Lagrangian statistics and flow topology in forced two-dimensional turbulence

Abstract

A study of the relationship between Lagrangian statistics and flow topology in fluid turbulence is presented. The topology is characterized using the Weiss criterion, which provides a conceptually simple tool to partition the flow into topologically different regions: elliptic (vortex dominated), hyperbolic (deformation dominated), and intermediate (turbulent background). The flow corresponds to forced two-dimensional Navier-Stokes turbulence in doubly periodic and circular bounded domains, the latter with no-slip boundary conditions. In the double periodic domain, the probability density function (pdf) of the Weiss field exhibits a negative skewness consistent with the fact that in periodic domains the flow is dominated by coherent vortex structures. On the other hand, in the circular domain, the elliptic and hyperbolic regions seem to be statistically similar. We follow a Lagrangian approach and obtain the statistics by tracking large ensembles of passively advected tracers. The pdfs of residence time in the topologically different regions are computed introducing the Lagrangian Weiss field, i.e., the Weiss field computed along the particles' trajectories. In elliptic and hyperbolic regions, the pdfs of the residence time have self-similar algebraic decaying tails. In contrast, in the intermediate regions the pdf has exponential decaying tails. The conditional pdfs (with respect to the flow topology) of the Lagrangian velocity exhibit Gaussian-like behavior in the periodic and in the bounded domains. In contrast to the freely decaying turbulence case, the conditional pdfs of the Lagrangian acceleration in forced turbulence show a comparable level of intermittency in both the periodic and the bounded domains. The conditional pdfs of the Lagrangian curvature are characterized, in all cases, by self-similar power-law behavior with a decay exponent of order -2.

Fractional Brownian motion, the Matérn process, and stochastic modeling of turbulent dispersion

“…The result that the diffusivity is the zero-frequency value of velocity spectrum is not entirely new. It is implicit in a result of Kampé de Fériet (1939), see p. 527-528 of Monin and Yaglom (2007). It is also pointed out in Davis (1983, p. 175) and is mentioned in LaCasce (2008).…”

“…On the practical side, we find the Matérn process to be an excellent match for Lagrangian velocity spectra from a numerical simulation of two-dimensional turbulence, a classical system in fluid dynamics that has been the subject of a large number of studies, (e.g. Lin, 1972;McWilliams, 1990a;Dritschel et al, 2008;Bracco and McWilliams, 2010;Kadoch et al, 2011;Scott and Dritschel, 2013). The Matérn process allows one to simultaneously vary the values of the three most important properties of Lagrangian trajectories: the kinetic energy, the degree of small-scale roughness or fractal dimension, and the long-time diffusive behavior.…”

Directional change of fluid particles in two-dimensional turbulence and of football players

“…The curvature in turbulent flows was studied in references [3][4][5][6][7][8]. The extension to a time scaledependent curvature-related statistical measure was only recently proposed in Ref.…”

Finite-time statistics of scalar diffusion in Lagrangian coherent structures

“…Okubo-Weiss parameter [11,12]. Addition of random noise and use of FTLE make the present work realistic and objective.…”