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

We investigate the utility of the convex hull ofmany Lagrangian tracers to analyze transport properties of turbulent flowswith different anisotropy. In direct numerical simulations of statistically homogeneous and stationaryNavier–Stokes turbulence, neutral fluid Boussinesq convection, and MHDBoussinesq convection a comparisonwith 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 dispersemost efficiently in the formof extreme value statistics andflow 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, theGumbel 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.