Buoyancy-induced Lagrangian chaos: the differentially-heated cavity revisited

P S Contreras,H J H Clercx,M F M Speetjens

doi:10.1088/1742-6596/745/3/032039

P S Contreras, H J H Clercx + Show 1 more

Open Access

https://doi.org/10.1088/1742-6596/745/3/032039

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Abstract

Natural convection plays a key role in fluid dynamics owing to its ubiquitous presence in nature and industry. Buoyancy-driven flows are prototypical systems in the study of thermal instabilities and pattern formation. The differentially-heated cavity problem has been widely studied for the investigation of buoyancy-induced oscillatory flow. However, far less attention has been devoted to the three-dimensional Lagrangian transport properties in such flows. This study seeks to address this by investigating Lagrangian transport in the steady flow inside differentially-heated cavities. The theoretical and numerical analysis expands on previously reported similarities between the current flow and lid-driven flows. First results reveal that the convective terms in the momentum and energy balances cause non-trivial (and potentially chaotic) Lagrangian transport.

Highlights

Natural convection plays a key role in fluid dynamics owing to its ubiquitous presence in nature and industry
This study seeks to address this by investigating Lagrangian transport in the steady flow inside differentially-heated cavities
First results reveal that the convective terms in the momentum and energy balances cause non-trivial Lagrangian transport

Summary

Introduction

Natural convection is a canonical subject of investigation in nonlinear dynamics and the various types of buoyancy mechanisms (stemming from different heating and boundary conditions) are archetypal systems in the study of complex phenomena [1]. Relating dynamical systems theory to fluid dynamics has provided a solid framework for theoretical, computational and experimental studies on Lagrangian transport phenomena over the past few decades. This has revealed important differences between 2D and 3D features and many challenges remain in the latter case, see [5,6,7,8] and references therein. The authors considered the linear problem (i.e., the governing equations without the convective terms) and noted important similarities with other systems studied in the field of fluid mixing, granular flows and volume-preserving systems and, with the previously mentioned lid-driven cylinder flow studied in [6, 8,9,10, 13].

Flow model

Linear problem

Response to nonlinear perturbations

Conclusions