J. C. Vassilicos

Scalings and decay of fractal-generated turbulence

A total of 21 planar fractal grids pertaining to three different fractal families have been used in two different wind tunnels to generate turbulence. The resulting turbulent flows have been studied using hot wire anemometry. Irrespective of fractal family, the fractal-generated turbulent flows and their homogeneity, isotropy, and decay properties are strongly dependent on the fractal dimension Df≤2 of the grid, its effective mesh size Meff (which we introduce and define) and its ratio tr of largest to smallest bar thicknesses, tr=tmax∕tmin. With relatively small blockage ratios, as low as σ=25%, the fractal grids generate turbulent flows with higher turbulence intensities and Reynolds numbers than can be achieved with higher blockage ratio classical grids in similar wind tunnels and wind speeds U. The scalings and decay of the turbulence intensity u′∕U in the x direction along the tunnel’s center line are as follows (in terms of the normalized pressure drop CΔP and with similar results for v′∕U and w′∕U)...

Dissipation and decay of fractal-generated turbulence

Space-filling fractal square grids fitted at the entrance of a wind tunnel’s test section generate unusually high Reynolds number homogeneous isotropic turbulence which decays locked into a single length-scale l. Specifically, during turbulence decay along the streamwise coordinate x, E11(k1,x)=u′2lf(k1l) over the entire range of wavenumbers, where l and the function f are about the same for all the grids tried here. As a result, this fractal-generated turbulence has the following properties which we have also observed in the decaying region: L∕λ is constant, independent of the x grid and Reλ; ϵ∼Reλ−1u′3∕Lu; and E11(k1)∼(u′3∕Lu)2∕3k1−5∕3 instead of E11(k1)∼ϵ2∕3k1−5∕3 in the observed range of wavenumbers where f(k1l)∼(k1l)−5∕3.

Turbulent clustering of stagnation points and inertial particles

In high-Reynolds-number two-dimensional turbulence with a −5/3 power-law energy spectrum, the clustering of inertial particles reflects the clustering of acceleration stagnation points for all particle relaxation times smaller than the integral time scale

Universal Dissipation Scaling for Nonequilibrium Turbulence

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Richardson's pair diffusion and the stagnation point structure of turbulence

of the turbulence. Acceleration stagnation points and small inertial particles on these points are swept together by large-scale motions. In synthetic turbulence where there is no sweeping and acceleration stagnation points do not cluster, inertial particles do nevertheless cluster as a result of the repelling action of persistent velocity stagnation-point clusters. This repelling action has a negligible effect on the clustering of inertial particles in the presence of acceleration stagnation points clustering.

Self-similar clustering of inertial particles and zero-acceleration points in fully developed two-dimensional turbulence

It is experimentally shown that the nonclassical high Reynolds number energy dissipation behavior, C(ε)≡εL/u(3)=f(Re(M))/Re(L), observed during the decay of fractal square grid-generated turbulence (where Re(M) is a global inlet Reynolds number and Re(L) is a local turbulence Reynolds number) is also manifested in decaying turbulence originating from various regular grids. For sufficiently high values of the global Reynolds numbers Re(M), f(Re(M))~Re(M).

Particle pair diffusion and persistent streamline topology in two-dimensional turbulence

DNS and laboratory experiments show that the spatial distribution of straining stagnation points in homogeneous isotropic 3D turbulence has a fractal structure with dimension D(s)=2. In kinematic simulations the exponent gamma in Richardsons law and the fractal dimension D(s) are related by gamma=6/D(s). The Richardson constant is found to be an increasing function of the number density of straining stagnation points in agreement with pair diffusion occurring in bursts when pairs meet such points in the flow.

A unified sweep-stick mechanism to explain particle clustering in two- and three-dimensional homogeneous, isotropic turbulence

Clustering of inertial particles in fully developed two-dimensional inverse cascading turbulence occurs for all particle relaxation times ranging from an order of magnitude under the smallest eddy turnover time to an order of magnitude above the largest eddy turnover time. Particle voids and clusters are statistically self-similar over a finite range of scales within the inertial range and are explained in terms of coarse-grained vorticity and resonant eddies (for voids) and in terms of zero-acceleration points (for clusters). The clustering of inertial particles reflects the clustering of zero-acceleration points. Essential to both explanations is the sweeping of small eddies by large ones. An important implication is that particle clustering can be explicitly described just in terms of the fluid acceleration field without the need for Lagrangian particle integrations.

The turbulence dissipation constant is not universal because of its universal dependence on large-scale flow topology

From observations of direct numerical simulations (DNS) of two- dimensional turbulence with inverse energy cascade, two physical pictures of particle pair diffusion are proposed based on persistent streamline topology associated with stagnation points. One picture describes the step-by-step separation process of individual pairs in a local frame moving with them, whereas the other serves as a statistical description of particle pair diffusion in a global frame which we define. These two pictures lead to the same characteristic time scale for particle pair diffusion. Based on this time scale, a new model of particle pair diffusion is proposed which predicts the temporal evolutions of the mean square separation, and of the probability density function (PDF) of separations. Our PDF equation turns out to be a generalization of Richardsons diffusion equation (Richardson L F 1926 Proc. R. Soc. A 110 709). DNS verifications support all the predictions of our model. A generalization of our approach to d-dimensional turbulence with energy spectrum proportional to k −p is given for the purpose of demonstrating that the PDF equation and the exponent of mean square separation are directly related with the fractal dimension of the spatial distribution of stagnation points.

The non-equilibrium region of grid-generated decaying turbulence

Our work focuses on the sweep-stick mechanism of particle clustering in turbulent flows introduced by Chen et al. [L. Chen, S. Goto, and J. C. Vassilicos, “Turbulent clustering of stagnation points and inertial particles,” J. Fluid Mech. 553, 143 (2006)] for two-dimensional (2D) inverse cascading homogeneous, isotropic turbulence (HIT), whereby heavy particles cluster in a way that mimics the clustering of zero-acceleration points. We extend this phenomenology to three-dimensional (3D) HIT, where it was previously reported that zero-acceleration points were extremely rare. Having obtained a unified mechanism we quantify the Stokes number dependency of the probability of the heavy particles to be at zero-acceleration points and show that in the inertial range of Stokes numbers, the sweep-stick mechanism is dominant over the conventionally proposed mechanism of heavy particles being centrifuged from high vorticity regions to high strain regions. Finally, having a clustering coincidence between particles and...