The dynamics of coherent structures in the wall region of a turbulent boundary layer

Aubry, Nadine; Holmes, Philip; Lumley, John L.; Stone, Emily

doi:10.1017/s0022112088001818

Cited by 1,090 publications

(763 citation statements)

References 30 publications

(38 reference statements)

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“…Inclusion of a large number of POD basis functions creates very large POD-Galerkin ROMs that are still very computationally expensive to solve. Addition of turbulence models is equally undesirable because the empirical terms modify the dynamics of the Navier-Stokes equations (Rempfer & Fasel 1994;Aubry et al 1988;Ukeiley et al 2001;Sirisup & Karniadakis 2004;Iliescu & Wang 2012;Bailon-Cuba et al 2012).…”

Section: Introductionmentioning

confidence: 99%

Low-dimensional modelling of high-Reynolds-number shear flows incorporating constraints from the Navier–Stokes equation

2013

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A new approach to model order reduction of the Navier-Stokes equations at high Reynolds number is proposed. Unlike traditional approaches, this method does not rely on empirical turbulence modeling or modification of the Navier-Stokes equations. It provides spatial basis functions different from the usual proper orthogonal decomposition basis function in that, in addition to optimally representing the training data set, the new basis functions also provide stable and accurate reduced-order models. The proposed approach is illustrated with two test cases: two-dimensional flow inside a square lid-driven cavity and a two-dimensional mixing layer.

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Section: Introductionmentioning

confidence: 99%

Low-dimensional modelling of high-Reynolds-number shear flows incorporating constraints from the Navier–Stokes equation

2013

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“…In a subsequent step, the POD basis can be truncated to obtain low-dimensional systems of ordinary differential equations from the Navier-Stokes equations via Galerkin projections. This approach has been used by Aubry et al (1988) to represent the dynamics of near-wall structures in a turbulent boundary layer. Using similar techniques, Moin & Moser (1989) extracted three-dimensional coherent structures from direct numerical simulations (DNS) of channel flow via POD.…”

Section: Introductionmentioning

confidence: 99%

Reduced-order representation of near-wall structures in the late transitional boundary layer

et al. 2014

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Direct numerical simulations (DNS) of controlled H-and K-type transitions to turbulence in an M = 0.2 (where M is the Mach number) nominally zero-pressuregradient and spatially developing flat-plate boundary layer are considered. Sayadi, Hamman & Moin (J. Fluid Mech., vol. 724, 2013, pp. 480-509) showed that with the start of the transition process, the skin-friction profiles of these controlled transitions diverge abruptly from the laminar value and overshoot the turbulent estimation. The objective of this work is to identify the structures of dynamical importance throughout the transitional region. Dynamic mode decomposition (DMD) (Schmid, J. Fluid Mech., vol. 656, 2010, pp. 5-28) as an optimal phase-averaging process, together with triple decomposition (Reynolds & Hussain, J. Fluid Mech., vol. 54 (02), 1972, pp. 263-288), is employed to assess the contribution of each coherent structure to the total Reynolds shear stress. This analysis shows that low-frequency modes, corresponding to the legs of hairpin vortices, contribute most to the total Reynolds shear stress. The use of composite DMD of the vortical structures together with the skin-friction coefficient allows the assessment of the coupling between near-wall structures captured by the low-frequency modes and their contribution to the total skin-friction coefficient. We are able to show that the low-frequency modes provide an accurate estimate of the skin-friction coefficient through the transition process. This is of interest since large-eddy simulation (LES) of the same configuration fails to provide a good prediction of the rise to this overshoot. The reduced-order representation of the flow is used to compare the LES and the DNS results within this region. Application of this methodology to the LES of the H-type transition illustrates the effect of the grid resolution and the subgrid-scale model on the estimated shear stress of these low-frequency modes. The analysis shows that although the shapes and frequencies of the low-frequency modes are independent of the resolution, the amplitudes are underpredicted in the LES, resulting in underprediction of the Reynolds shear stress.

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“…First works on stabilization experimented in adding artificial viscosity [9] to the reduced equations. The idea was further developed by extending the spectral vanishing viscosity method of Tadmor [115] to the Navier-Stokes equations in [111].…”

Section: Stabilization Of Roms For Unsteady Navier-stokes Equationsmentioning

confidence: 99%

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

Lassila

Manzoni

Quarteroni

et al. 2014

Reduced Order Methods for Modeling and Computational Reduction

161

179

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This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities -which are mainly related either to nonlinear convection terms and/or some geometric variability -that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration. We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of inf-sup stability, certification through error estimation, computational issues and -in the unsteady case -long-time stability of the reduced model. Moreover, we provide an extensive list of literature references.

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The dynamics of coherent structures in the wall region of a turbulent boundary layer

Cited by 1,090 publications

References 30 publications

Low-dimensional modelling of high-Reynolds-number shear flows incorporating constraints from the Navier–Stokes equation

Low-dimensional modelling of high-Reynolds-number shear flows incorporating constraints from the Navier–Stokes equation

Reduced-order representation of near-wall structures in the late transitional boundary layer

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

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