Lagrangian Dynamics of Anisotropic Crystals in Vigorous Mantle Convection

The dynamics of anisotropic crystals in cellular convective flows are critical for understanding the development of seismic anisotropy and chemical mixing in the Earth's mantle. In this study, we investigate the transport and orientation of slender rigid inclusions, proxies for anisotropic minerals such as olivine, using a Lagrangian framework. The crystals are modelled as inertialess rod-like tracers, with translational motion derived by averaging the background flow velocity along the crystal's major axis, and rotational dynamics determined by the moment of the background velocity field evaluated along the length. Unlike passive point tracers, these extended objects exhibit intrinsically coupled translation and rotation, resulting in preferred orientations (LPO) that depend sensitively on both the convective flow structure and crystal aspect ratio.

To benchmark the model, crystal dynamics are first examined in idealised laminar flows relevant to mantle kinematics, including two-dimensional Taylor–Green cellular flow and eigenmodes of Rayleigh–Bénard convection. These configurations allow for the analysis of crystal trajectories, stability near stagnation points, and the influence of density contrasts (settling) on crystal residence times. The study is then extended to vigorous, chaotic thermal convection by generating high-Rayleigh-number flows using direct numerical simulations of the Boussinesq-approximated Navier–Stokes equations. Crystals are introduced into the statistically steady flow field to simulate entrainment and mixing processes.

Confinement effects, representing lithospheric boundaries or phase transitions, are modelled using a soft-wall collision scheme, while periodic boundary conditions mimic the lateral extent of the mantle. We quantify crystal dispersion and alignment over a range of geophysical parameters, exploring variations in the Rayleigh number and crystal geometry. Statistical analyses focus on long-time orientation distribution functions (ODFs) and dispersion rates. Our results reveal how convective vigour and coherent structures (e.g., plumes and downwellings) jointly govern the evolution of fabric in the mantle, offering a controlled framework for interpreting seismic anisotropy in thermally driven flows.