We investigate the role of the bulk eddy-viscosity variation on the well-known log-layer mismatch problem. An analysis of the mean momentum-balance shows that the modeled stress term close to the wall can dominate because of the bulk eddy-viscosity. Consequently, the momentum-balance equation lacks a degree-of-freedom and the mean velocity conforms to an incorrect profile to satisfy the momentum-balance. We show that zonal enforcement of the target mass flow-rate can be an effective strategy to introduce an additional degree of freedom to the mean momentum-balance, which led to a significant reduction in the log-layer mismatch. When the mass flow-rate is enforced zonally, the filtered velocity field attains its own constant velocity-scale above the Reynolds-averaged field, supporting the hypothesis that there exists an artificial boundary layer above the Reynolds-averaged region. We simulate turbulent channel flows at friction Reynolds numbers of 2000 and 5200 on coarse meshes that would put the first point away from the wall well into the logarithmic layer. Second-order turbulence statistics and one-dimensional velocity spectra agree well with the direct numerical simulation benchmark data when results are normalized by the velocity-scale extracted from the filtered velocity field. Additionally, the error in the skin-friction coefficient for friction Reynolds numbers of 2000 decreased from $14.1\%$ to $2.5\%$ when we enforced the mass flow-rate zonally.
Motivated by the concept of eddy viscosity tensor in improved Boussinesq hypothesis, a transport model of high-order eddy viscosity tensor in 2D-3C turbulence structure is derived from the second-order moment model by tensorial analysis.
In isotropic helical turbulence, a new single helical model is suggested for large eddy simulation. Based on the Kolmogrov's hypotheses, the helical model is proposed according to the balance of helicity dissipation and the average of helicity flux across the inertial range, and the helical model is a kind of eddy viscosity model. The coefficient of the helical model is constant and can be also determined dynamically. Numerical simulations of forced and decaying isotropic helical turbulence demonstrate that the helical model predicts the energy and helicity evolution well. The statistical char…
The predictions of resolvent analysis for turbulent channel flow are evaluated for a friction Reynolds number of Retau = 550. In addition to the standard resolvent operator with kinematic viscosity, a resolvent operator augmented with the Cess eddy viscosity is considered. Adding eddy viscosity significantly alters the low-rank behavior of the resolvent. Regardless of the wave speed selected, the eddy resolvent is low-rank for spanwise wavelengths of ly+ = 80 and ly/h = 3.5 in comparison to the standard resolvent whose low-rank behavior depends on the wave speed. The leading eddy modes have hi…
In this paper, we have used renormalized viscosity for performing large eddy simulations (LES) of decaying homogeneous and isotropic turbulence inside a periodic cube on coarse grids ($32^3$, $64^3$ and $128^3$) at initial Taylor Reynolds number ${\mathrm{Re}_λ \approx 315} $. The LES results were compared with direct numerical simulation (DNS) results on $512^3$ grid. We observe good agreement between LES and DNS results on the temporal evolution of turbulence kinetic energy ${E(t)}$, kinetic energy spectrum ${E_{u}(k)}$, kinetic energy flux ${Π_u(k)}$. The isosurfaces of velocity magnitude a…
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 filtered Direct Numerical Simulation. First, we consider pointwise match in the physical space and the main finding is that with a fixed cutoff wavenumber $k_c…
Response modes computed via linear resolvent analysis of a turbulent mean-flow field have been shown to qualitatively capture characteristics of the observed turbulent coherent structures in both wall-bounded and free shear flows. To make such resolvent models predictive, the nonlinear forcing term must be closed. Strategies to do so include imposing self-consistent sets of triadic interactions, proposing various source models, or through turbulence modelling. For the latter, several investigators have proposed using the mean-field eddy viscosity acting linearly on the fluctuation field. In th…
Impact of perturbed eddy-viscosity modeling on stability and shape sensitivity of the hydro-turbine vortex rope using linearized Reynolds-averaged Navier-Stokes equations
This work presents a converged framework of Machine-Learning Assisted Turbulence Modeling (MLATM). Our objective is to develop a turbulence model directly learning from high fidelity data (DNS/LES) with eddy-viscosity hypothesis induced. First, the target machine-learning quantity is discussed in order to avoid the ill-conditioning problem of RANS equations. Then, the novel framework to build the turbulence model using the prior estimation of traditional models is demonstrated. A close-loop computational chain is designed to ensure the convergence of result. Besides, reasonable non-dimensional…
In this paper we employ renormalized viscosity and thermal diffusivity to construct a subgrid-scale model for large eddy simulation (LES) of turbulent thermal convection. For LES, we add $ν_\mathrm{ren} \propto Π_u^{1/3} (π/Δ)^{-1/3}$ to the kinematic viscosity; here $Π_u$ is the turbulent kinetic energy flux, and $Δ$ is the grid spacing. In our model, the turbulent Prandtl number is unity. We performed LES of turbulent thermal convection on a $128^3$ grid and compare the results with direct numerical simulation (DNS) on a $512^3$ grid. There is a good agreement between the LES and DNS results…
In this study, we utilize a novel approach to solve the Ekman equations for eddy viscosity profiles in the stable boundary layer. By doing so, a well-known expression for the stable boundary layer height by Zilitinkevich (Boundary-Layer Meteorology, 1972, Vol. 3, 141--145) is rediscovered.
