Kinematic simulation for stably stratified and rotating turbulence

The properties of one-particle and particle-pair diffusion in rotating and stratified turbulence are studied by applying the rapid distortion theory (RDT) to a kinematic simulation (KS) of the Boussinesq equation with a Coriolis term.Scalings for one- and two-particle horizontal and vertical diffusions in purely rotating turbulence are proposed for small Rossby numbers.Particular attention is given to the locality-in-scale hypothesis for two-particle diffusion in purely rotating turbulence both in the horizontal and the vertical directions. It is observed that both rotation and stratification decrease the pair diffusivity and improve the validity of the locality-in-scale hypothesis. In the case of stratification the range of scales over which the locality-in-scale hypothesis is observed is increased.It is found that rotation decreases the diffusion in the horizontal direction as well as, though to a much lesser extent, in the vertical direction.     

Invariant subgrid modelling in large-eddy simulation of heat convection turbulence

Symmetries have an important role in turbulence. To some extent, they contain the physics of the equations (conservation laws, etc.), and it is essential that turbulence models respect them. However, as observed by Oberlack (Annual Research Briefs. Stanford University, Stanford 1997) and next by Razafindralandy and Hamdouni (Direct and Large-Eddy Simulation 6: Proceedings of the 6th International ERCOFTAC Workshop on Direct and Large-Eddy Simulation. Springer, Heidelberg, 2006) in the case of an isothermal fluid, only few subgrid stress tensor models preserve the symmetries of the Navier–Stokes equations. In this communication, we present the symmetries of the equations of a non-isothermal fluid flow and analyze some common subgrid stress tensor and flux models under the point of view of these symmetries.      

Inlet grid-generated turbulence for large-eddy simulations

A new technique of generating turbulence in large-eddy simulations (LES) has been investigated and results compared with previous studies for validation. The proposed gridInlet technique uses a grid pattern on the inlet boundary patch to produce grid-generated turbulence as used in wind tunnel experiments. This allows the turbulence integral length scale to be controlled by changing the grid size, while the turbulence intensity is controlled by changing the inlet distance. The objective of this paper is to investigate domain and mesh requirements to implement the gridInlet technique. This technique is most suited to studies on the influence of high-intensity isotropic turbulence on objects, particularly if comparisons are to be made to experimental data obtained with grid-generated turbulence.     

Temporal large-eddy simulation of unstratified and stably stratified turbulent channel flows

Recently, Pruett et al. [Pruett, C.D., Gatski, T.B., Grosch, C.E., Thacker, W.D., 2003. The temporally filtered Navier–Stokes equations: properties of the residual stress. Phys. Fluids 15, 2127–2140] proposed an approach to large-eddy simulation (LES) based on time-domain filtering; their approach was termed temporal large-eddy simulation or TLES. In a continuation of their work, Pruett and collaborators tested their methodology by successfully performing TLES of unstratified turbulent channel flow up to Reynolds number of 590 (based on channel half-height and friction velocity) [Pruett, C.D., Thomas, B.C., Grosch, C.E., Gatski, T.B., 2006. A temporal approximate deconvolution model for LES. Phys. Fluids 18, 028104, 4p]. Here, we carefully analyze the TLES methodology in order to understand the role of its key components and in the process compare TLES to more traditional approaches of spatial LES. Furthermore, we extend the methodology to stably stratified turbulent channel flow.     

Direct numerical simulation of homogeneous stratified rotating turbulence

The effects of the Prandtl number on stratified rotating turbulence have been studied in homogeneous turbulence by using direct numerical simulations and a rapid distortion theory. Fluctuations under strong stable-density stratification can be theoretically divided into the WAVE and the potential vorticity (PV) modes. In low-Prandtl-number fluids, the WAVE mode deteriorates, while the PV mode remains. Imposing rotation on a low-Prandtl-number fluid makes turbulence two-dimensional as well as geostrophic; it is found from the instantaneous turbulent structure that the vortices merge to form a few vertically-elongated vortex columns. During the period toward two-dimensionalization, the vertical vortices become asymmetric in the sense of rotation. Communicated by S. Obi PACS 47.55.Hd     

Direct and large eddy simulation of stratified turbulence

Simulations of geophysical turbulent flows require a robust and accurate subgrid-scale turbulence modeling. To evaluate turbulence models for stably stratified flows, we performed direct numerical simulations (DNSs) of the transition of the three-dimensional Taylor–Green vortex and of homogeneous stratified turbulence with large-scale horizontal forcing. In these simulations we found that energy dissipation is concentrated within thin layers of horizontal tagliatelle-like vortex sheets between large pancake-like structures. We propose a new implicit subgrid-scale model for stratified fluids, based on the Adaptive Local Deconvolution Method (ALDM). Our analysis proves that the implicit turbulence model ALDM correctly predicts the turbulence energy budget and the energy spectra of stratified turbulence, even though dissipative structures are not resolved on the computational grid.     

