Tadmor & Morzyński, 2004; Noack, Papas & Monkewitz, 2005; Tadmor et al. 2004; Siegel, Cohen, & McLaughlin 2003; Siegel et al. 2007, 2008) or the cavity flow (Little et al.”
Input–output analysis, model reduction and control of the flat-plate boundary layer (2009, background): “However, examples of successful adaptations of POD modes can be found in Noack et al. (2003) and Siegel et al. (2008) for the globally unstable flow past a circular cylinder.”
Enhancing computational fluid dynamics with machine learning (2021, background): “4 for the simple ﬂow past a cylinder, where it is known that the energetic coherent structures evolve on a parabolic sub-manifold in the POD subspace [104].”
Closed-loop control of an open cavity flow using reduced-order models (2009, background): “…Navier–Stokes equations via a Galerkin expansion the vast majority of the system’s energy can be captured has spawned a substantial body of literature on low-dimensional models for complex flow dynamics (see e.g. Noack et al. 2003; Buffoni, Camarri & Iollo 2006; Galletti et al. 2007 and others).”
Dynamic mode decomposition of numerical and experimental data (2008, methodology): “This method is capable of extracting information from snapshots of the flow field and is thus applicable to experimental data (see Herzog 1986; Bonnet et al. 1994; Noack et al. 2003).”
On closures for reduced order models—A spectrum of first-principle to machine-learned avenues (2021, neutral): “Indeed, this analogy has been demonstrated theoretically and numerically for different ﬂow scenarios (e.g., ﬂow over a cylinder 244 and a turbulent ﬂow past a backward-facing step 103 ) Thus, truncating the low-energy”
GLOBAL INSTABILITIES IN SPATIALLY DEVELOPING FLOWS: Non-Normality and Nonlinearity (2005, background): “…prediction based on the specific nonnormality of the global linear operator is confirmed by the numerical simulations of Zielinska et al. (1997) and Noack et al. (2003): These authors observe strong nonlinear modifications of the basic flow capable of affecting the length of the recirculation…”
Proper Orthogonal Decomposition for Linear-Quadratic Optimal Control (2013, methodology): “Proper orthogonal decomposition, model-order reduction, apriori and a-posteriori error analysis, linear-quadratic optimal control, primal-dual active set strategy.”
Modal Analysis of Fluid Flows: Applications and Outlook (2019, methodology): “ eld, we simply use Eq. (3). The pressure gradient term drops out from the Galerkin model due to the boundary condition for most ows. Extensive discussions are provided in Holmes [2] and Noack et al. [56]. For modeling the cylinder wake, Deane et al. [57] noticed that the use of only 4 POD modes res”