The aim of this study is to improve the prediction of near-wall mean streamwise velocity profile $U^+$ by using a simple method. The $U^+$ profile is obtained by solving the momentum equation which is written as an ordinary differential equation. An eddy viscosity formulation based on a near-wall turbulent kinetic energy $k^+$ function (R. Absi, Analytical solutions for the modeled $k$-equation, ASME J. Appl. Mech. \textbf{75}, 044501, 2008) and the van Driest mixing length equation (E.R. van Driest, On turbulent flow near a wall, J. Aero. Sci. \textbf{23}, 1007, 1956) is used. The parameters …
Most turbulence models used in Reynolds-averaged Navier-Stokes (RANS) simulations are partial differential equations (PDE) that describe the transport of turbulent quantities. Such quantities include turbulent kinetic energy for eddy viscosity models and the Reynolds stress tensor (or its anisotropy) in differential stress models. However, such models all have limitations in their robustness and accuracy. Inspired by the successes of machine learning in other scientific fields, researchers have developed data-driven turbulence models. Recently, a nonlocal vector-cloud neural network with embed…
We use laser-Doppler velocimetry (LDV) experiments and Reynolds-averaged Navier--Stokes (RANS) simulations to study the characteristic flow patterns downstream of a standardized clockwise swirl disturbance generator. After quantifying the impact of the mesh size, we evaluate the potential of various eddy-viscosity turbulence models in providing reasonable approximations with respect to the experimental reference. The choice of turbulent models reflects current industry practice. Our results suggest that models from the $k$-$ε$ family are more accurate in predicting swirling flows than models f…
By analyzing the Karman-Howarth equation for filtered velocity fields in turbulent flows, we show that the two-point correlation between filtered strain-rate and subfilter stress tensors plays a central role in the evolution of filtered-velocity correlation functions. Two-point correlations-based {\it statistical priori tests} thus enable rigorous and physically meaningful studies of turbulence models. Using data from direct numerical simulations of isotropic and channel flow turbulence we show that local eddy viscosity models fail to exhibit the long tails observed in the real subfilter stres…
We propose a variational approach to identification of an optimal nonlinear eddy viscosity as a subscale turbulence representation for POD models. The ansatz for the eddy viscosity is given in terms of an arbitrary function of the resolved fluctuation energy. This function is found as a minimizer of a cost functional measuring the difference between the target data coming from a resolved direct or large-eddy simulation of the flow and its reconstruction based on the POD model. The optimization is performed with a data-assimilation approach generalizing the 4D-VAR method. POD models with optima…
The stability of flows in layers of finite thickness $H$ is examined against small scale three dimensional (3D) perturbations and large scale two-dimensional (2D) perturbations. The former provide an indication of a forward transfer of energy while the later indicate an inverse transfer and the possibility of an inverse cascade. The analysis is performed using a Floquet-Bloch code that allows to examine the stability of modes with arbitrary large scale separation. For thin layers the 3D perturbations become unstable when the layer thickness $H$ becomes larger than $H > c_1 (ν\ell_{_U}/U)^{1/2}…
The eddy viscosity for a turbulent compressible fluid with a relativistic equation of state is derived. Compressibility allows for sound modes, but the eddy viscosity in the shear mode is found to be the same as for incompressible fluids. For two space dimensions (which is the relevant case for the dynamics of relativistic heavy-ion collisions) the eddy viscosity in the shear mode is negative, reducing the effective viscosity below its microscopic value. This could explain the tiny viscosity found at RHIC. Implications for the experimentally accessible elliptic flow coefficient at the LHC are …
For the purpose of Uncertainty Quantification (UQ) of Reynolds-Averaged Navier-Stokes closures, we introduce a framework in which perturbations in the eigenvalues of the anisotropy tensor are made in order to bound a Quantity-of-Interest based on limiting states of turbulence. To make the perturbations representative of local flow features, we introduce two additional transport equations for linear combinations of these aforementioned eigenvalues. The location, magnitude and direction of the eigenvalue perturbations are now governed by the model transport equations. The general behavior of our…
