Abstract:

This dataset contains all the data used for reproducing the figures in the paper “Turbulence intermittency in a multiple-time-scale Navier-Stokes-based reduced model” by P. Johnson & C. Meneveau (Phys. Rev. Fluids 2, 072601(R), 2017, DOI: 10.1103/PhysRevFluids.2.072601). The dataset consists of 10 subdirectories named according to the figure numbers in the paper. In each subdirectory, the data for each figure is contained in a '.npy'; file which can be read by numerical python (numpy) routine (numpy.load). Each subdirectory contains a '.py' file which reads and plots the data, generating a plot identical to the one in the paper. The python scripts should work with python2 and python3.

Suggested Citation:

Johnson, Perry; Meneveau, Charles. 2018. Turbulence intermittency in a multiple-time-scale Navier-Stokes-based reduced model. Distributed by: GRIIDC, Harte Research Institute, Texas A&M University–Corpus Christi. doi:10.7266/N76H4FVJ

Publications:

Johnson, P. L., & Meneveau, C. (2017). Turbulence intermittency in a multiple-time-scale Navier-Stokes-based reduced model. Physical Review Fluids, 2(7). doi:10.1103/physrevfluids.2.072601

Purpose:

To create a multiple-time-scale stochastic model for the Lagrangian evolution of the full velocity gradient tensor in fluid turbulence at arbitrarily high Reynolds numbers.

Data Parameters and Units:

Data are in dimensionless form as reported in the paper "Turbulence intermittency in a multiple-time-scale Navier-Stokes-based reduced model" by P. Johnson & C. Meneveau (Phys. Rev. Fluids 2, 072601(R), 2017, DOI: 10.1103/PhysRevFluids.2.072601). Figure 1a: ordinate is the longitudinal component of the velocity gradient tensor for a single trajectory in the stochastic ensemble simulated using the RDGF model with 1 (top), 2 (middle), and 3 (bottom) timescale levels; abscissa is time normalized by the Kolmogorov timescale Figure 1b: ordinate is the probability density function for longitudinal component of the velocity gradient tensor resulting from the stochastic ensemble of the RDGF model with number of timescale levels increasing from 1 to 5 in the direction indicated by the arrow (solid colored lines)... also plotted are results for a non-integer number of levels (dashed line) and which can be directly compared with results of a fully resolved Navier-Stokes simulation (dotted line); abscissa is the value of the longitudinal velocity gradient component Figure 1c: same as Figure 1b, but for the transverse component of the velocity gradient Figure 2a: ordinate is the skewness factor of the longitudinal velocity gradient component of the RDGF stochastic model (blue circles), fully resolved Navier-Stokes simulations (open circles and triangles), and experimental results (plusses); abscissa is the Reynolds number based on the Taylor microscale Figure 2b: ordinate is the flatness factor of the longitudinal or transverse velocity gradient components, blue circles indicate longitudinal component from the RDGF stochastic model, green squares indicate the transverse component from the RDGF stochastic model, open circles and triangles indicate longitudinal component from Navier-Stokes simulations, open squares indicate transverse component from Navier-Stokes simulations, and plusses indicate experimental results for the longitudinal component Figure 2c: ordinate is the power-law scaling exponent with respect to Taylor-scale Reynolds number for normalized central moments (generalized hyper-flatnesses), yellow/red/cyan symbols indicate RDGF model results for different choices of the model parameter "beta" (6, 10, 20 respectively), open symbols indicate simulation and experimental results, solid blue line indicates the prediction of the She-Leveque model, dotted black line indicates the prediction of the p-model with p=0.7, dashed magenta line indicates the prediction of the lognormal model with mu=0.2, dot-dashed green line indicates the prediction of the lognormal model with mu=0.25; abscissa is the order of the normalized central moment Figure 3a: ordinate is the probability density function for the cosine of the angle between the vorticity vector and the three strain-rate eigenvectors ordered by decreasing eigenvalue, blue with circles indicates the first eigenvector, green with triangles indicates the second eigenvector, red with squares indicates the third eigenvector, solid lines indicate RDGF model results, dashed lines indicate Navier-Stokes simulation results; abscissa is the value of the cosine of the angle Figure 3b: ordinate is probability density function for the s-star parameter of Lund and Rogers (1994, "An improved measure of strain state probability in turbulent flows", Physics of Fluids, Vol 6, pp 1838) which indicates the prevalence of oblate versus prolate fluid deformations in a turbulent flow, solid line indicates RDGF model results, dashed line indicates Navier-Stokes simulation results; abscissa is the value of the s-star parameter Figure 3c: ordinate is the second invariant of the velocity gradient tensor, Q = -1/2 * trace(A dot A), normalized by the ensemble averaged strain-rate magnitude; abscissa is the third invariant of the velocity gradient tensor, R = -1/3 * trace(A dot A dot A), normalized by the ensemble averaged strain-rate magnitude; contour lines are logarithmically-spaced iso-contours of the joint probability density function for Q and R from the RDGF model with values 10, 1, 0.1, 0.01, 0.001 from the center outward; the greyscale shading also indicates the value of same joint probability density function with log-base-10 values indicated in the color bar Figure 3d: same as Figure 3c, except with data from fully resolved Navier-Stokes simulations

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