A hybrid spectral/finite-difference large-eddy simulator of turbulent processes in the upper ocean (original) (raw)
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Water Resources Research, 2006
1] Large-eddy simulation (LES) of atmospheric boundary layer (ABL) flow is performed over a homogeneous surface with different heat flux forcings. The goal is to test the performance of dynamic subgrid-scale models in a numerical framework and to compare the results with those obtained in a recent field experimental study (HATS (Kleissl et al., 2004)). In the dynamic model the Smagorinsky coefficient c s is obtained from test filtering and analysis of the resolved large scales during the simulation. In the scale-invariant dynamic model the coefficient is independent of filter scale, and the scaledependent model does not require this assumption. Both approaches provide realistic results of mean vertical profiles in an unstable boundary layer. The advantages of the scale-dependent model become evident in the simulation of a stable boundary layer and in the velocity and temperature spectra of both stable and unstable cases. To compare numerical results with HATS data, a simulation of the evolution of the ABL during a diurnal cycle is performed. The numerical prediction of c s from the scale-invariant model is too small, whereas the coefficients obtained from the scale-dependent version of the model are consistent with results from HATS. LES of the ABL using the scale-dependent dynamic model give reliable results for mean profiles and spectra at stable, neutral, and unstable atmospheric stabilities. However, simulations under strongly stable conditions (horizontal filter size divided by Obukhov length >3.8) display instabilities due to basic flaws in the eddy viscosity closure, no matter how accurately the coefficient is determined. Citation: Kleissl, J., V. Kumar, C. Meneveau, and M. B. Parlange (2006), Numerical study of dynamic Smagorinsky models in largeeddy simulation of the atmospheric boundary layer: Validation in stable and unstable conditions, Water Resour. Res., 42, W06D10W06D10,
A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows
Physics of Fluids, 2005
A scale-dependent dynamic subgrid model based on Lagrangian time averaging is proposed and tested in large eddy simulations ͑LES͒ of high-Reynolds number boundary layer flows over homogeneous and heterogeneous rough surfaces. The model is based on the Lagrangian dynamic Smagorinsky model in which required averages are accumulated in time, following fluid trajectories of the resolved velocity field. The model allows for scale dependence of the coefficient by including a second test-filtering operation to determine how the coefficient changes as a function of scale. The model also uses the empirical observation that when scale dependence occurs ͑such as when the filter scale approaches the limits of the inertial range͒, the classic dynamic model yields the coefficient value appropriate for the test-filter scale. Validation tests in LES of high Reynolds number, rough wall, boundary layer flow are performed at various resolutions. Results are compared with other eddy-viscosity subgrid-scale models. Unlike the Smagorinsky-Lilly model with wall-damping ͑which is overdissipative͒ or the scale-invariant dynamic model ͑which is underdissipative͒, the scale-dependent Lagrangian dynamic model is shown to have good dissipation characteristics. The model is also tested against detailed atmospheric boundary layer data that include measurements of the response of the flow to abrupt transitions in wall roughness. For such flows over variable surfaces, the plane-averaged version of the dynamic model is not appropriate and the Lagrangian averaging is desirable. The simulated wall stress overshoot and relaxation after a jump in surface roughness and the velocity profiles at several downstream distances from the jump are compared to the experimental data. Results show that the dynamic Smagorinsky coefficient close to the wall is very sensitive to the underlying local surface roughness, thus justifying the use of the Lagrangian formulation. In addition, the Lagrangian formulation reproduces experimental data more accurately than the planar-averaged formulation in simulations over heterogeneous rough walls.
Development of Large Eddy Simulation Turbulence Models
2000
A new approach for a non-viscosity one-equation large eddy simulation (LES) subgrid stress model is presented. The new approach uses a tensor coefficient obtained from the dynamic modeling approach of Germano (1991) and scaling that is provided by the sub-grid kinetic energy. Mathematical and conceptual issues motivating the development of this new model are explored. The basic equations that originate in dynamic modeling approaches are Fredholm integral equations of the second kind. These equations have solvability requirements that have not been previously addressed in the context of LES. These conditions are examined for traditional dynamic Smagorinsky modeling (i.e. zeroequation approaches) and the one-equation sub-grid model of Ghosal et al. (1995). It is shown that standard approaches do not always satisfy the integral equation solvability condition. It is also shown that traditional LES models that use the resolved scale strainrate to estimate the sub-grid stresses scale poorly with filter level leading to significant errors in the modeling of the sub-grid scale stress. The poor scaling in traditional LES I would like to express my sincere gratitude to my advisor, Professor Christopher Rutland, for his guidance, technical assistance, encouragement and freedom provided to me during the past five years. I also would like to thank Professor Frederick Elder and Professor David Foster for their assistance in the graduate school admission process.
A new turbulence model for Large Eddy Simulation
Advanced Studies in Theoretical Physics
The present - day Large Eddy Simulation models based on the Smagorinsky assumption and the drawbacks of the dynamic calcula- tion of the closure coe-cient for the generalised subgrid scale turbulent stress tensor are presented. The relations between numerical scheme conservation property of mass, momentum and kinetic energy and the drawbacks of the dynamic Smagorinsky - type turbulence models are shown. A new turbulence model is proposed. The proposed model: a) is able to take into account the anisotropy of the turbulence; b) remove any balance assumption between the production and dissipation of sub- grid scale turbulent kinetic energy; c) is able to eliminate the numerical efiects produced by the non conservation a priori of the resolved kinetic energy. New closure relations for the unknown terms of the subgrid scale viscous dissipation balance equation are proposed. The flltered momentum equations are solved by using a sixth order flnite difierence scheme. The proposed model is t...
