A convective fluid pendulum revealing states of order and chaos
| Title: | A convective fluid pendulum revealing states of order and chaos |
|---|---|
| Authors: | Mac Huang, Jinzi, Moore, Nicholas J. |
| Publication Year: | 2023 |
| Collection: | Mathematics Mathematical Physics Physics (Other) |
| Subject Terms: | Physics - Fluid Dynamics, Mathematical Physics, Mathematics - Dynamical Systems |
| More Details: | 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. |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2307.13146 |
| Accession Number: | edsarx.2307.13146 |
| Database: | arXiv |
| Description not available. |