Xiyuan Bao | Search arXiv

arXiv2026

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

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.

physics.flu-dyn↗

arXiv2026

Morphology, interactions, and evolution of laminar thermal plumes revealed by time-resolved volumetric velocity measurements and analysis: Application to Earth's mantle

Plume-laden convection plays a fundamental role in thermal transport in geophysical and industrial flows. While the dynamics of isolated laminar plumes have been extensively studied, their collective interactions and evolution in a multi-plume system remains poorly quantified due to the lack of four-dimensional (4D, in space and time) flow measurements for viscous convection, common in the turbulence community. Here we present a time-resolved experimental study of clustered plume dynamics in a high-Prandtl-number Rayleigh-Bénard system with temperature-dependent viscosity from 4D velocity measurements. Building on our companion methodology (Bao and Lithgow-Bertelloni, 2025), we characterize the spatiotemporal distribution, morphological evolution, and interaction modes of tens of coexisting plumes. We identify a wide spectrum of dynamical behaviors--merging, splitting, branching, pulsing, and head detachment--that arise from coupled interactions among plumes, multiscale flow, and the evolving thermal boundary layers. We synthesize prior behaviors into a unified, time-resolved framework of plume evolutionary pathways. Characteristic length and timescales, including spacing and initiation times, are compared with previous theoretical and experimental studies. We find thinner plumes with greater minimum spacing. The fraction of isolated plumes (e.g., Hawaii-like) varies dramatically (0--60%) as the flow evolves. Our results provide new insight into plume self-organization and spatiotemporal variability under Earth-like conditions, crucial for understanding geochemical evolution and mapping geochemical anomalies from hotspot lavas to deep sources. These results quantitatively complement previous experimental work and numerical studies on interacting plumes, serving as a benchmark for comparison with geodynamical simulations of mantle convection.

physics.flu-dyn↗