Mushroom-cloud development and transport of radioactive materials and dust: A numerical study of the Nagasaki atomic bombing

Abstract In this study, the blast-wave formation and mushroom-cloud development associated with the Nagasaki atomic bombing were numerically investigated to construct initial conditions for subsequent meteorological simulations of “black rain.” To evaluate the three-dimensional transport of hazardous materials within the cloud, two distinct material tracers were treated as passive scalars in an Eulerian framework and solved together with the compressible airflow: bomb-derived radioactive material, assumed to represent plutonium released from the bomb, and ground-derived dust, representing non-radioactive smoke and dust associated with urban fires and disturbed surface materials. The computation was carried out in three stages: a one-dimensional theoretical blast-wave calculation, a high-resolution three-dimensional simulation of the early blast-wave/fireball interaction, and a large-domain three-dimensional simulation of the subsequent mushroom-cloud rise. The numerical results showed that sufficient grid resolution is required in both the blast-wave and mushroom-cloud stages to reproduce the cloud-rise behavior accurately. In the blast-wave stage, coarse grids smeared the reflected-shock/fireball interaction and led to an underestimation of the later cloud-top height. The background atmospheric profile also affected the buoyant rise, and a dry adiabatic atmosphere showed better agreement with historical nuclear-test data than the International Standard Atmosphere. The three-dimensional blast-wave simulation clarified that the reflected shock wave deforms the fireball and induces a strong axial updraft, which provides the initial flow structure for the subsequent mushroom-cloud rise. The mushroom-cloud simulation reproduced the buoyant ascent of the hot fireball, the horizontal spreading of the cloud head, and the development of a vortex-ring structure. The potential-temperature perturbation field visualized the hot core and updraft, while the relative-humidity field indicated possible condensate-cloud formation in the upper part of the cloud. The two solid-phase components exhibited distinct transport behaviors depending on their initial locations. Ground-derived dust was entrained mainly through the central updraft, whereas bomb-derived radioactive material was preferentially incorporated into the vortex-ring region around the cloud head. These results provide the three-dimensional initial distribution of hazardous materials for meteorological simulations of black rain.