Resolvent-based estimation of turbulent channel flow using wall measurements

Abstract

We employ a resolvent-based methodology to estimate velocity and pressure fluctuations within turbulent channel flows at friction Reynolds numbers of approximately 180, 550 and 1000 using measurements of shear stress and pressure at the walls, taken from direct numerical simulation (DNS) databases. Martini et al. (J. Fluid Mech., vol. 900, 2021, A2) showed that the resolvent-based estimator is optimal when the true space-time forcing statistics are utilized, thus providing an upper bound for the accuracy of any linear estimator. We use this framework to determine the flow structures that can be linearly estimated from wall measurements, and we characterize these structures and the estimation errors in both physical and wavenumber space. We also compare these results to those obtained using approximate forcing models - an eddy-viscosity model and white-noise forcing - and demonstrate the significant benefit of using true forcing statistics. All models lead to accurate results up to the buffer-layer, but only using the true forcing statistics allows accurate estimation of large-scale log-layer structures, with significant correlation between the estimates and DNS results throughout the channel. The eddy-viscosity model displays an intermediate behaviour, which may be related to its ability to partially capture the forcing colour. Our results show that structures that leave a footprint on the channel walls can be accurately estimated using the linear resolvent-based methodology, and the presence of large-scale wall-attached structures enables accurate estimations through the logarithmic layer.

arXiv comment40 pages, 31 figures

References in corpus (18)

• Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis
• Direct numerical simulation of turbulent channel flow up to $R{e}_{\tau }\approx 5200$
• A critical layer model for turbulent pipe flow
• Spectral analysis of jet turbulence
• On coherent structure in wall turbulence
• Stochastic Structural Stability Theory applied to roll/streak formation in boundary layer shear flow
• Resolvent-based modelling of coherent wavepackets in a turbulent jet
• Resolvent-based estimation of space-time flow statistics
• Optimal eddy viscosity for resolvent-based models of coherent structures in turbulent jets
• On the relevance of Reynolds stresses in resolvent analyses of turbulent wall-bounded flows
• SPOD and resolvent analysis of near-wall coherent structures in turbulent pipe flows
• The colour of forcing statistics in resolvent analyses of turbulent channel flows
• Energy transfer in turbulent channel flows and implications for resolvent modelling
• A minimal model of self-sustaining turbulence
• Logarithmic-layer turbulence: a view from the wall
• Analysis of wall-pressure fluctuation sources from DNS of turbulent channel flow
• A realizable data-driven approach to delay bypass transition with control theory
• Convolutional-network models to predict wall-bounded turbulence from wall quantities

Cited by in corpus (13)

• Self-similar mechanisms in wall turbulence studied using of resolvent analysis
• Resolvent-based tools for optimal estimation and control via the Wiener-Hopf formalism
• Spectral proper orthogonal decomposition of harmonically forced turbulent flows
• Towards real-time reconstruction of velocity fluctuations in turbulent channel flow
• Experimental control of Tollmien-Schlichting waves using the Wiener-Hopf formalism
• Resolvent-based approach for H2-optimal estimation and control: an application to the cylinder flow
• Identification of cross-frequency interactions in compressible cavity flow using harmonic resolvent analysis
• Model-based multi-sensor fusion for reconstructing wall-bounded turbulence
• Some effects of limited wall-sensor availability on flow estimation with 3D-GANs
• A resolvent-based perspective on the generation of Mach wave radiation from compressible boundary layers
• Coherent pressure structures in turbulent channel flow
• Resolvent-based estimation and control of a laminar airfoil wake
• LES-informed resolvent-based estimation of turbulent pipe flow