On axisymmetric gravity currents with internal stratification

We investigate the propagation of high-Reynolds-number internally stratified axisymmetric gravity currents released from a lock into a homogeneous ambient. Using an inviscid Boussinesq shallow-water framework, we model how internal density variations enhance the driving buoyancy force, leading to thinner currents and increased propagation speeds compared to constant density counterparts. Our results indicate that, for certain current stratifications, a unique “bare spot” phenomenon occurs in the similarity solutions—a region of zero thickness at the center of the domain (r=0) that emerges due to radial divergence. Additionally, we provide a definitive analytical criterion for the transition from the inertial to the viscous regime (rV) and determine stability thresholds using Richardson number criteria. The model is specifically presented for two-layer and linearly internal-stratified configurations, providing a comprehensive theoretical foundation for predicting the morphology and dynamics of complex stratified axisymmetric flows.