A Finite-Time Thermodynamics of Unsteady Fluid Flows

Noack, Bernd R.; Schlegel, Michael; Ahlborn, B.; Mutschke, Gerd; Morzyński, Marek; Comte, Pierre; Tadmor, Gilead

doi:10.1515/jnetdy.2008.006

Cited by 79 publications

(82 citation statements)

References 54 publications

(99 reference statements)

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“…41 Having defined an acceptable number of modes, a Galerkin system of evolution equations is written for the modes in terms of advective and dissipative terms, with the latter modeled to prevent excessive energy build-up (some form of cascade is required). Approaches are inspired by an eddy-viscosity approach, 41 with more advanced closures incorporating linear approximations to the nonlinear terms 67 or nonlinear interactions directly, 68 and comparative analyses demonstrating the utility of these more advanced formulations. 42 While dyadic wavelet modes are locally correlated at singularities (providing the basis for multifractal methods 25 ), they provide an approximately orthogonal or orthonormal basis that is also conditioned on frequency.…”

Section: B Implications Of the Results For Reduced Order Modelingmentioning

confidence: 99%

Gradual wavelet reconstruction of the velocity increments for turbulent wakes

2015

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This work explores the properties of the velocity increment distributions for wakes of contrasting local Reynolds number and nature of generation (a cylinder wake and a multiscale-forced case, respectively). It makes use of a technique called gradual wavelet reconstruction (GWR) to generate constrained randomizations of the original data, the nature of which is a function of a parameter, ϑ. This controls the proportion of the energy between the Markov-Einstein length (∼ 0.8 Taylor scales) and integral scale that is fixed in place in the synthetic data. The properties of the increments for these synthetic data are then compared to the original data as a function of ϑ. We write a Fokker-Planck equation for the evolution of the velocity increments as a function of spatial scale, r, and, in line with previous work, expand the drift and diffusion terms in terms up to fourth order in the increments and find no terms are relevant beyond the quadratic terms. Only the linear contribution to the expansion of the drift coefficient is non-zero and it exhibits a consistent scaling with ϑ for different flows above a low threshold. For the diffusion coefficient, we find a local Reynolds number independence in the relation between the constant term and ϑ for the multiscale-forced wakes. This term characterizes small scale structure and can be contrasted with the results for the Kolmogorov capacity of the zero-crossings of the velocity signals, which measures structure over all scales and clearly distinguishes between the types of forcing. Using GWR shows that results for the linear and quadratic terms in the expansion of the diffusion coefficient are significant, providing a new means for identifying intermittency and anomalous scaling in turbulence datasets. All our data showed a similar scaling behavior for these parameters irrespective of forcing type or Reynolds number, indicating a degree of universality to the anomalous scaling of turbulence. Hence, these terms are a useful metric for testing the efficacy of synthetic turbulence generation schemes used in large eddy simulation, and we also discuss the implications of our approach for reduced order modeling of the Navier-Stokes equations.

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Section: B Implications Of the Results For Reduced Order Modelingmentioning

confidence: 99%

Gradual wavelet reconstruction of the velocity increments for turbulent wakes

2015

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“…These considerations are based on POD Galerkin models extracted from experimental and numerical flow data and calibrated to the flow attractor. We are currently pursuing flow control using a reduced-order model based on turbulence closure (see Noack et al 2008Noack et al , 2010Noack & Niven 2012) and OID for noise control design (see Schlegel et al 2009). …”

Section: Discussionmentioning

confidence: 99%

On least-order flow representations for aerodynamics and aeroacoustics

et al. 2012

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We propose a generalization of proper orthogonal decomposition (POD) for optimal flow resolution of linearly related observables. This Galerkin expansion, termed 'observable inferred decomposition' (OID), addresses a need in aerodynamic and aeroacoustic applications by identifying the modes contributing most to these observables. Thus, OID constitutes a building block for physical understanding, leastbiased conditional sampling, state estimation and control design. From a continuum of OID versions, two variants are tailored for purposes of observer and control design, respectively. Firstly, the most probable flow state consistent with the observable is constructed by a 'least-residual' variant. This version constitutes a simple, easily generalizable reconstruction of the most probable hydrodynamic state to preprocess efficient observer design. Secondly, the 'least-energetic' variant identifies modes with the largest gain for the observable. This version is a building block for Lyapunov control design. The efficient dimension reduction of OID as compared to POD is demonstrated for several shear flows. In particular, three aerodynamic and aeroacoustic goal functionals are studied: (i) lift and drag fluctuation of a two-dimensional cylinder wake flow; (ii) aeroacoustic density fluctuations measured by a sensor array and emitted from a two-dimensional compressible mixing layer; † Email address for correspondence: michael.schlegel@tu-berlin.de

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“…where, after some manipulations based on energetic conservation (see [35] for the derivation of the energetic residual),…”

Section: Stabilization Of Reduced Order Modelsmentioning

confidence: 99%

Enablers for robust POD models

Bergmann

Bruneau

Iollo

2009

Journal of Computational Physics

277

286

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This paper focuses on improving the stability as well as the approximation properties of Reduced Order Models (ROM) based on Proper Orthogonal Decomposition (POD). The ROM is obtained by seeking a solution belonging to the POD subspace and that at the same time minimizes the Navier-Stokes residuals. We propose a modified ROM that directly incorporates the pressure term in the model. The ROM is then stabilized making use of a method based on the fine scale equations. An improvement of the POD solution subspace is performed thanks to an hybrid method that couples direct numerical simulations and reduced order model simulations. The methods proposed are tested on the two-dimensional confined square cylinder wake flow in laminar regime.

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A Finite-Time Thermodynamics of Unsteady Fluid Flows

Cited by 79 publications

References 54 publications

Gradual wavelet reconstruction of the velocity increments for turbulent wakes

Gradual wavelet reconstruction of the velocity increments for turbulent wakes

On least-order flow representations for aerodynamics and aeroacoustics

Enablers for robust POD models

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