Lagrangian velocity autocorrelation and eddy viscosity in two‐dimensional anisotropic turbulence

1991 ◽  
Vol 3 (10) ◽  
pp. 2426-2437 ◽  
Author(s):  
Toshiyuki Gotoh ◽  
Yukio Kaneda
Keyword(s):  
Eddy Viscosity ◽  
Two Dimensional ◽  
Anisotropic Turbulence ◽  
Velocity Autocorrelation ◽  
Lagrangian Velocity

Evaluation of Turbulence Models Using Direct Numerical and Large-Eddy Simulation Data

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Hassan Raiesi ◽  
Ugo Piomelli ◽  
Andrew Pollard
Keyword(s):  
Boundary Layer ◽  
Large Eddy Simulation ◽  
Eddy Viscosity ◽  
Predictive Accuracy ◽  
Turbulence Models ◽  
Special Treatment ◽  
Two Dimensional ◽  
Square Duct ◽  
Eddy Simulation ◽  
Large Eddy

The performance of some commonly used eddy-viscosity turbulence models has been evaluated using direct numerical simulation (DNS) and large-eddy simulation (LES) data. Two configurations have been tested, a two-dimensional boundary layer undergoing pressure-driven separation, and a square duct. The DNS and LES were used to assess the k−ε, ζ−f, k−ω, and Spalart–Allmaras models. For the two-dimensional separated boundary layer, anisotropic effects are not significant and the eddy-viscosity assumption works well. However, the near-wall treatment used in k−ε models was found to have a critical effect on the predictive accuracy of the model (and, in particular, of separation and reattachment points). None of the wall treatments tested resulted in accurate prediction of the flow field. Better results were obtained with models that do not require special treatment in the inner layer (ζ−f, k−ω, and Spalart–Allmaras models). For the square duct calculation, only a nonlinear constitutive relation was found to be able to capture the secondary flow, giving results in agreement with the data. Linear models had significant error.

Parameterization of dispersion in two-dimensional turbulence

2001 ◽  
Vol 439 ◽  
pp. 279-303 ◽  
Author(s):  
C. PASQUERO ◽  
A. PROVENZALE ◽  
A. BABIANO
Keyword(s):  
Velocity Distribution ◽  
Single Particle ◽  
Stochastic Models ◽  
Particle Dispersion ◽  
Turbulent Dispersion ◽  
Two Dimensional ◽  
Component Process ◽  
Velocity Autocorrelation ◽  
Coherent Vortices ◽  
Non Gaussian

We investigate the performance of standard stochastic models of single-particle dispersion in two-dimensional turbulence. Owing to the presence of coherent vortices, particle dispersion in two-dimensional turbulence is characterized by a non-Gaussian velocity distribution and a non-exponential velocity autocorrelation, and it cannot be properly captured by either linear or nonlinear stochastic models with a single component process. Based on physical and dynamical considerations, we introduce a family of two-process stochastic models that provide a better parameterization of turbulent dispersion in rotating barotropic flows.

Reynolds stress and eddy viscosity in direct numerical simulations of sheared two-dimensional turbulence

2010 ◽  
Vol 657 ◽  
pp. 394-412 ◽  
Author(s):  
PATRICK F. CUMMINS ◽  
GREG HOLLOWAY
Keyword(s):  
Reynolds Stress ◽  
Large Scale ◽  
Eddy Viscosity ◽  
Finite Domain ◽  
Spectral Space ◽  
Two Dimensional ◽  
Initial Value ◽  
Theoretical Predictions ◽  
Eddy Field ◽  
Scale Shear

The Reynolds stress associated with the adjustment of two-dimensional isotropic eddies subject to a large-scale shear flow is examined in a series of initial-value calculations in a periodic channel. Several stages in the temporal evolution of the stress can be identified. Initially, there is a brief period associated with quasi-passive straining of the eddy field in which the net Reynolds stress and the associated eddy viscosity remain essentially zero. In spectral space this is characterized by mutual cancellation of contributions to the Reynolds stress at high and low eddy wavenumbers. Subsequently, eddy–eddy interactions produce a tendency to restore isotropy at higher eddy wavenumbers, leading to an overall positive eddy viscosity associated with the dominant contribution to the Reynolds stress at low eddy wavenumbers. These results are consistent with theoretical predictions of positive eddy viscosity for initially isotropic homogeneous two-dimensional turbulence. Due to the inverse cascade, the accumulation with time of energy at the scale of the channel produces a competing tendency to negative eddy viscosity associated with linear shearing of the disturbances. This finite-domain effect may become dominant if the nonlinearity of the eddy field is relatively weak.

scholarly journals SUBGRID MODELLING IN DEPTH INTEGRATED FLOWS

1988 ◽  
Vol 1 (21) ◽  
pp. 35 ◽  
Author(s):  
P.A. Madsen ◽  
M. Rugbjerg ◽  
I.R. Warren
Keyword(s):  
Shear Stress ◽  
Large Scale ◽  
Eddy Viscosity ◽  
Grid Size ◽  
Coastal Engineering ◽  
Shear Stresses ◽  
Two Dimensional ◽  
Bottom Shear Stress ◽  
Hydrodynamic Simulations ◽  
Engineering Studies

Hydrodynamic simulations in coastal engineering studies are still most commonly carried out using two-dimensional vertically integrated mathematical models. As yet, threedimensional models are too expensive to be put into general use. However, the tendency with 2-D models is to use finer and finer resolution so that it becomes necessary to include approximations to some 3-D phenomena. It has been shown by many authors that simulations of large scale eddies can be quite realistic in 2-D models (c.f. Abbott et al. 1985). Basically there exists two different mechanisms of circulation generation. The first one is based on a balance between horizontally and grid-resolved momentum transfers and the bed resistance - i.e. a balance between the convective momentum terms and the bottom shear stress. The second one is due to momentum transfers that are not resolved at the grid scale but appears instead as horizontally distributed shear stresses. In many practical situations the circulations will be governed by the first mechanism. This is the case if the diameter of the circulation and the grid size is much larger than the water depth. In this situation the eddies are friction dominated so that the effect of sub-grid eddy viscosity is limited. In this case 2-D models are known to produce very realistic results and several comparisons with measurements have been reported in the literature.

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