Energy exchange between convection and electrovortex flow in a liquid metal battery experiment

The liquid metal battery is a promising grid-scale energy storage device where the melt in both electrodes is subject to both Lorentz (due to electrical current) and thermal forcing (due to Joule heating). The flow dynamics under the combined effects of these forces is not well understood. In a laboratory experiment we try to understand this interactions at different current densities relevant to batteries. We investigated the dynamics at different thermal forcings, finding a transition around a ratio of induced-to-external field, β, of 0.02, in all of them consistent with previous work on electrovortex flow, EVF, only (Abdelshafy et al., 2025). Additionally, we see different large scale behaviors as indicated by both the root-mean-square velocity and proper orthogonal decomposition (POD). At lower currents, more than 60% of the POD energy is in the convection modes, and we see peak frequencies similar to those reported by Cheng et al. 2022 in the same apparatus but without electrical current. However, as the current increases, two things happen: 1. the peak frequencies change and new harmonics arise since the circulation induced by the localized Lorentz force around the electrode remains strong as thermal modes compete for energy, and 2. the distribution of energy across different POD modes changes -- specifically, the energy gets distributed across more modes and new modes arise from the interaction of the two forcings.