Flow regimes in the evolution of a hot buoyant vortex dipole

Vortices and vortex dipoles play a critical role in turbulence, facilitating scalar mixing, diffusion, and energy dissipation. When a temperature gradient is present, buoyancy effects become significant, and buoyant vortices and dipoles emerge as characteristic features of such flows. In this study, we examine the evolution of a buoyant vortex dipole (BVD) arising from a temperature difference between the vortex dipole and the surrounding fluid. Using the Oberbeck-Boussinesq approximation, we derive the governing equations in non-dimensional form to capture the essential physics. The computational domain is periodic, and simulations are performed using the open-source spectral solver Dedalus. The interplay of thermal diffusion, viscous diffusion, and buoyancy drives the evolution of various coherent structures. Based on these interactions, we identify four distinct topological features and classify the evolution of the BVD into six regimes: (a) thermal diffusion-dominated regime, (b) viscous diffusion-dominated regime, (c) balanced diffusion regime, (d) weak wake street regime, (e) buoyancy-driven transition regime, and (f) multiple tertiary wakes regime. This classification provides a comprehensive framework to understand the dynamics of BVDs under varying physical influences.