Measurements of nearly isotropic turbulence downstream of an active grid in the Corrsin wind tunnel are performed as a high-Reynolds number (Re λ ≈ 720) update of the Comte-Bellot & Corrsin (1971) data set. Energy spectra at four downstream distances from the grid, ranging from x/M = 20 to x/M = 48, are measured and documented for subsequent initialization of, and comparison with, Large Eddy Simulations (LES). Data are recorded using an array of four X-wire probes which enables measurement of filtered velocities, filtered in the streamwise (using

High-Reynolds number flow over tree-like fractals is considered, with emphasis on the drag forces produced. Fractal objects display large scale-disparity and complexity while being amenable to a simple and standardized description. Hence, they offer an elegant idealization of the actual boundaries in practical applications where turbulence interacts with boundaries that are characterized by multiple length-scales. First, using large-eddy-simulation of flow over prefractal shapes with increasing numbers of branch generations, the dependence of the tree drag on the inner cutoff-scale of the fractal is studied. It is found that the convergence of the drag coefficient towards a value that is independent of inner cutoff-scale is very slow. In order to address this fundamental difficulty and avoid the need to resolve all the small-scale branches of the fractal, a new numerical modeling technique called renormalized numerical simulation (RNS) is introduced. RNS models the drag of the unresolved branches using drag coefficients measured from both resolved branches and unresolved branches as modeled in previous iterations of the procedure. The RNS technique and its convergence properties are tested by means of a series of simulations using different levels of resolution. Then, RNS is used to investigate the influence of the tree fractal dimension on the drag coefficient. The increase of the drag with fractal dimension is quantified for two types of tree geometry, in two flow configurations. Results illustrate that RNS enables numerical modeling of physical processes associated with fractal geometries using affordable computational resolution.

The dynamic model for large-eddy simulation (LES) of turbulent flows requires test filtering the resolved velocity fields in order to determine model coefficients. However, test filtering is costly to perform in LES of complex geometry flows, especially on unstructured grids. The objective of this work is to develop and test an approximate but less costly dynamic procedure which does not require test filtering. The proposed method is based on Taylor series expansions of the resolved velocity fields. Accuracy is governed by the derivative schemes used in the calculation and the number of terms considered in the approximation to the test filtering operator. The expansion is developed up to fourth order, and results are tested a priori based on direct numerical simulation data of forced isotropic turbulence in the context of the dynamic Smagorinsky model. The tests compare the dynamic Smagorinsky coefficient obtained from filtering with those obtained from application of the Taylor series expansion. They show that the expansion up to second order provides a reasonable approximation to the true dynamic coefficient (with errors on the order of about 5% for c 2 s ), but that including higher-order terms does not necessarily lead to improvements in the results due to inherent limitations in accurately evaluating high-order derivatives. A posteriori tests using the Taylor series approximation in LES of forced isotropic turbulence and channel flow confirm that the Taylor series approximation yields accurate results for the dynamic coefficient. Moreover, the simulations are stable and yield accurate resolved velocity statistics.

We review the fundamentals of a new numerical modeling technique called Renormalized Numerical Simulation (RNS). The goal of RNS is to model the drag force produced by high Reynolds-number turbulent flow over objects that display scale-invariant properties, objects such as tree-like fractals. The hallmark of RNS in this application is that the drag of the unresolved tree branches is modeled using drag coefficients measured from the resolved branches and unresolved branches (as modeled in previous iterations of the procedure). In the present paper, RNS is used to study the effects of branch orientation on the drag force generated by highly idealized trees in which trunk and branches have square cross-section, and the branches all lie in a plane perpendicular to the incoming flow. Then, the procedure is generalized to the more general case of non-planar branch arrangements. Results illustrate that RNS may enable numerical modeling of environmental flow processes associated with fractal geometries using affordable computational resolution.

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