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Register a new userCoherent structure extraction in turbulent channel flow using boundary adapted wavelets
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We present a construction of isotropic boundary adapted wavelets, which are orthogonal and yield a multi-resolution analysis. We analyze direct numerical simulation data of turbulent channel flow computed at a friction Reynolds number of 395, and investigate the role of coherent vorticity. Thresholding of the vorticity wavelet coefficients allows to split the flow into two parts, coherent and incoherent vorticity. The coherent vorticity is reconstructed from their few intense wavelet coefficients. The statistics of the coherent part, i.e., energy and enstrophy spectra, are close to the statistics of the total flow, and moreover, the nonlinear energy budgets are very well preserved. The remaining incoherent part, represented by the large majority of the weak wavelet coefficients, corresponds to a structureless, i.e., noise-like, background flow whose energy is equidistributed.
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On the basis of (i) Particle Image Velocimetry data of a Turbulent Boundary Layer with large field of view and good spatial resolution and (ii) a mathematical relation between the energy spectrum and specifically modeled flow structures, we show that the scalings of the streamwise energy spectrum $E_{11}(k_{x})$ in a wavenumber range directly affected by the wall are determined by wall-attached eddies but are not given by the Townsend-Perry attached eddy models prediction of these spectra, at least at the Reynolds numbers $Re_{tau}$ considered here which are between $10^{3}$ and $10^{4}$. Instead, we find $E_{11}(k_{x}) sim k_{x}^{-1-p}$ where $p$ varies smoothly with distance to the wall from negative values in the buffer layer to positive values in the inertial layer. The exponent $p$ characterises the turbulence levels inside wall-attached streaky structures conditional on the length of these structures.
Hairpin vortices are widely studied as an important structural aspect of wall turbulence. The present work describes, for the first time, nonlinear traveling wave solutions to the Navier--Stokes equations in the channel flow geometry -- exact coherent states (ECS) -- that display hairpin-like vortex structure. This solution family comes into existence at a saddle-node bifurcation at Reynolds number Re=666. At the bifurcation, the solution has a highly symmetric quasistreamwise vortex structure similar to that reported for previously studied ECS. With increasing distance from the bifurcation, however, both the upper and lower branch solutions develop a vortical structure characteristic of hairpins: a spanwise-oriented head near the channel centerplane where the mean shear vanishes connected to counter-rotating quasistreamwise legs that extend toward the channel wall. At Re=1800, the upper branch solution has mean and Reynolds shear-stress profiles that closely resemble those of turbulent mean profiles in the same domain.
Turbulence modeling is a classical approach to address the multiscale nature of fluid turbulence. Instead of resolving all scales of motion, which is currently mathematically and numerically intractable, reduced models that capture the large-scale behavior are derived. One of the most popular reduced models is the Reynolds averaged Navier-Stokes (RANS) equations. The goal is to solve the RANS equations for the mean velocity and pressure field. However, the RANS equations contain a term called the Reynolds stress tensor, which is not known in terms of the mean velocity field. Many RANS turbulence models have been proposed to model the Reynolds stress tensor in terms of the mean velocity field, but are usually not suitably general for all flow fields of interest. Data-driven turbulence models have recently garnered considerable attention and have been rapidly developed. In a seminal work, Ling et al (2016) developed the tensor basis neural network (TBNN), which was used to learn a general Galilean invariant model for the Reynolds stress tensor. The TBNN was applied to a variety of flow fields with encouraging results. In the present study, the TBNN is applied to the turbulent channel flow. Its performance is compared with classical turbulence models as well as a neural network model that does not preserve Galilean invariance. A sensitivity study on the TBNN reveals that the network attempts to adjust to the dataset, but is limited by the mathematical form that guarantees Galilean invariance.
We present direct numerical simulations of turbulent channel flow with passive Lagrangian polymers. To understand the polymer behavior we investigate the behavior of infinitesimal line elements and calculate the probability distribution function (PDF) of finite-time Lyapunov exponents and from them the corresponding Cramers function for the channel flow. We study the statistics of polymer elongation for both the Oldroyd-B model (for Weissenberg number $Wi <1$) and the FENE model. We use the location of the minima of the Cramers function to define the Weissenberg number precisely such that we observe coil-stretch transition at $Wiapprox1$. We find agreement with earlier analytical predictions for PDF of polymer extensions made by Balkovsky, Fouxon and Lebedev [Phys. Rev. Lett., 84, 4765 (2000).] for linear polymers (Oldroyd-B model) with $Wi<1$ and by Chertkov [Phys. Rev. Lett., 84, 4761 (2000).] for nonlinear FENE-P model of polymers. For $Wi>1$ (FENE model) the polymer are significantly more stretched near the wall than at the center of the channel where the flow is closer to homogenous isotropic turbulence. Furthermore near the wall the polymers show a strong tendency to orient along the stream-wise direction of the flow but near the centerline the statistics of orientation of the polymers is consistent with analogous results obtained recently in homogeneous and isotropic flows.
We present numerical simulations of laminar and turbulent channel flow of an elastoviscoplastic fluid. The non-Newtonian flow is simulated by solving the full incompressible Navier-Stokes equations coupled with the evolution equation for the elastoviscoplastic stress tensor. The laminar simulations are carried out for a wide range of Reynolds numbers, Bingham numbers and ratios of the fluid and total viscosity, while the turbulent flow simulations are performed at a fixed bulk Reynolds number equal to 2800 and weak elasticity. We show that in the laminar flow regime the friction factor increases monotonically with the Bingham number (yield stress) and decreases with the viscosity ratio, while in the turbulent regime the the friction factor is almost independent of the viscosity ratio and decreases with the Bingham number, until the flow eventually returns to a fully laminar condition for large enough yield stresses. Three main regimes are found in the turbulent case, depending on the Bingham number: for low values, the friction Reynolds number and the turbulent flow statistics only slightly differ from those of a Newtonian fluid; for intermediate values of the Bingham number, the fluctuations increase and the inertial equilibrium range is lost. Finally, for higher values the flow completely laminarises. These different behaviors are associated with a progressive increases of the volume where the fluid is not yielded, growing from the centerline towards the walls as the Bingham number increases. The unyielded region interacts with the near-wall structures, forming preferentially above the high speed streaks. In particular, the near-wall streaks and the associated quasi-streamwise vortices are strongly enhanced in an highly elastoviscoplastic fluid and the flow becomes more correlated in the streamwise direction.
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