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arXiv · 2307.13146

A convective fluid pendulum revealing states of order and chaos

Jinzi Mac Huang·Nicholas J. Moore
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Abstract

We examine thermal convection in a two-dimensional annulus using fully resolved direct numerical simulation (DNS) in conjunction with a low-dimensional model deriving from Galerkin truncation of the governing Navier-Stokes Boussinesq (NSB) equations. The DNS is based on fast and accurate pseudo-spectral discretization of the full NSB system with implicit-explicit time stepping. Inspired by the numerical results, we propose a reduced model that is based on a Fourier-Laurent truncation of the NSB system and can generalize to any degree of accuracy. We demonstrate that the lowest-order model capable of satisfying all boundary conditions on the annulus successfully captures reversals of the large-scale circulation (LSC) in certain regimes. Based on both the DNS and stability analysis of the reduced model, we identify a sequence of transitions between (i) a motionless conductive state, (ii) a state of steady circulation, (iii) non-periodic dynamics and chaotic reversals of the LSC, (iv) a high Rayleigh-number state in which LSC reversals are periodic despite turbulent fluctuations at the small scale. The reduced model reveals a link to a damped pendulum system with a particular form of external forcing. The oscillatory pendulum motion provides an accurate prediction for the LSC reversal frequency in the high Rayleigh-number regime.

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Jinzi Mac Huang, Nicholas J. Moore. 2023-07-24. A convective fluid pendulum revealing states of order and chaos. https://arxiv.org/abs/2307.13146

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