Nikki Vercauteren, Freie Universität Berlin

**"What is… Turbulence closure models based on scale similarity principles?"**

In the range of turbulent flow prediction tools, Large Eddy Simulations (LES) stand in the middle, between direct numerical simulations (DNS) where all the scales of motion are resolved, and Reynolds Averaged Navier-Stokes (RANS) methods where all the turbulent scales are modeled. In LES, all the large, energy containing scales that one can computationally afford to capture on a numerical grid (the resolved scales) are simulated, and the dynamics of the small turbulent eddies (subgrid scales) that cannot be captured and their effect on the larger scales are parameterized based on resolved, or filtered, quantities.

With scale similarity in the inertial range of turbulence, a subgrid-scale (SGS) model which respects the scale-similarity should in principle be applicable at different filter scales. This principle is exploited in the dynamic SGS model to determine numerical coefficients in the model. The most widely used version is the dynamic Smagorinsky model, in which the dynamic procedure is applied to determine the appropriate value of the Smagorinsky model coefficient. Usually the appropriate coefficient is determined as the one that most accurately represents energy transfer across scales and calculating it involves averaging over directions of statistical homogeneity of the flow (for example over flow trajectories). With a refined dynamic procedure, scale-dependent coefficients are used to mitigate the assumption of scale invariance; this has proven to be useful in the vicinity of the lower boundary where the subgrid scales account for a large portion of the flow and in stably stratified conditions.

Another, structural approach is to treat the turbulent flow as a set of flow structures moving in a Lagrangian frame and to track their interactions. This is used in coherent vortex simulation methods (CVS), in which a wavelet-filer decomposes the Navier-Stokes equations solutions Wavelets are then dynamically selected to track the flow evolution with a reduced number of modes. Quantifying self-similarity in such coherent vortex approaches would give a way to extrapolate ensemble of coherent flow structures from a coarse grid to generate unresolved fluctuations, thereby defining a new turbulence closure based on self-similarity principles. This is part of the aims of project B07.