Enhanced drag of a sphere settling in a stratified fluid at small Reynolds numbers

Abstract

We present a combined experimental and numerical investigation of a sphere settling in a linearly stratified fluid at small Reynolds numbers. Using time-lapse photography and numerical modelling, we observed and quantified an increase in drag due to stratification. For a salt stratification, the normalized added drag coefficient scales as Ri[superscript 0.51], where R i = a[superscript 3]N[superscript 2]/(νU) is the viscous Richardson number, a the particle radius, U its speed, ν the kinematic fluid viscosity and N the buoyancy frequency. Microscale synthetic schlieren revealed that a settling sphere draws lighter fluid downwards, resulting in a density wake extending tens of particle radii. Analysis of the flow and density fields shows that the added drag results from the buoyancy of the fluid in a region of size (ν/N)[superscript 1/2] surrounding the sphere, while the bulk of the wake does not influence drag. A scaling argument is provided to rationalize the observations. The enhanced drag can increase settling times in natural aquatic environments, affecting retention of particles at density interfaces and vertical fluxes of organic matter.