Particle clouds in homogeneous and stratified environments

We examine the settling of monodisperse heavy particles released into a fluid when the resulting motion is sufficiently vigorous that the particle cloud initially assumes the form of a turbulent thermal. A laboratory study is complemented by numerical simulations of particle cloud dynamics in both homogeneous and stratified ambients. In the homogeneous ambient, the cloud generated by a total buoyancy excess Q = gNpVp , where g ′ is the reduced gravity of the Np spherical particles of volume Vp =4πa /3, evolves in a manner consistent with a classical fluid thermal. The cloud grows through turbulent entrainment and decelerates until its speed is exceeded by that of the individual particles ws , at which point the particles rain out as individuals. For particle Reynolds numbers Rep =wsa/ν in the range of 0.1–300, the fallout height Zf is found to be Zf /a=(11± 2)(Q/(wsa)). For high Rep particles, the fallout height assumes the simple form: Zf /a=(9 ± 2)N p . Following fallout, the particles sink at their individual settling speeds in the form of a bowl-shaped swarm. In a stratified environment characterized by a constant Brunt–Väisälä frequency N , the mode of fallout depends explicitly on the stratified cloud number, Ns =wsQ −1/4N−1/2. For Ns < 1, the cloud overshoots, rebounds past, then intrudes at the neutral height, ZN , of the equivalent fluid thermal. The particles fall out between the depth of maximum penetration and the spreading neutral cloud, and may be distributed over a relatively broad area. For Ns > 1, the particles fall out in the form of a bowlshaped swarm at a height Zf 4, the fallout height is largely uninfluenced by the stratification and is adequately described by the homogeneous result. Regardless of Ns , following particle fallout in a stratified ambient, the fluid entrained by the thermal ascends and intrudes at a rebound height given to leading order by 3Zf /4. Criteria for three distinct modes of particle deposition in a stratified ambient are developed.