Pui-Kuen Yeung

Very fine structures in scalar mixing

We explore very fine scales of scalar dissipation in turbulent mixing, below Kolmogorov and around Batchelor scales, by performing direct numerical simulations at much finer grid resolution than was usually adopted in the past. We consider the resolution in terms of a local fluctuating Batchelor scale and study the effects on the tails of the probability density function and multifractal properties of the scalar dissipation. The origin and importance of these very fine-scale fluctuations are discussed. One conclusion is that they are unlikely to be related to the most intense dissipation events.

Reynolds number dependence of relative dispersion statistics in isotropic turbulence

Direct numerical simulation results for a range of relative dispersion statistics over Taylor-scale Reynolds numbers up to 650 are presented in an attempt to observe and quantify inertial subrange scaling and, in particular, Richardson’s t3 law. The analysis includes the mean-square separation and a range of important but less-studied differential statistics for which the motion is defined relative to that at time t=0. It seeks to unambiguously identify and quantify the Richardson scaling by demonstrating convergence with both the Reynolds number and initial separation. According to these criteria, the standard compensated plots for these statistics in inertial subrange scaling show clear evidence of a Richardson range but with an imprecise estimate for the Richardson constant. A modified version of the cube-root plots introduced by Ott and Mann [J. Fluid Mech. 422, 207 (2000)] confirms such convergence. It has been used to yield more precise estimates for Richardson’s constant g which decrease with Taylo...

Kolmogorov similarity scaling for one-particle Lagrangian statistics

We use direct numerical simulation data up to a Taylor scale Reynolds number Rλ = 1000 to investigate Kolmogorov similarity scaling in the inertial sub-range for one-particle Lagrangian statistics. Although similarity scaling is not achieved at these Reynolds numbers for the Lagrangian velocity structure function, we show clearly that it is achieved for the Lagrangian acceleration frequency spectrum and the scaling range becomes wider with increasing Reynolds number. Stochastic and heuristic model calculations suggest that the difference in behavior observed for the structure function and spectrum is simply a consequence of different rates of convergence to scaling behavior with increasing Reynolds number. Our estimate C0 ≈ 6.9 ± 0.2 for the Lagrangian structure function constant is close to earlier estimates based on extrapolation of the peak value of the compensated structure function. The results presented here suggest prospects for studying Kolmogorov similarity for Lagrangian statistics using the lat...

Multi-particle and tetrad statistics in numerical simulations of turbulent relative dispersion

The evolution in size and shape of three and four-particle clusters (triangles and tetrads, respectively) in isotropic turbulence is studied using direct numerical simulations at grid resolution up to 40963 and Taylor-scale Reynolds numbers from 140 to 1000. A key issue is the attainment of inertial range behavior at high Reynolds number, while the small- and large-time limits of ballistic and diffusive regimes, respectively, are also considered in some detail. Tetrad size expressed by the volume (V) and (more appropriately) the gyration radius (R) is shown to display inertial range scaling consistent with a Richardson constant close to 0.56 for two-particle relative dispersion. For tetrads of initial size in a suitable range moments of shape parameters, including the ratio V2/3/R2 and normalized eigenvalues of a moment-of-inertia-like dispersion tensor, show a regime of near-constancy which is identified with inertial-range scaling. Sheet-like structures are dominant in this period, while pancakes and ne...

Visual Analytics for Finding Critical Structures in Massive Time-Varying Turbulent-Flow Simulations

Visualization and data analysis are crucial in analyzing and understanding a turbulent-flow simulation of size 4,096³ cells per time slice (68 billion cells) and 17 time slices (one trillion total cells). The visualization techniques used help scientists investigate the dynamics of intense events individually and as these events form clusters.

The Turbulent Schmidt Number

We analyze a large database generated from recent direct numerical simulations (DNS) of passive scalars sustained by a homogeneous mean gradient and mixed by homogeneous and isotropic turbulence on grid resolutions of up to 40963 and extract the turbulent Schmidt number over large parameter ranges: the Taylor microscale Reynolds number between 8 and 650 and the molecular Schmidt number between 1/2048 and 1024. While the turbulent Schmidt number shows considerable scatter with respect to the Reynolds and molecular Schmidt numbers separately, it exhibits a sensibly unique functional dependence with respect to the molecular Peclet number. The observed functional dependence is motivated by a scaling argument that is standard in the phenomenology of three-dimensional turbulence.