Shear-improved Smagorinsky model for large-eddy simulation of wall-bounded turbulent flows
Journal of Fluid Mechanics, 2007
A shear-improved Smagorinsky model is introduced based on results concerning mean-shear effects in wall-bounded turbulence. The Smagorinsky eddy-viscosity is modified as ν T = (C s ∆) 2 (|S|−| S |): the magnitude of the mean shear | S | is subtracted from the magnitude of the instantaneous resolved rate-of-strain tensor |S|; C S is the standard Smagorinsky constant and ∆ denotes the grid spacing. This subgrid-scale model is tested in large-eddy simulations of plane-channel flows at Reynolds numbers Re τ = 395 and Re τ = 590. First comparisons with the dynamic Smagorinsky model and direct numerical simulations for mean velocity, turbulent kinetic energy and Reynolds stress profiles, are shown to be extremely satisfactory. The proposed model, in addition to being physically sound and consistent with the scale-by-scale energy budget of locally homogeneous shear turbulence, has a low computational cost and possesses a high potential for generalization to complex non-homogeneous turbulent flows.
An Assessment of Dynamic Subgrid-Scale Sea-Surface Roughness Models
Flow, Turbulence and Combustion, 2013
Covered by waves with various lengths, the mobile sea surface represents a great challenge to the large-eddy simulation (LES) of atmospheric boundary layer flow over the ocean surface. In this study, we report recent developments and tests of dynamic modeling approaches for the subgrid-scale (SGS) sea-surface roughness for LES. In the model, introduced originally in Yang et al. (J. Fluid Mech., in press, 2013), the SGS roughness is quantified by an integral of the SGS wave spectrum, σ η , weighted based on the wind-wave kinematics, with an unknown model coefficient α w as pre-factor. The coefficient α w is determined dynamically based on the basic constraint that the total surface drag force must be independent of the LES filter scale. The weighted integral σ η represents the effective amplitude of the SGS waves, for which five candidate models are reviewed. Following the computational tests presented in Yang et al. (J. Fluid Mech., in press, 2013), in this study the performance of the dynamic SGS sea-surface roughness models is assessed by a theoretical approach, in which the roughness model is coupled with the critical-layer theory of wind-wave interaction. This theoretical approach mimics the averaged behavior of the LES. Meanwhile, its low computation cost allows the assessment of the model dynamic modeling approach can reliably model the roughness length of the SGS waves without ad-hoc prescription of the model parameter α w . Also, we confirm that to model σ η , an expression based on the kinematics of wind-wave relative motion achieves the best performance among the five candidate models considered.
Simulation of Ekman Boundary Layers by Large Eddy Model with Dynamic Mixed Subfilter Closure
Environmental Fluid Mechanics, 2000
Theoretical analysis of boundary layer turbulence has suggested a feasibility of sufficiently accurate turbulence resolving simulations at relatively coarse meshes. However, large eddy simulation (LES) codes, which employ traditional eddy-viscosity turbulence closures, fail to provide adequate turbulence statistics at coarse meshes especially within a surface layer. Manual tuning of parameters in these turbulence closures may correct low order turbulence statistics but severely harms spectra of turbulence kinetic energy (TKE). For more than decade, engineering LES codes successfully employ dynamic turbulence closures. A dynamic Smagorinsky turbulence closure (DSM) has been already tried in environmental LES. The DSM is able to provide adequate turbulence statistics at coarse meshes but it is not completely consistent with the LES equations. This paper investigates applicability of an advanced dynamic mixed turbulence closure (DMM) to simulations of Ekman boundary layers of high Reynolds number flows. The DMM differs from the DSM by explicit calculation of the Leonard term in the turbulence stress tensor. The Horizontal Array Turbulence Study (HATS) field program has revealed that the Leonard term is indeed an important component of the real turbulence stress tensor.
2004
A new dynamic, scale-dependent subgrid model based on Lagrangian time averaging is proposed. The model is tested in large eddy simulations (LES) of high-Reynolds number boundary layer flows over homogeneous and heterogeneous rough surfaces. The model computes averages over time, following fluid trajectories of the resolved velocity field. The model allows for scale-dependence of the coefficient by including a second test-filtering operation to determine how the coefficient changes as a function of scale. Validation tests in LES of high Reynolds number boundary layer flow over homogeneous surfaces are performed at various resolutions. The model is also tested against detailed atmospheric boundary layer data that include measurements of the response of the flow to abrupt transitions in wall roughness. Results show that the dynamic Smagorinsky coefficient close to the wall is very sensitive to the underlying local surface roughness, thus justifying the use of the Lagrangian formulation. It also reproduces experimental data more accurately than the planar-averaged formulation in simulations over heterogeneous rough surfaces.
Large eddy simulation of subharmonic transition of a spatially developing zero pressure gradient boundary layer at Ma = 0.2 is investigated using three different subgrid scale (SGS) models: Dynamic Smagorinsky [1], dynamic model involving the SGS kinetic energy [2] and dynamic scale similarity model. The interest lies in assessing the capability of each model in predicting the location of transition and the overshoot in the skin friction coefficient which is specific to this transition scenario. In the case of dynamic Smagorinsky model results were obtained for four different grid resolutions and it is observed that the location of transition is largely unaffected, indicating robust performance of the dynamic model in this respect. However, after breakdown and in the turbulent region the simulations with coarsest grids produce insufficient eddy viscosity to sustain the correct value of skin friction along the plate. As a result the coarsest resolution is employed to compare the perf...