Dynamic Smagorinsky model on anisotropic grids

Large Eddy Simulation (LES) of complex-geometry flows often involves highly anisotropic meshes. To examine the performance of the dynamic Smagorinsky model in a controlled fashion on such grids, simulations of forced isotropic turbulence are performed using highly anisotropic discretizations. The resulting model coefficients are compared with a theoretical prediction (Scotti et al., 1993). Two extreme cases are considered: pancake-like grids, for which two directions are poorly resolved compared to the third, and pencil-like grids, where one direction is poorly resolved when compared to the other two. For pancake-like grids the dynamic model yields the results expected from the theory (increasing coefficient with increasing aspect ratio), whereas for pencil-like grids the dynamic model does not agree with the theoretical prediction (with detrimental effects only on smallest resolved scales). A possible explanation of the departure is attempted, and it is shown that the problem may be circumvented by using an isotropic test-filter at larger scales. Overall, all models considered give good large-scale results, confirming the general robustness of the dynamic and eddy-viscosity models. But in all cases, the predictions were poor for scales smaller than that of the worst resolved direction

Material Transport in the Ocean Mixed Layer: Recent Developments Enabled by Large Eddy Simulations

Material transport in the ocean mixed layer (OML) is an important component of natural processes such as gas and nutrient exchanges. It is also important in the context of pollution (oil droplets, microplastics, etc.). Observational studies of small-scale three-dimensional turbulence in the OML are difficult, especially if one aims at a systematic coverage of relevant parameters and their effects, under controlled conditions. Numerical studies are also challenging due to the large-scale separation between the physical processes dominating transport in the horizontal and vertical directions. Despite this difficulty, the application of large eddy simulation (LES) to study OML turbulence and, more specifically, its effects on material transport has resulted in major advances in the field in recent years. In this paper we review the use of LES to study material transport within the OML and then summarize and synthesize the advances it has enabled in the past decade or so. In the first part we describe the LES technique and the most common approaches when applying it in OML material transport investigations. In the second part we review recent results on material transport obtained using LES and comment on implications

Comparing local energy cascade rates in isotropic turbulence using structure function and filtering formulations

Two common definitions of the spatially local rate of kinetic energy cascade at some scale $\ell$ in turbulent flows are (i) the cubic velocity difference term appearing in the generalized Kolmogorov-Hill equation (GKHE) (structure function approach), and (ii) the subfilter-scale energy flux term in the transport equation for subgrid-scale kinetic energy (filtering approach). We perform a comparative study of both quantities based on direct numerical simulation data of isotropic turbulence at Taylor-scale Reynolds number of 1250. While observations of negative subfilter-scale energy flux (backscatter) have in the past led to debates regarding interpretation and relevance of such observations, we argue that the interpretation of the local structure function-based cascade rate definition is unambiguous since it arises from a divergence term in scale space. Conditional averaging is used to explore the relationship between the local cascade rate and the local filtered viscous dissipation rate as well as filtered velocity gradient tensor properties such as its invariants. We find statistically robust evidence of inverse cascade when both the large-scale rotation rate is strong and the large-scale strain rate is weak. Even stronger net inverse cascading is observed in the ``vortex compression'' $R>0$, $Q>0$ quadrant where $R$ and $Q$ are velocity gradient invariants. Qualitatively similar, but quantitatively much weaker trends are observed for the conditionally averaged subfilter scale energy flux. Flow visualizations show consistent trends, namely that spatially the inverse cascade events appear to be located within large-scale vortices, specifically in subregions when $R$ is large

An inertial range length scale in structure functions

It is shown using experimental and numerical data that within the traditional inertial subrange defined by where the third order structure function is linear that the higher order structure function scaling exponents for longitudinal and transverse structure functions converge only over larger scales, $r>r_S$, where $r_S$ has scaling intermediate between $\eta$ and $\lambda$ as a function of $R_\lambda$. Below these scales, scaling exponents cannot be determined for any of the structure functions without resorting to procedures such as extended self-similarity (ESS). With ESS, different longitudinal and transverse higher order exponents are obtained that are consistent with earlier results. The relationship of these statistics to derivative and pressure statistics, to turbulent structures and to length scales is discussed.Comment: 25 pages, 9 figure

Dynamic Smagorinsky model on anisotropic grids

To examine the performance of the dynamic Smagorinsky model in a controlled fashion on anisotropic grids, simulations of forced isotropic turbulence are performed using highly anisotropic discretizations. The resulting model coefficients are compared with an earlier prediction. Two extreme cases are considered: pancake-like grids, for which two directions are poorly resolved compared to the third, and pencil-like grids, where one direction is poorly resolved when compared to the other two

Chaotic Cascades with Kolmogorov 1941 Scaling

We define a (chaotic) deterministic variant of random multiplicative cascade models of turbulence. It preserves the hierarchical tree structure, thanks to the addition of infinitesimal noise. The zero-noise limit can be handled by Perron-Frobenius theory, just as the zero-diffusivity limit for the fast dynamo problem. Random multiplicative models do not possess Kolmogorov 1941 (K41) scaling because of a large-deviations effect. Our numerical studies indicate that deterministic multiplicative models can be chaotic and still have exact K41 scaling. A mechanism is suggested for avoiding large deviations, which is present in maps with a neutrally unstable fixed point.Comment: 14 pages, plain LaTex, 6 figures available upon request as hard copy (no local report #

Pattern Formation on Trees

Networks having the geometry and the connectivity of trees are considered as the spatial support of spatiotemporal dynamical processes. A tree is characterized by two parameters: its ramification and its depth. The local dynamics at the nodes of a tree is described by a nonlinear map, given rise to a coupled map lattice system. The coupling is expressed by a matrix whose eigenvectors constitute a basis on which spatial patterns on trees can be expressed by linear combination. The spectrum of eigenvalues of the coupling matrix exhibit a nonuniform distribution which manifest itself in the bifurcation structure of the spatially synchronized modes. These models may describe reaction-diffusion processes and several other phenomena occurring on heterogeneous media with hierarchical structure.Comment: Submitted to Phys. Rev. E, 15 pages, 9 fig