Evolution of three-dimensional coherent structures in a flat-plate boundary layer

Rempfer, Dietmar; Fasel, Hermann F.

doi:10.1017/s0022112094003551

Cited by 184 publications

(110 citation statements)

References 18 publications

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“…The reconstruction of this vortical structure using one, two and three low-frequency DMD modes is shown in figure 7(b-d) and illustrates good (quantitative) convergence towards the full Λ-vortex, further corroborating the ability of the DMD in capturing the important coherent structures. Rempfer & Fasel (1994) applied POD to the same transition scenarios (K-and H-type) and reported similar results. This is to be expected as, during the initial stages of transition, when the skin-friction coefficient is beginning to depart from its laminar correlation and Λ-vortices are starting to form, the coherent structures in the flow are energetically dominant.…”

Section: Application To Early Transitional Flowmentioning

confidence: 67%

“…Despite its early concentration on turbulent fluid motion, POD has also been applied to transitional flows, see e.g. Rempfer & Fasel (1994). The majority of POD studies, however, have focused on identifying structures in near-wall turbulence or on detecting three-dimensional structures arising from a secondary instability in transitional flows.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Application To Early Transitional Flowmentioning

confidence: 67%

Section: Introductionmentioning

confidence: 99%

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

et al. 2014

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“…The adjoint variable is accessible through a forward integration of the state dynamics (20-21) and a backward integration of the adjoint variable dynamics (34). Let us point out that considering a final condition for the state variable (through a similar cost function term as for the initial condition) would change the null initial condition of the adjoint dynamics into a term similar to the one involved in the derivative with respect to the initial condition control variable.…”

Section: Adjoint Modelmentioning

confidence: 99%

“…This artificial viscosity is added to the flow kinematic viscosity and enables after a proper tuning of its value to improve the system's numerical stability. Rempfer and Fasel [34] and Rempfer [33] have proposed modal viscosities that affect differently the modes of the decomposition. More recently, Karamanos and Karniadakis [17] employed a dissipative model called spectral vanishing viscosity model to formulate an alternative approach.…”

Section: Introductionmentioning

confidence: 99%

Strong and weak constraint variational assimilations for reduced order fluid flow modeling

Artana¹,

Cammilleri²,

Carlier³

et al. 2012

Journal of Computational Physics

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In this work we propose and evaluate two variational data assimilation techniques for the estimation of low order surrogate experimental dynamical models for fluid flows. Both methods are built from optimal control recipes and rely on proper orthogonal decomposition and a Galerkin projection of the Navier Stokes equation. The techniques proposed differ in the control variables they involve. The first one introduces a weak dynamical model defined only up to an additional uncertainty time-dependent function whereas the second one, handles a strong dynamical constraint in which the dynamical system's coefficients constitute the control variables. Both choices correspond to different approximations of the relation between the reduced basis on which is expressed the motion field and the basis components that have been neglected in the reduced order model construction. The techniques have been assessed on numerical data and for real experimental conditions with noisy Image Velocimetry data.

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“…POD has been successfully implemented in conjunction with experimental (e.g., [3-6,? ]) as well as with numerical studies (e.g., [7,2,[8][9][10][11][12]) in thermal convection, shear layers, cavity flows and external flows, to mention just a few.…”

Section: Introductionmentioning

confidence: 99%

A Spectral Vanishing Viscosity Method for Stabilizing Low-Dimensional Galerkin Systems

Sirisup¹,

Karniadakis²

2002

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Low-dimensional flow dynamical systems are susceptible to instabilities after longtime integration. In this paper, we investigate the stability of such two-dimensional models constructed from Karhunen-Loeve expansions for flows past a circular cylinder. We first demonstrate that although the short-term dynamics may be predicted accurately with only a handful of modes retained, instabilities arise after a few hundred vortex shedding cycles. We then propose a dissipative model based on a spectral vanishing viscosity (SVV) diffusion convolution operator as an effective way of stabilizing low-dimensional Galerkin systems.

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Evolution of three-dimensional coherent structures in a flat-plate boundary layer

Cited by 184 publications

References 18 publications

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

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

Strong and weak constraint variational assimilations for reduced order fluid flow modeling

A Spectral Vanishing Viscosity Method for Stabilizing Low-Dimensional Galerkin Systems

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