A new development of the dynamic procedure in large-eddy simulation based on a Finite Volume integral approach. Application to stratified turbulence

A Finite Volume-based large-eddy simulation method is proposed along with a suitable extension of the dynamic modelling procedure that takes into account for the integral formulation of the governing filtered equations. Discussion about the misleading interpretation of FV in some literature is addressed. Then, the classical Germano identity is congruently rewritten in such a way that the determination of the modelling parameters does not require any arbitrary averaging procedure and thus retains a fully local character. The numerical modelling of stratified turbulence is the specific problem considered in this study, as an archetypal of simple geophysical flows. The original scaling formulation of the dynamic sub-grid scale model proposed by Wong and Lilly (Phys. Fluids 6(6), 1994) is suitably extended to the present integral formulation. This approach is preferred with respect to traditional ones since the eddy coefficients can be independently computed by avoiding the addition of unjustified buoyancy production terms in the constitutive equations. Simple scaling arguments allow us not to use the equilibrium hypothesis according to which the dissipation rate should equal the sub-grid scale energy production. A careful a priori analysis of the relevance of the test filter shape as well as the filter-to-grid ratio is reported. Large-eddy simulation results are a posteriori compared with a reference pseudo-spectral direct numerical solution that is suitably post-filtered in order to have a meaningful comparison. In particular, the spectral distribution of kinetic and thermal energy as well as the viscosity and diffusivity sub-grid scale profiles are illustrated. The good performances of the proposed method, in terms of both evolutions of global quantities and statistics, are very promising for the future development and application of the method.     

Scaling law of resolved-scale isotropic turbulence and its application in large-eddy simulation

Eddy-damping quasinormal Markovian （EDQNM） theory is employed to calculate the resolved-scale spectrum and transfer spectrum, based on which we investigate the resolved-scale scaling law. Results show that the scaling law of the resolved-scale turbulence, which is affected by several factors, is far from that of the full-scale turbulence and should be corrected. These results are then applied to an existing subgrid model to improve its performance. A series of simulations are performed to verify the necessity of a fixed scaling law in the subgrid modeling.     

Hybrid numerical method for wall-resolved large-eddy simulations of compressible wall-bounded turbulence

Acta Mechanica Sinica - Bogies are responsible for a significant amount of aerodynamic resistance and noise, both of which negatively affect high-speed train performance and passenger comfort. In...     

Structural subgrid-scale modeling for large-eddy simulation: A review

Accurately modeling nonlinear interactions in turbulence is one of the key challenges for large-eddy simu-lation (LES) of turbulence. In this article, we review recent studies on structural subgrid scale modeling, focusing on evaluating how well these models predict the effects of small scales. The article discusses a priori and a posteriori test results. Other nonlinear models are briefly discussed, and future prospects are noted.     

Wall modeling for implicit large-eddy simulation and immersed-interface methods

We propose and analyze a wall model based on the turbulent boundary layer equations (TBLE) for implicit large-eddy simulation (LES) of high Reynolds number wall-bounded flows in conjunction with a conservative immersed-interface method for mapping complex boundaries onto Cartesian meshes. Both implicit subgrid-scale model and immersed-interface treatment of boundaries offer high computational efficiency for complex flow configurations. The wall model operates directly on the Cartesian computational mesh without the need for a dual boundary-conforming mesh. The combination of wall model and implicit LES is investigated in detail for turbulent channel flow at friction Reynolds numbers from Re _τ  = 395 up to Re _τ =100,000 on very coarse meshes. The TBLE wall model with implicit LES gives results of better quality than current explicit LES based on eddy viscosity subgrid-scale models with similar wall models. A straightforward formulation of the wall model performs well at moderately large Reynolds numbers. A logarithmic-layer mismatch, observed only at very large Reynolds numbers, is removed by introducing a new structure-based damping function. The performance of the overall approach is assessed for two generic configurations with flow separation: the backward-facing step at Re _h = 5,000 and the periodic hill at Re _H = 10,595 and Re _H = 37,000 on very coarse meshes. The results confirm the observations made for the channel flow with respect to the good prediction quality and indicate that the combination of implicit LES, immersed-interface method, and TBLE-based wall modeling is a viable approach for simulating complex aerodynamic flows at high Reynolds numbers. They also reflect the limitations of TBLE-based wall models.     

