Numerical implementation and evaluation of resolvent-based estimation for space–time energy spectra in turbulent channel flows

Self Cite

Composite sweeping-enhanced resolvents, referred to as the ${\boldsymbol {R}}_s^2$ model, are proposed to predict the space–time statistics of large-scale structures in turbulent channel flows. This model incorporates two key mechanisms: (i) eddy damping is introduced to represent random sweeping decorrelation caused by nonlinear forcing, leading to a sweeping-enhanced resolvent ${{\boldsymbol {R}}_s}$ ; and (ii) the sweeping-enhanced resolvent ${{\boldsymbol {R}}_s}$ is composited into its iterations ${\boldsymbol {R}}_s^2$ to yield non-zero Taylor time microscales. The resulting ${\boldsymbol {R}}_s^2$ model can correctly predict the frequency spectra and two-point cross-spectra of large-scale structures. This model is compared numerically with eddy-viscosity-enhanced resolvent models. The latter are designed to represent energy transfer instead for time decorrelation, and thus underpredict the characteristic decay time scales. The ${\boldsymbol {R}}_s^2$ model correctly yields the characteristic decay time scales in turbulent channel flows.

Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Composition of resolvents enhanced by random sweeping for large-scale structures in turbulent channel flows

He²

2023

Self Cite

“…2020; Yang et al. 2020). On the other hand, since the RBE method only estimates the ‘observed’ forcing, its prediction deteriorates with the decrease of correlation between the signals of measurements and the predicted locations.…”

Section: The Existing Methodsmentioning

confidence: 99%

“…Second, the RBE infers the forcing statistics from the measurements without imposing assumptions on the form of the forcing profile. The RBE has been validated to be efficient for predicting the field where the turbulence is highly correlated with the measured reference points (Towne et al 2020;Yang et al 2020). However, since it only estimates the 'observed' forcing, its prediction accuracy deteriorates with increasing distance between the measurements and the predicted locations.…”

mentioning

confidence: 99%

A resolvent-based prediction framework for incompressible turbulent channel flow with limited measurements

Ying,

Liang,

et al. 2023

A new resolvent-based method is developed to predict the space–time properties of the flow field. To overcome the deterioration of the prediction accuracy with increasing distance between the measurements and predictions in the resolvent-based estimation (RBE), the newly proposed method utilizes the RBE to estimate the relative energy distribution near the wall rather than the absolute energy directly estimated from the measurements. Using this extra information from RBE, the new method modifies the energy distribution of the spatially uniform and uncorrelated forcing that drives the flow system by minimizing the norm of the cross-spectral density tensor of the error matrix in the near-wall region in comparison with the RBE-estimated one, and therefore it is named as the resolvent-informed white-noise-based estimation (RWE) method. For validation, three time-resolved direct numerical simulation (DNS) datasets with the friction Reynolds numbers $Re_\tau = 180$ , 550 and 950 are generated, with various locations of measurements ranging from the near-wall region ( $y^+ = 40$ ) to the upper bound of the logarithmic region ( $y/h \approx 0.2$ , where h is the half-channel height) for the predictions. Besides the RWE, three existing methods, i.e. the RBE, the $\lambda$ -model and the white-noise-based estimation (WBE), are also included for the validation. The performance of the RBE and scale-dependent model ( $\lambda$ -model) in predicting the energy spectra shows a strong dependence on the measurement locations. The newly proposed RWE shows a low sensitivity on $Re_{\tau }$ and the measurement locations, which may range from the near-wall region to the upper bound of the logarithmic region, and has a high accuracy in predicting the energy spectra. The RWE also performs well in predicting the space–time properties in terms of the correlation magnitude and the convection velocity. We further utilize the new method to reconstruct the instantaneous large-scale structures with measurements from the logarithmic region. Both the RWE and RBE perform well in estimating the instantaneous large-scale structure, and the RWE has smaller errors in the estimations near the wall. The structural inclination angles around $15^\circ$ are predicted by the RWE and WBE, which generally recover the DNS results.

Variability of convection velocities and structure inclination angles in wall-bounded turbulence

Cui,

Jacobi

2024

The scale-dependent variability of convective velocities and structure inclination angles in wall-bounded turbulence was studied experimentally via space–time energy spectrum measurements. We found that the variability of convection velocities for large-scale motions (LSMs) decreased inversely with streamwise wavenumbers, and that the variability trend was not fully explained by earlier applications of Kraichnan's ‘random-sweeping’ model of turbulence that assumed perfect scale separation. By analytically extending the random-sweeping model to allow for a dominant large scale in the random-sweeping signal that can interact with other LSMs, we showed how scale interactions can explain the variability trend in convection velocities for LSMs. The variability in convection velocities was also shown to correlate with the scale-dependent inclination angles of coherent structures that were obtained via cross-spectral analysis. Large-scale motions tended to exhibit shallower inclination to the wall with increasing convection velocity, while small-scale motions and those far from the wall exhibited the reverse behaviour. We proposed that these two opposite relationships between inclination angle and convection velocity can be explained in terms of a balance between opposing effects of the mean shear and the coherent structure geometry. Descriptions and models of convection velocity variability effects are useful both for modelling turbulence spectra and explaining the geometry of coherent structures.