Bulletin of the American Physical Society
74th Annual Meeting of the APS Division of Fluid Dynamics
Volume 66, Number 17
Sunday–Tuesday, November 21–23, 2021; Phoenix Convention Center, Phoenix, Arizona
Session E04: Turbulence: Wall-Bounded Flows II: Linearized and Quasilinear Approaches |
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Chair: Beverley McKeon, Caltech Room: North 121 B |
Sunday, November 21, 2021 2:45PM - 2:58PM |
E04.00001: On the parametric refinement of data-enhanced linearized Navier-Stokes for modeling near-wall turbulence Seyedalireza Abootorabi, Armin Zare Data-enhanced physics-based models that are based on the Navier-Stokes equations have been shown to capture various structural and statistical features of turbulent flows. In this study, we evaluate the predictive capability of the stochastic dynamical models proposed by Zare, Jovanovic, and Georgiou (J. Fluid Mech., vol. 812, 2017) in capturing spatio-temporal features of the near-wall-cycle. These models are formed by systematically introducing low-rank dynamical modifications to the linearized Navier-Stokes operator allowing them to not only match the one-dimensional energy spectrum, but to provide good estimates of two-point correlations of the turbulent velocity field. For a turbulent channel flow at a friction Reynolds number of 186, we show that the quality of predicting two-point velocity correlations and the spatio-temporal frequency response depends on the choice of a low-rank inducing parameter that alters the structure of dynamical modifications to the linearized operator. We fine tune this parameter to better predict signatures of the near-wall cycles and compare the stochastic and optimal harmonic response of the resulting data-enhanced model with that of the eddy-viscosity-enhanced linearized Navier-Stokes equations. |
Sunday, November 21, 2021 2:58PM - 3:11PM |
E04.00002: A Comparison of Structure and Dynamics Underlying Quasilinear and DNS Turbulence Brian Farrell, Marios-Andreas Nikolaidis, Petros Ioannou A POD-based analysis was carried out on numerical data obtained from a DNS of a turbulent Poiseuille flow at Re=1650 and the corresponding quasilinear (QL) simulation. Striking similarity between the velocity fields of the streamwise mean roll-streak structure was seen in the two simulations. Compelling similarity was also seen between the perturbation velocity fields co-located with the streamwise mean roll-streak in the two simulations. This correspondence in the structure of the primary dynamical components underlying turbulence in QL and DNS suggests a similar dynamics is operating to maintain turbulence in these systems. Moreover, it is known that the QL system is a close approximation to a second order statistical state dynamics (SSD) formulation. This consideration invites exploiting the comprehensively characterized dynamics of turbulence in the second order SSD formulation to advance understanding of DNS turbulence. It is concluded that the SSP identified in the second order SSD, which is the same as that operating in QL turbulence, is also operating in DNS turbulence. This fundamental dynamical structure in the streamwise mean flow is identified as the roll-streak while the primary dynamical structure in the perturbation field is found to consist of a large cohort of decaying oblique waves. |
Sunday, November 21, 2021 3:11PM - 3:24PM |
E04.00003: Generalised quasilinear approximations of turbulent channel flow: streamwise nonlinear energy transfer Carlos G Gonzalez Hernandez, Qiang Yang, Yongyun Hwang A generalised quasilinear (GQL) is applied to turbulent channel flow at $Re_\tau \simeq 1700$ ($Re_\tau$ is the friction Reynolds number), with emphasis on the energy transfer in the streamwise wavenumber space. The flow is decomposed into low and high streamwise wavenumber groups, the former of which is solved by considering the full nonlinear equations whereas the latter is obtained from the linearised equations around the former. The performance of the GQL approximation is subsequently compared with that of a QL model, in which the low-wavenumber group only contains zero streamwise wavenumber. It is found that the QL model exhibits a considerably reduced multi-scale behaviour at the given moderately high Reynolds number. This is improved significantly by the GQL approximation which incorporates only a few more streamwise Fourier modes into the low-wavenumber group, and it reasonably well recovers the distance-from-the-wall scaling in the turbulence statistics and spectra. Finally, it is proposed that the energy transfer from the low to the high-wavenumber group in the GQL approximation, referred to as the `scattering' mechanism, depends on the neutrally stable leading Lyapunov spectrum of the linearised equations for the high wavenumber group. In particular, it is shown that if the threshold wavenumber distinguishing the two groups is sufficiently high, the scattering mechanism can completely be absent due to the linear nature of the equations for the high-wavenumber group. |
Sunday, November 21, 2021 3:24PM - 3:37PM Not Participating |
E04.00004: Generalised quasilinear approximations for homogeneous shear turbulence Zhenghao Luo, Carlos G Gonzalez Hernandez, Yongyun Hwang The spectral energetics of a generalised quasilinear (GQL) model is studied in homogeneous shear turbulence. The GQL approximation decomposes the velocity into low and high streamwise wavenumber groups, the former of which is solved by considering the full nonlinear equations whereas the latter is obtained from the linearised equations around the former. In contrast to the QL model, the GQL model exhibits a healthy energy cascade in the streamwise direction, and the energy cascade is mediated by slightly anisotropic small-scale motions, which are close to the nearly isotropic small-scale motions in direct numerical simulation. We examine the spectral energetics of the GQL model in the streamwise and spanwise wavenumber space, and a series of supporting numerical experiments with different combinations of modes are carried out. The turbulence statistics and spectra of velocity, component-wise energy transport and pressure strain are investigated. |
