Energy partitioning of thermally driven flows confined in Hele-Shaw systems*

Thermally driven flows in strongly confined environments, such as permeable media, are ubiquitous in nature, and they contribute to the heat transfer across the Earth's lithosphere and fluid mixing process within aquifers. The Hele-Shaw system is an ideal laboratory analogue to investigate geometrically constrained convective flows. However, in these environments, the energy pathways have not been characterized experimentally. In this work, we study the energy pathways of thermal convection in Hele-Shaw systems by laboratory experiments. Transparent fluid layers built for the laboratory experiments allow elucidating kinetic and potential energies of the whole domain by particle image velocimetry and background oriented schlieren method. The experimental results are then compared with theoretical and numerical results that characterize the energy partitioning as a function of the controlling parameters, the Rayleigh-Darcy number, the Prandtl, and the anisotropic ratio of the Hele-Shaw cell. We will discuss the flow features, energy partitioning, and mixing efficiency of thermal convection in Hele-Shaw systems.