A convective fluid pendulum revealing states of order and chaos

TL;DR

This study investigates thermal convection in a 2D annulus, combining DNS and a low-dimensional model to reveal transitions from order to chaos and accurately predict large-scale circulation reversals.

Contribution

It introduces a novel reduced Fourier-Laurent model that captures complex convection dynamics and LSC reversals, extending understanding of fluid behavior in annular geometries.

Findings

Identified sequence of flow states from conduction to chaos.

Reduced model accurately predicts LSC reversal frequency.

Revealed a link between convection dynamics and a damped pendulum system.

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.