Formation of thermal vortex rings

Geophysical convection is usually characterized by Reynolds number in the range typical for turbulent flow. Despite that, it displays features of organization.  Thermal vortex rings are considered candidates for the basic elements of that order (Yano 2023, ch. 16). In this work, the process of their formation from a spherical buoyancy anomaly is studied numerically. The buoyancy distribution is assumed to be uniform with a discontinuity at the interface. The rising anomaly experiences a collapse at the bottom, and initially spherical shape is transformed into a torus. Neglecting diffusive processes, the system is uniquely defined by the vortex sheet coincident with the interface. For that reason, its evolution is considered on the grounds of vorticity dynamics with Lagrangian approach.The vortex sheet is intensified by buoyancy and further subjected to Kelvin-Helmholtz instability. This starts in high wavenumbers increasing the effective thickness by purely advective mechanism. A similar instability is then launched in lower wavenumbers, and the phenomenon repeats hierarchically. As a result, the energy is transferred from small to large scales. The same mechanism also drives the interfacial mixing by applying stretching and folding repetitively. This makes it a good starting point for further studies on the entrainment rate and order emerging out of chaos.