Decay of velocity fluctuations in a stably stratified suspension

Abstract

The evolution of velocity fluctuations in a stably stratified suspension settling under the influence of gravity is studied. Based on a continuum model for sedimentation dynamics, decay of long-wave fluctuations in the particle density is found. Substantial reduction in velocity fluctuations is an important consequence. Specifically, the evolution of the particle density in a stably stratified suspension immediately leads to particle distributions, where the variance in the velocity is bounded as the container size grows to infinity. This result is a possible explanation for why velocity fluctuations have been observed to depend on container size in numerical simulations but generally not in physical experiments.