This study highlights the importance of satisfying the eddy viscosity equivalence below the logarithmic layer, to deriving accurate compressibility transformations. First, we analyze the ability of known transformations to satisfy the eddy viscosity equivalence and show that the accuracy of these transformation is strongly dependent on this ability. Secondly, in a step-by-step manner, we devise new transformations that satisfy this hypothesis. An approach based on curve fitting of the incompressible Direct Numerical Simulation data for eddy viscosity profiles below the logarithmic layer provid…
In the present paper, we address the important point of the proportionality between the longitudinal integral lengthscale ($L$) and the characteristic mean flow width ($δ$) using experimental data of an axisymmetric wake and a turbulent planar jet. This is a fundamental hypothesis when deriving the self-similar scaling laws in free shear flows, irrespective of turbulence dissipation scaling. We show that $L/δ$ is indeed constant, at least in a range of streamwise distances between 15 and 50 times the characteristic inlet dimension ($L_{ref}$, nozzle width or wake generator size). Furthermore, …
We present a hydrodynamic theory for electron-hole magnetotransport in graphene incorporating carrier-population imbalance, energy, and momentum relaxation processes. We focus on the electric response and find that the carrier and energy imbalance relaxation processes strongly modify the shear viscosity, so that an effective viscosity can be negative in the vicinity of charge neutrality. We predict an emergent eddy flow pattern of swirling currents and explore its manifestation in nonlocal resistivity oscillations in a strip of graphene driven by a source current.
Linear stability analysis has proven to be a useful tool in the analysis of dominant coherent structures, such as the von Kármán vortex street and the global spiral mode associated with the vortex breakdown of swirling jets. In recent years, linear stability analysis has been applied successfully to turbulent time-mean flows, instead of laminar base-flows, \textcolor{black}{which requires turbulent models that account for the interaction of the turbulent field with the coherent structures. To retain the stability equations of laminar flows, the Boussinesq approximation with a spatially nonunif…
In this paper, we propose a variational approach to estimate eddy viscosity using forward sensitivity method (FSM) for closure modeling in nonlinear reduced order models. FSM is a data assimilation technique that blends model's predictions with noisy observations to correct initial state and/or model parameters. We apply this approach on a projection based reduced order model (ROM) of the one-dimensional viscous Burgers equation with a square wave defining a moving shock, and the two-dimensional vorticity transport equation formulating a decay of Kraichnan turbulence. We investigate the capabi…
Recently the generation of eddy currents by interacting surface waves was observed experimentally. The phenomenon provides the possibility for manipulation of particles which are immersed in the fluid. The analysis shows that the amplitude of the established eddy currents produced by stationary surface waves does not depend on the fluid viscosity in the free surface case. The currents become parametrically larger being inversely proportional to the square root of the fluid viscosity in the case when the fluid surface is covered by an almost incompressible thin liquid (i.e. shear elasticity is …
Magnetic induction in magnetohydrodynamic fluids at magnetic Reynolds number (Rm) less than~1 has long been known to cause magnetic drag. Here, we show that when $\mathrm{Rm} \gg 1$ and the fluid is in a hydrodynamic-dominated regime in which the magnetic energy is much smaller than the kinetic energy, induction due to a mean shear flow leads to a magnetic eddy viscosity. The magnetic viscosity is derived from simple physical arguments, where a coherent response due to shear flow builds up in the magnetic field until decorrelated by turbulent motion. The dynamic viscosity coefficient is approx…
This paper introduces a new approach to Large-Eddy Simulation (LES) where subgrid-scale (SGS) dissipation is applied proportionally to the degree of local spectral broadening, hence mitigated or deactivated in regions dominated by large-scale and/or laminar vortical motion. The proposed Coherent vorticity preserving (CvP) LES methodology is based on the evaluation of the ratio of the test-filtered to resolved (or grid-filtered) enstrophy $σ$. Values of $σ$ close to 1 indicate low sub-test-filter turbulent activity, justifying local deactivation of the SGS dissipation. The intensity of the SGS …
