Extreme-value statistics from Lagrangian convex hull analysis for homogeneous turbulent Boussinesq convection and MHD convection

TL;DR

This paper demonstrates that convex hull analysis of Lagrangian tracers effectively captures the dispersive behavior, anisotropy, and extreme events in turbulent convection and MHD flows, providing insights beyond traditional pair dispersion methods.

Contribution

It introduces convex hull geometric analysis combined with extreme value theory to study turbulence, revealing new insights into flow anisotropy and extreme dispersion events.

Findings

Convex hull statistics match asymptotic dispersive behavior.

Maximal extensions follow Gumbel extreme value distribution.

Convex hull analysis complements standard turbulence diagnostics.

Abstract

We investigate the utility of the convex hull of many Lagrangian tracers to analyze transport properties of turbulent flows with different anisotropy. In direct numerical simulations of statistically homogeneous and stationary Navier-Stokes turbulence, neutral fluid Boussinesq convection, and MHD Boussinesq convection a comparison with Lagrangian pair dispersion shows that convex hull statistics capture the asymptotic dispersive behavior of a large group of passive tracer particles. Moreover, convex hull analysis provides additional information on the sub-ensemble of tracers that on average disperse most efficiently in the form of extreme value statistics and flow anisotropy via the geometric properties of the convex hulls. We use the convex hull surface geometry to examine the anisotropy that occurs in turbulent convection. Applying extreme value theory, we show that the maximal square extensions of convex hull vertices are well described by a classic extreme value distribution, the Gumbel distribution. During turbulent convection, intermittent convective plumes grow and accelerate the dispersion of Lagrangian tracers. Convex hull analysis yields information that supplements standard Lagrangian analysis of coherent turbulent structures and their influence on the global statistics of the flow.