Spectral proper orthogonal decomposition

Sieber, Moritz; Paschereit, Christian Oliver; Oberleithner, Kilian

doi:10.1017/jfm.2016.103

Cited by 308 publications

(231 citation statements)

References 39 publications

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“…The structures φ k (r, x) represent the SPOD modes, in the terminology of Picard & Delville [11], and as used in recent literature [20,21]. Unfortunately, the same name is also used by Sieber et al [12] for a different modal decomposition, which is not employed here.…”

Section: A Extraction Of Spod Modes From Experimental Datamentioning

confidence: 99%

Resolvent-based modeling of coherent wave packets in a turbulent jet

et al. 2019

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Coherent turbulent wavepacket structures in a jet at Reynolds number 460 000 and Mach number 0.4 are extracted from experimental measurements, and are modelled as linear fluctuations around the mean flow. The linear model is based on harmonic optimal forcing structures and their associated flow response at individual Strouhal numbers, obtained from analysis of the global linear resolvent operator. These forcing/response wavepackets ('resolvent modes') are first discussed with regard to relevant physical mechanisms that provide energy gain of flow perturbations in the jet. Modal shear instability and the non-modal Orr mechanism are identified as dominant elements, cleanly separated between the optimal and sub-optimal forcing/response pairs. A theoretical development in the framework of spectral covariance dynamics then explicates the link between linear harmonic forcing/response structures and the cross-spectral density (CSD) of stochastic turbulent fluctuations. A lowrank model of the CSD at given Strouhal number is formulated from a truncated set of linear resolvent modes. Corresponding experimental CSD matrices are constructed from extensive two-point velocity measurements. Their eigenmodes (spectral proper orthogonal decomposition or SPOD modes) represent coherent wavepacket structures, and these are compared to their counterparts obtained from the linear model. Close agreement is demonstrated in the range of 'preferred mode' Strouhal numbers, around a value of 0.4, between the leading coherent wavepacket structures as educed from the experiment and from the linear resolventbased model.

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Section: A Extraction Of Spod Modes From Experimental Datamentioning

confidence: 99%

Resolvent-based modeling of coherent wave packets in a turbulent jet

et al. 2019

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“…Several methods have also been proposed in literature aimed at improving the POD modes [49][50][51][52] . There are also different variants of POD that have been introduced, like spatio-temporal biorthogonal decomposition 53 , spectral POD (SPOD) 54 , frequency based POD that is also called as SPOD 55 , multiscale POD (MPOD) 56 which splits the correlation matrix into the contribution of different scales.…”

Section: Introductionmentioning

confidence: 99%

A deep learning enabler for nonintrusive reduced order modeling of fluid flows

et al. 2019

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In this paper, we introduce a modular deep neural network (DNN) framework for data-driven reduced order modeling of dynamical systems relevant to fluid flows. We propose various deep neural network architectures which numerically predict evolution of dynamical systems by learning from either using discrete state or slope information of the system. Our approach has been demonstrated using both residual formula and backward difference scheme formulas. However, it can be easily generalized into many different numerical schemes as well. We give a demonstration of our framework for three examples: (i) Kraichnan-Orszag system, an illustrative coupled nonlinear ordinary differential equations, (ii) Lorenz system exhibiting chaotic behavior, and (iii) a non-intrusive model order reduction framework for the two-dimensional Boussinesq equations with a differentially heated cavity flow setup at various Rayleigh numbers. Using only snapshots of state variables at discrete time instances, our data-driven approach can be considered truly non-intrusive, since any prior information about the underlying governing equations is not required for generating the reduced order model. Our a posteriori analysis shows that the proposed data-driven approach is remarkably accurate, and can be used as a robust predictive tool for non-intrusive model order reduction of complex fluid flows.

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“…Such an approach relies on an empirical modal decomposition (e.g. Schmid 2010;Sieber et al 2016), which is beyond the scope of the present study.…”

Section: Global Approachmentioning

confidence: 99%

Inviscid instabilities in rotating ellipsoids on eccentric Kepler orbits

Vidal

Cébron

2017

J. Fluid Mech.

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We consider the hydrodynamic stability of homogeneous, incompressible and rotating ellipsoidal fluid masses. The latter are the simplest models of fluid celestial bodies with internal rotation and subjected to tidal forces. The classical problem is the stability of Roche-Riemann ellipsoids moving on circular Kepler orbits. However previous stability studies have to be reassessed. Indeed they only consider global perturbations of large wavelength or local perturbations of short wavelength. Moreover many planets and stars undergo orbital motions on eccentric Kepler orbits, implying time-dependent ellipsoidal semi-axes. This time dependence has never been taken into account in hydrodynamic stability studies. In this work we overcome these stringent assumptions. We extend the hydrodynamic stability analysis of rotating ellipsoids to the case of eccentric orbits. We have developed two open source and versatile numerical codes to perform global and local inviscid stability analyses. They give sufficient conditions for instability. The global method, based on an exact and closed Galerkin basis, handles rigorously global ellipsoidal perturbations of unprecedented complexity. Tidally driven and libration-driven elliptical instabilities are first recovered and unified within a single framework. Then we show that new global fluid instabilities can be triggered in ellipsoids by tidal effects due to eccentric Kepler orbits. Their existence is confirmed by a local analysis and direct numerical simulations of the fully nonlinear and viscous problem. Thus a non-zero orbital eccentricity may have a strong destabilising effect in celestial fluid bodies, which may lead to space-filling turbulence in most of the parameters range.

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Spectral proper orthogonal decomposition

Cited by 308 publications

References 39 publications

Resolvent-based modeling of coherent wave packets in a turbulent jet

Resolvent-based modeling of coherent wave packets in a turbulent jet

A deep learning enabler for nonintrusive reduced order modeling of fluid flows

Inviscid instabilities in rotating ellipsoids on eccentric Kepler orbits

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