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.
Highlights
Turbulent transport governs the spreading of contaminants in the environment, mixing of chemical constituents in combustion engines or in stellar interiors, accretion in proto-stellar molecular clouds, acceleration of cosmic rays, and escape of hot particles from fusion machines
In simulations Navier–Stokes case (NST), hydrodynamic Boussinesq convection (HC), and magnetohydrodynamic convection (MC) we examine the relative dynamics of larger groups of particles
A different behavior is observed for the magnetohydrodynamic convection (MC) simulation since largerscale magnetic fluctuations have a strong impact on small-scale dynamics; far higher surface–volume ratios are attained than in the other two cases
Summary
Faculty of Science, Technology, Engineering and Mathematics, Open University, Milton Keynes, United Kingdom licence.
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