A method for measuring and analyzing four-dimensional flow fields in viscous Rayleigh-Bénard convection

Abstract

Laboratory investigation of convective flow in viscous fluids is crucial for various engineering and geophysical applications, including vigorous convection in planetary mantles, which involves multiple rising plumes. Many experimental techniques have been developed to visualize the flow and plumes, but most previous measurements remain largely qualitative. Here we present a method to measure and analyze four-dimensional (4D) plume-bearing viscous fluid flow, extending volumetric velocimetry approaches to the high Prandtl-number laminar regime relevant to mantle convection. First, a customized three dimensional (3D) Scanning Stereoscopic Particle Image Velocimetry (SSPIV) system is applied to a Rayleigh-Bénard experiment suitable to study the dynamics of Earth's interior. We report the first quantitative 4D velocity measurements of multiple interacting laminar plumes at high Prandtl numbers. The raw velocity data are postprocessed with a Lagrangian Coherent Structure (LCS) and cluster analysis pipeline, tailored for clusters of viscous plumes, which allows quantitative, transport-based material boundary tracking of the plumes in space and time. We show example results to demonstrate the power of our method while fully exploring the dynamics in a companion paper Bao and Lithgow-Bertelloni (2025). Our analysis quantifies the rich dynamical behavior of multiple interacting plumes. We suggest our method of measurement and analysis can help better quantify the morphology, interaction, and evolutionary pathways of plumes feeding Earth's volcanic hotspots and other planetary interiors.