We perform a direct numerical simulation (DNS) of forced homogeneous isotropic turbulence with a passive scalar that is forced by mean gradient. The DNS data are used to study the properties of subgrid-scale flux of a passive scalar in the framework of large eddy simulation (LES), such as alignment trends between the flux, resolved, and subgrid-scale flow structures. It is shown that the direction of the flux is strongly coupled with the subgrid-scale stress axes rather than the resolved flow quantities such as strain, vorticity, or scalar gradient. We derive an approximate transport equation for the subgrid-scale flux of a scalar and look at the relative importance of the terms in the transport equation. A particular form of LES tensor-viscosity model for the scalar flux is investigated, which includes the subgrid-scale stress. Effect of different models for the subgrid-scale stress on the model for the subgrid-scale flux is studied.

A new class of subgrid scale models (dynamic structure models) for large eddy simulation is proposed for subgrid scalar flux and dissipation terms. The structure of the modeled terms is taken from the corresponding Leonard terms by the use of the test filter size equal to the base filter size, and a particular form of the scaling factor is proposed. The models are evaluated using available direct numerical simulation data. The evaluation results compare well with viscosity and similarity models. The dynamic structure models have been found to be robust and to work well under various conditions, including various test-to-base filter size ratios and filter skewnesses.

Lagrangian mean evolution of the invariants of the velocity gradient tensor in different regions of a turbulent boundary layer is investigated using data from a direct numerical simulation of a zero pressure gradient turbulent boundary layer. Conditional mean trajectories (CMTs) are calculated for the evolution of invariants based on their mean rate of change, conditioned on their location in the (RA, QA) plane, which determines the focal or non-focal nature of flow at that point. CMTs are calculated over a larger range of gradients than previously reported boundary layer measurements and show a distinct difference in topological evolution depending on the resolution and the range of invariants considered. In the present case, CMTs for strong gradients in all regions of the boundary layer pass around a focus at the origin and asymptote towards the right-hand side of a saddle point located near the right-hand side of the line dividing unstable focal and unstable nodal structures, consistent with viscous diffusion dominated evolution. Closer to the origin, weaker gradients follow an almost periodic clockwise spiraling evolution from stable-focus stretching to unstable-focus contraction, unstable-node saddle/saddle, and stable-node saddle/saddle topology, similar to that observed in homogeneous isotropic turbulence. Mean time-scales associated with the spiraling evolution in terms of inner scales are estimated at 67.9 \documentclass[12pt]{minimal}\begin{document}$\nu /u^2_\tau$\end{document}ν/uτ2 in the viscous layer, 151 \documentclass[12pt]{minimal}\begin{document}$\nu /u^2_\tau$\end{document}ν/uτ2 in the buffer layer, and 658 \documentclass[12pt]{minimal}\begin{document}$\nu /u^2_\tau$\end{document}ν/uτ2 in the log and wake region. Iso-contours of coherent vortices indicate that these structures typically involve stronger gradients beyond that of the spiraling evolution.

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SUMMARYLarge eddy simulation (LES) is based on separation of variable of interest into two parts-resolved and subgrid. The resolved part is obtained numerically using modiÿed transport equation while the e ect of the subgrid part is modelled using subgrid-scale (SGS) models. In this paper we present and discuss new one-equation LES models for SGS scalar ux, SGS scalar dissipation and SGS energy dissipation. The proposed models belong to a new family of SGS models-dynamic structure (DS) models. The DS models borrow the structure of the modelled term from the corresponding Leonard term, and a special scaling factor is then used which does not contain user-speciÿed constants. The models are evaluated a priori using available DNS data for a non-reacting mixing layer and decaying isotropic turbulence; the evaluation results compare well with viscosity and similarity models. During the a priori tests, the DS models were found to perform better than dynamic viscosity and similarity models for various test-to-base ÿlter size ratios and non-symmetric ÿlters. For a posteriori evaluation, the models are implemented into a high-order ÿnite-di erence code and an LES of decaying isotropic turbulence is performed. The results match the data available from the literature and DNS simulations.