Nonlinear gravity-wave interactions in stratified turbulence

To investigate the dynamics of gravity waves in stratified Boussinesq flows, a model is derived that consists of all three-gravity-wave-mode interactions (the GGG model), excluding interactions involving the vortical mode. The GGG model is a natural extension of weak turbulence theory that accounts for exact three-gravity-wave resonances. The model is examined numerically by means of random, large-scale, high-frequency forcing. An immediate observation is a robust growth of the so-called vertically sheared horizontal flow (VSHF). In addition, there is a forward transfer of energy and equilibration of the nonzero-frequency (sometimes called “fast”) gravity-wave modes. These results show that gravity-wave-mode interactions by themselves are capable of systematic interscale energy transfer in a stratified fluid. Comparing numerical simulations of the GGG model and the full Boussinesq system, for the range of Froude numbers (Fr) considered (0.05 ≤ Fr ≤ 1), in both systems the VSHF is hardest to resolve. When adequately resolved, VSHF growth is more vigorous in the GGG model. Furthermore, a VSHF is observed to form in milder stratification scenarios in the GGG model than the full Boussinesq system. Finally, fully three-dimensional nonzero-frequency gravity-wave modes equilibrate in both systems and their scaling with vertical wavenumber follows similar power-laws. The slopes of the power-laws obtained depend on Fr and approach ?2 (from above) at Fr = 0.05, which is the strongest stratification that can be properly resolved with our computational resources.     

Spectral structure of stratified turbulence: direct numerical simulations and predictions by large eddy simulation

Density stratification has a strong impact on turbulence in geophysical flows. Stratification changes the spatial turbulence spectrum and the energy transport and conversion within the spectrum. We analyze these effects based on a series of direct numerical simulations (DNS) of stratified turbulence. To facilitate simulations of real-world problems, which are usually beyond the reach of DNS, we propose a subgrid-scale turbulence model for large eddy simulations of stratified flows based on the Adaptive Local Deconvolution Method (ALDM). Flow spectra and integral quantities predicted by ALDM are in excellent agreement with direct numerical simulation. ALDM automatically adapts to strongly anisotropic turbulence and is thus a suitable tool for studying turbulent flow phenomena in atmosphere and ocean.     

Temporal large-eddy simulation: theory and implementation

Large-eddy simulation (LES) has relied almost exclusively on spatial filtering to separate resolved and unresolved scales. For many reasons, temporal filtering may be more natural, particularly for flows of engineering interest. The paper develops the theory of temporal LES (TLES) and provides a demonstration of the concept by simulations of viscous Burger’s flow and incompressible plane-channel flow. The latter is accomplished by adapting the approximate deconvolution model (ADM) of Stolz and Adams (Phys. Fluids 11:1699, 1999) to causal, time-domain filtering. The temporal variant of the ADM is termed the TADM.      

A dynamic global-coefficient mixed subgrid-scale model for large-eddy simulation of turbulent flows

A dynamic global-coefficient mixed subgrid-scale eddy-viscosity model for large-eddy simulation of turbulent flows in complex geometries is developed. In the present model, the subgrid-scale stress is decomposed into the modified Leonard stress, cross stress, and subgrid-scale Reynolds stress. The modified Leonard stress is explicitly computed assuming a scale similarity, while the cross stress and the subgrid-scale Reynolds stress are modeled using the global-coefficient eddy-viscosity model. The model coefficient is determined by a dynamic procedure based on the global-equilibrium between the subgrid-scale dissipation and the viscous dissipation. The new model relieves some of the difficulties associated with an eddy-viscosity closure, such as the nonalignment of the principal axes of the subgrid-scale stress tensor and the strain rate tensor and the anisotropy of turbulent flow fields, while, like other dynamic global-coefficient models, it does not require averaging or clipping of the model coefficient for numerical stabilization. The combination of the global-coefficient eddy-viscosity model and a scale-similarity model is demonstrated to produce improved predictions in a number of turbulent flow simulations.     

Time evolution of structures in rotating and stratified turbulence

Rotating and stably stratified turbulence exhibit not only significant anisotropies but also dynamics, which are qualitatively different from purely rotating or stratified turbulence. Furthermore, the different time scales due to rotation, stratification and the turbulence one open up a wide field of possibilities for the temporal evolution of rotating and stratified turbulence.We analyze results from DNS with different parameters α = f/N by visualizing iso-enstrophy surfaces, the temporal evolution of velocity correlation length scales and angular energy spectra.We retrieve standard results, such as a large anisotropy for small scales in rotating turbulence and a large anisotropy for intermediate scales in the vortex mode of stratified turbulence. Furthermore, at large times we find qualitatively different phenomena for cases α = 10 and α = 0.1 such as modified cascades due to the existence of potential energy or small scale vorticity production respectively.