Sunday, November 21, 2021 3:37PM - 3:50PM |
E04.00005: Quasilinear Simulation of Annular Pipe Flows Chenyu Zhang, Brad B Marston, Jeff S Oishi, Steven Tobias Fluid flowing in long pipes undergo a transition from laminar to turbulent as the speed of the flow increases. We seek to understand this transition by constructing a minimal reduced model for the flow. Our main tool is a the quasi-linear (QL) approximation, which has a long history beginning at least as early as the 1950s. The flow is Reynolds decomposed into the sum of a mean component and fluctuations. The mean flow is chosen to be the average of the velocity and pressure over the azimuthal angle. We investigate whether the transition to turbulence can be captured by the QL approximation. |
Sunday, November 21, 2021 3:50PM - 4:03PM |
E04.00006: Extended Orr-Sommerfeld Stability Analysis Vilda K Markeviciute, Rich R Kerswell The idea of statistical stability of turbulent states was first introduced by Malkus in 1956 (J. Fluid Mech. 1(5), 521-539). Despite the debate about the validity of Malkus's theory, his proposed approach of solving a linear Orr-Sommerfeld equation around a turbulent mean velocity profile remains a popular tool in turbulence analysis (see for example Beneddine et al 2016, J. Fluid Mech. 798 485-504). Inspired by the statistical nature of turbulence and Malkus's ideas, we use statistical state equations truncated at second order (see Farrell & Ioannou 2017, Phys. Rev. Fluids 2, 084608) to derive the Extended Orr-Sommerfeld linear stability analysis model in primitive variables space. By incorporating two-point correlations of the flow, this model takes into account the fluctuation-fluctuation interactions between the base and the perturbations fields. We apply the new stability model to a range of statistically steady states obtained via direct numerical simulations of 2D channel flow, discovering an improvement in statistical stability classification for some of the test cases. We carefully test the assumptions made in the model to understand when the improvement can be expected. |
Sunday, November 21, 2021 4:03PM - 4:16PM |
E04.00007: On the Wall Pressure and Shear Stress Spectra in Turbulent Boundary Layers Anthony Leonard, Simon S Toedtli, Beverley J McKeon The spectra of the wall pressure fluctuations and the shear stress components ∂u/∂y and ∂v/∂y are determined via |
Sunday, November 21, 2021 4:16PM - 4:29PM |
E04.00008: Synchronization of wall turbulence Mengze Wang, Tamer A Zaki The reconstruction of turbulence from limited observations does not guarantee that the estimated state is synchronized with the true trajectory (M. Wang and T. Zaki, 2021, J. Fluid Mech. 917, A9). Furthermore, the design of the observations that ensure synchronization has not been systematically examined in wall-bounded flows. We first investigate the synchronization of a horizontal layer of turbulence in channel flow, when the observations are the fully resolved fields outside that layer. Synchronization of the emergent turbulence to the true flow trajectory is only possible when that horizontal layer smaller than a critical thickness on the order of the Taylor microscale. We proceed to analyze synchronization of different configurations, including multiple missing volumes within the channel and the case where the observations are limited to surface values. |
Sunday, November 21, 2021 4:29PM - 4:42PM Not Participating |
E04.00009: Large-eddy simulation of turbulent plane-Couette flow Dale I Pullin, Wan Cheng, Ravi Samtaney, Xisheng Luo We describe DNS, wall-resolved and wall-modeled LES of plane Couette (PC) flow. Subgrid-scale (SGS) motion is represented using the stretched-spiral vortex SGS model while the virtual-wall model is utilized for wall-modeling. Cases studied include DNS at friction Reynolds numbers Reτ = 220, wall-resolved LES at Reτ = 500- 3,600 and wall-modeled LES at Ret = 3,600-2.85x105. All LES performed show the presence of approximately span-wise periodic sets of stream-wise rolls. Averaged wall-normal profiles of the mean stream-wise velocity show a consistent log region across all Reynolds numbers. Both the mean-flow roll energy and circulation, scaled with outer variables, decrease monotonically for Ret > 500. At lower Ret the mean stream-wise zero-velocity line follows a wavy form in the span-wise direction, while at larger Reτ, a mushroom shape emerges which could potentially enhance local momentum transport in the span-wise direction and be responsible for the weakening of the span-wise rolls. |
Sunday, November 21, 2021 4:42PM - 4:55PM Not Participating |
E04.00010: Numerical simulation of turbulent plane Poiseuille-Couette flow Ravi Samtaney, Dale I Pullin, Wan Cheng, Xisheng Luo We describe a study of plane Poiseuille-Couette (PPC) flow via DNS, wall-resolved LES and wall-modeled LES for flows where the wall velocity difference and mean pressure gradient are aligned. In LES, the stretched-vortex subgrid-scale model and virtual-wall model are employed. Two Reynolds numbers exist in PPC flow, $Re_c=U_c h/\nu$ based on the wall velocity $U_c $ and $Re_M = M/\nu$ with $M$ the volume flux per unit span, where $2h$ is the distance between walls and $\nu$ the kinematic viscosity. In DNS, we start from plane Couette flow ($Re_M=0$) and search for the presence of stream-wise rolls in a moderate Reynolds-number quadrant of the $Re_c$-$Re_M$ plane. In WRLES and WMLES, we focus on a curve in this quadrant where the velocity gradient on one wall is zero. The behavior of turbulent PPC flow including velocity profiles, turbulent intensities and other flow features, will be discussed. |
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