In RANS simulations for turbulent scalar transport, it is common that using an eddy-viscosity (EV) model to close the Reynolds stress yields reasonable mean flow predictions but large errors in scalar transfer results regardless of scalar flux model inadequacies. This failure mode of EV models is generally related to the fact that the transport of momentum and scalar depends on different Reynolds stress components. The present work addresses two common issues relevant to such failures in turbulent scalar transport around obstacles. The first issue is the general overprediction of scalar transf…
The Quasi-Spectral Viscosity (QSV) method is a novel closure for a high-order finite-difference discretization of the filtered compressible Navier-Stokes equations capable of unifying dynamic sub-filter scale (SFS) modeling and shock capturing under a single mathematical framework. Its innovation lies in the introduction of a physical-space implementation of a spectral-like SFS dissipation term by leveraging residuals of filter operations, achieving two goals: (1) estimating the energy of the resolved solution near the grid cutoff; (2) imposing a plateau-cusp shape to the spectral distribution…
A large number of models which address the dynamics of particle-laden turbulent flows have been developed based on the assumption of local isotropy and use the Kolmogorov constant that correlates the spectral distribution of turbulent kinetic energy with the turbulent dissipation rate. Many turbulence models (Stochastic and LES models) use the Kolmogorov constant in the formulation. Compilation of a large number of experimental data for different flow configurations has revealed that the Kolmogorov constant is independent of Reynolds number in the limit of high Reynolds number (Sreenivasan, 19…
We investigate a hierarchy of eddy-viscosity terms in POD Galerkin models to account for a large fraction of unresolved fluctuation energy. These Galerkin methods are applied to Large Eddy Simulation data for a flow around the vehicle-like bluff body call Ahmed body. This flow has three challenges for any reduced-order model: a high Reynolds number, coherent structures with broadband frequency dynamics, and meta-stable asymmetric base flow states. The Galerkin models are found to be most accurate with modal eddy viscosities as proposed by Rempfer & Fasel (1994). Robustness of the model solutio…
We present a prognostic, one-equation model for eddy-mean flow interactions to parameterize the divergence of the Eliassen-Palm flux tensor (EPFT) that arises from thickness-weighted averaging (TWA) the hydrostatic Boussinesq equations. The TWA system of equations does not invoke approximations beyond those for which the hydrostatic Boussinesq equations are valid, constituting a mathematically consistent framework with clear physical interpretations. This model is intended for the adiabatic interior of zonally symmetric flows, in the absence of topographic features, where terms corresponding t…
Predicting the behavior of turbulent flows using large-eddy simulation requires modeling of the subgrid-scale stress tensor. This tensor can be approximated using mixed models, which combine the dissipative nature of functional models with the capability of structural models to approximate out-of-equilibrium effects. We propose a mathematical basis to mix (functional) eddy-viscosity models with the (structural) Bardina model. By taking an anisotropic minimum-dissipation (AMD) model for the eddy viscosity, we obtain the (single-layer) AMD-Bardina model. In order to also obtain a physics-conform…
Sediment transport over wave-induced ripples is a very complex phenomenon where available models fail to provide accurate predictions. For coastal engineering applications, the 1-DV advection-diffusion equation could be used with an additional parameter α related to the process of vortex shedding above ripples (Absi, 2010). The aim of this study is to provide simple practical analytical tools. An analytical eddy viscosity profile was validated by DNS data of turbulent channel flows (Absi et al., 2011). In this study, we will show that: (1) the period-averaged eddy viscosity in oscillatory boun…
We generate explicit height-dependent eddy viscosity coefficients in the Ekman layer from convex wind speed profiles. The solutions we obtain are parameterized in terms of the relative deflection angle between the wind directions at the top and bottom of the flow, as well as the geostrophic wind speed and a velocity scale we interpret as the transfer rate of horizontal momentum in the vertical direction. The solutions may be used to infer the thickness of the Ekman layer for a variety of deflection angles different from deflection angle of the classic Ekman spiral.
