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

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.