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Register a new userOptimal Eddy Viscosity in Closure Models for 2D Turbulent Flows
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We consider the question of fundamental limitations on the performance of eddy-viscosity closure models for turbulent flows, focusing on the Leith model for 2D Large-Eddy Simulation. Optimal eddy viscosities depending on the magnitude of the vorticity gradient are determined subject to minimum assumptions by solving PDE-constrained optimization problems defined such that the corresponding optimal Large-Eddy Simulation best matches the Direct Numerical Simulation. The main finding is that with a fixed cutoff wavenumber $k_c$, the performance of the Large-Eddy Simulation systematically improves as the regularization in the solution of the optimization problem is reduced and this is achieved with the optimal eddy viscosities exhibiting increasingly irregular behavior with rapid oscillations. Since the optimal eddy viscosities do not converge to a well-defined limit as the regularization vanishes, we conclude that the problem of finding an optimal eddy viscosity is not in fact well posed.
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This study aims to quantify how turbulence in a channel flow mixes momentum in the mean sense. We applied the macroscopic forcing method to direct numerical simulation (DNS) of a turbulent channel flow at Re$_tau$=180 using two different forcing strategies that are designed to separately assess the anisotropy and nonlocality of momentum mixing. In the first strategy, the leading term of the Kramers-Moyal expansion of the eddy viscosity operator is quantified where the macroscopic forcing is employed to reveal all 81 tensorial coefficients that essentially represent the local-limit eddy viscosity. The results indicate: (1) eddy viscosity has significant anisotropy, (2) Reynolds stresses are generated by both mean strain rate and mean rotation rate tensors, and (3) the local-limit eddy viscosity generates asymmetric Reynolds stress tensors. In the second strategy, the eddy viscosity operator is considered as an integration kernel representing the nonlocal influence of mean gradients on the Reynolds stresses. Considering the average of this kernel in the homogeneous directions, the macroscopic forcing is designed to reveal the nonlocal effects in the wall-normal direction for all 9 components of the Reynolds stresses. Our results indicate that while the shear component of the Reynolds stress is reasonably controlled by the local mean gradients, other components of the Reynolds stress are highly nonlocal. These two analyses provide accurate verification data for quantitative testing of anisotropy and nonlocality effects in turbulence closure models.
In nature turbulent flows exist that are neither simply 2D nor 3D but boundary conditions, such as varying stratification, force them towards the one or the other. Here, we report the first evidence of the co-existence of 2D and 3D turbulence in an experimental flow driven by Faraday waves in water. We find that an inverse energy cascade at the fluid surface and a direct energy cascade in the 3D bulk flow underneath exist simultaneously. We base our analysis on temporally and spatially well-resolved velocity fields measured at horizontal and vertical planes. The findings suggest that the strongly turbulent 2D surface flow drives the 3D bulk flow through sporadic vertical jets as a source of momentum.
A new methodology based on energy flux similarity is suggested in this paper for large eddy simulation (LES) of transitional and turbulent flows. Existing knowledge reveals that the energy cascade generally exists in transitional and turbulent flows with different distributions, and the characteristic quantity of scale interaction in energy cascade processes is energy flux. Therefore, energy flux similarity is selected as the basic criterion to secure the flow field getting from LES highly similar to the real flow field. Through a priori tests, we find that the energy flux from the tensor-diffusivity (TD) model has high similarity with the real energy flux. Then, we modify the modelled energy flux from the TD model and obtain uniform formulas of energy flux similarity corresponding to different filter widths and locations in the wall-bounded turbulence. To secure the robustness of simulation and the LES results similar to the real flow, we apply the energy flux similarity method (EFSM) to the Smagorinsky model in the LES of compressible turbulent channel flow, compressible flat-plate flow, and flow over a compressible ramp. The a posteriori tests show that, overall, EFSM can better predict these flows than other subgrid-scale models. In the simulation of turbulent channel flow, EFSM can accurately predict the mean stream-wise velocity, Reynolds stress, and affluent coherent structures. In LES of compressible flat-plate flow, EFSM could provide accurate simulation results of the onset of transition and transition peak, skin friction, and mean stream-wise velocity in cases with three different grid scales. Meanwhile, for flow over a compressible ramp, EFSM could correctly describe the process of bypass transition, locations of separation and reattachment in the corner region, and abundant coherent vortex structures, etc.
For wall-bounded turbulent flows, Townsends attached eddy hypothesis proposes that the logarithmic layer is populated by a set of energetic and geometrically self-similar eddies. These eddies scale with a single length scale, their distance to the wall, while their velocity scale remains constant across their size range. To investigate the existence of such structures in fully developed turbulent pipe flow, stereoscopic particle image velocimetry measurements were performed in two parallel cross-sectional planes, spaced apart by a varying distance from 0 to 9.97$R$, for $Re_tau = 1310$, 2430 and 3810. The instantaneous turbulence structures are sorted by width using an azimuthal Fourier decomposition, allowing us to create a set of average eddy velocity profiles by performing an azimuthal alignment process. The resulting eddy profiles exhibit geometric self-similar behavior in the $(r,theta)$-plane for eddies with spanwise length scales ($lambda_theta/R$) spanning from 1.03 to 0.175. The streamwise similarity is further investigated using two-point correlations between the two planes, where the structures exhibit a self-similar behaviour with length scales ($lambda_theta/R$) ranging from approximately $0.88$ to $0.203$. The candidate structures thereby establish full three-dimensional geometrically self-similarity for structures with a volumetric ratio of $1:80$. Beside the geometric similarity, the velocity magnitude also exhibit self-similarity within these ranges. However, the velocity scale depends on eddy size, and follow the trends based on the scaling arguments proposed by cite{Perry1986}.
Phoresis, the drift of particles induced by scalar gradients in a flow, can result in an effective compressibility, bringing together or repelling particles from each other. Here, we ask whether this effect can affect the transport of particles in a turbulent flow. To this end, we study how the dispersion of a cloud of phoretic particles is modified when injected in the flow, together with a blob of scalar, whose effect is to transiently bring particles together, or push them away from the center of the blob. The resulting phoretic effect can be quantified by a single dimensionless number. Phenomenological considerations lead to simple predictions for the mean separation between particles, which are consistent with results of direct numerical simulations. Using the numerical results presented here, as well as those from previous studies, we discuss quantitatively the experimental consequences of this work and the possible impact of such phoretic mechanisms in natural systems.
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