Despite well-known limitations of Reynolds-averaged Navier-Stokes (RANS) simulations, this methodology remains the most widely used tool for predicting many turbulent flows, due to computational efficiency. Machine learning is a promising approach to improve the accuracy of RANS simulations. One major area of improvement is using machine learning models to represent the complex relationship between the mean flow field gradients and the Reynolds stress tensor. In the present work, modifications to improve the stability of previous optimal eddy viscosity approaches for RANS simulations are prese…
Physical damping, regarding the nonlinear Navier-Stokes viscous flow dynamics, refers to a tensorial turbulent dissipation term, attributed to adjacent moving macroscopic flow components. Mutual dissipation among these parts of fluid is described by a braking term in the momentum equation together with a heating term in the energy equation, both responsible of the damping of the momentum variation and of the viscous conversion of mechanical energy into heat. A macroscopic mixing scale length is currently the only characteristic length needed in the nonlinear modelling of viscous fluid dynamics…
The combination of the high-order accurate spectral difference discretization on unstructured grids with subgrid-scale modelling is investigated for large eddy simulation of a muffler at Re = 4.64 10^4 and low Mach number. The subgrid-scale stress tensor is modelled by the wall-adapting local eddy-viscosity model with a cut-off length which is a decreasing function of the order of accuracy of the scheme. Numerical results indicate that although the high-order solver without subgrid-scale modelling is already able to capture well the features of the flow, the coupling with the wall-adapting loc…
Unstable equilibrium solutions in a homogeneous shear flow with sinuous symmetry are numerically found in large-eddy simulations (LES) with no kinetic viscosity. The small-scale properties are determined by the mixing length scale $l_S$ used to define eddy viscosity, and the large-scale motion is induced by the mean shear at the integral scale, which is limited by the spanwise box dimension $L_z$. The fraction $ R_S= L_z/l_S$, which plays the role of a Reynolds number, is used as a numerical continuation parameter. It is shown that equilibrium solutions appear by a saddle-node bifurcation as $…
Large-eddy simulation (LES) of a turbulent flow through an array of building-like obstacles is an idealized model to study transport of contaminants in the urban atmospheric boundary layer (UABL). A reasonably accurate LES prediction of turbulence in such an UABL must resolve a significant proportion of the small but energetic eddies in the roughness sublayer, which remains prohibitive even though computational power has been increased significantly. In this article, we present a large-eddy simulation methodology to study turbulence in UABLs, where the turbulence closure is based on coupling t…
Direct numerical simulation (DNS) is very accurate however, the computational cost increases significantly with the increase in Reynolds number. On the other hand, we have the Reynolds Averaged Navier Stokes (RANS) method for simulating turbulent flows, which needs less computational power. Turbulence models based on linear eddy viscosity models (LEVM) in the RANS method, which use a linear stress-strain rate relationship for modelling the Reynolds stress tensor do not perform well for complex flows \cite{shih1995new} . In this work, we intend to study the performance of non linear eddy viscos…
We propose two-equations models in order to capture the dynamics of a turbulent plasma undergoing compression and experiencing large viscosity variations. The models account for possible relaminarization phases and rapid viscosity changes through closures dependent on the turbulent Reynolds and on the viscosity Froude numbers. These closures are determined from a data-driven approach using eddy-damped quasi normal markovian simulations. The best model is able to mimic the various self-similar regimes identified in \citet{Viciconte2018} and to recover the rapid transition limits identified by \…
