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arXiv · 2610.08024

A Lagrangian analysis of coherent structures in 2D annular Rayleigh-Bénard convection

Luis Álamo·Jezabel Curbelo·Kathrin Padberg-Gehle
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Abstract

Convective instabilities are studied from a Lagrangian perspective in order to gain new insights into how the resulting global, long-lived coherent flow structures organize themselves. We consider a 2D annular fluid layer uniformly heated from the inside and subject to radial gravity and propose several new Lagrangian diagnostics for characterizing its convective instabilities. In particular, we perform a comprehensive Lagrangian analysis of the flow field across a wide range of dimensionless parameters, establishing a heuristic correspondence between convective plumes and curves of local maxima of Finite-Time Lyapunov Exponent (FTLE) fields. Moreover, we characterize coherent swirling motions inside convective rolls, which are associated to the non-zero curvature of the flow. By introducing a sliding window method for our finite-time kinematic measures, we demonstrate a direct relationship with radial heat flux quantified by means of the Nusselt number and identify relevant dynamical transitions that leave a trace on both. Finally, we propose a formal criterion for determining viscous boundary layer (UBL) thickness by virtue of radial FTLE profiles and validated against a classical Eulerian method.

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Luis Álamo, Jezabel Curbelo, Kathrin Padberg-Gehle. 2026-10-06. A Lagrangian analysis of coherent structures in 2D annular Rayleigh-Bénard convection. https://arxiv.org/abs/2610.08024

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