The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows
Citations
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Cites background or methods from "The Proper Orthogonal Decomposition..."
...2, it is possible to obtain a lowrank approximation using dimensionality reduction techniques, such as the proper orthogonal decomposition (POD) (35, 37)....
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...The first two most energetic POD modes capture a significant portion of the energy, and steady-state vortex shedding is a limit cycle in these coordinates....
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...The POD (35, 37), provides a low-rank basis resulting in a hierarchy of orthonormal modes that, when truncated, capture the most energy of the original system for the given rank truncation....
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Cites background from "The Proper Orthogonal Decomposition..."
...Excellent reviews on the POD can be found in [1,45], and chapter 3 of [46]....
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References
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"The Proper Orthogonal Decomposition..." refers background or methods in this paper
...[See the formula for the conditional expectation of joint normal variables in Feller (1957).] Using (5....
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...Armbruster et al’s (1988) proof of structural stability of such heteroclinic cycles in O(2)-symmetric systems provides a mathematical foundation and does much to explain their robustness and persistence over a range of parameters and with different truncations (cf Armbruster et al 1989, Holmes 1991)....
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...In this section we comment on the connection between the POD and certain other analysis techniques. We start by describing the connection between the POD and linear stochastic estimation, as applied by Adrian and coworkers in Adrian (1979), Adrian & Moin (1988), Adrian et (1987), and Moin et al (1987)....
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...The best studied low-dimensional model is that developed by Aubry et al (1988) for the wall region of a turbulent boundary layer....
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...of coherent structures around the outbreak of the second world war, documented by J. T. C. Liu (1988). The existence of these structures was probably first articulated by Liepmann (1952), and was thoroughly exploited by Townsend (1956)....
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5,806 citations
"The Proper Orthogonal Decomposition..." refers methods in this paper
...In the following treatment, we adapt Lumley's application of the shot-noise decomposition (Rice 1944; Lumley 1971, 1981)....
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5,359 citations
"The Proper Orthogonal Decomposition..." refers background or methods in this paper
...The additional symmetry imposed on the ensemble of flows by artificial addition of images of flows under symmetry group elements, as advocated by Sirovich (1987), may therefore obscure the true nature a particular system....
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...This approach has been advocated by Sirovich (1987) and applied in many studies (e.g. Sirovich & Park 1990)....
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...XnE MZTHOD OF S}qA]~S~OXS This method was proposed by Sirovich (1987)....
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...Introductory discussions of the method in the context of fluid mechanical problems can also be found in Sirovich (1987) (1989) (1990) and Holmes (1990)....
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...Berkooz (1991b) gives an argument for the equivalence of the method of snapshots to the original formulation of the eigenvalue problem, as well as a linear independence condition omitted by Sirovich (1987)....
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