A New Power-Law Relation For The Vertical Distribution of Suspended Matter

Generally, the vertical distribution of suspendedmatter is described by a simplepower-law relation in which it is assumed that thefriction velocity is constant withheight. This is a simplification of the actual mechanismof turbulent transport, sinceturbulence will most likely be reduced in the presenceof suspended particles for avariety of reasons. Here we investigate analytically,by assuming a constant shearstress with height, how the increased density of thetwo-phase mixture reduces thefriction velocity. This reduces the upward turbulentflux of particles, which tends todecrease the drift density compared to a situation inwhich changes in friction velocityare neglected. A new power-law relation is derived,which in snowdrift predicts amaximum reduction in drift density of 25% (and 40%for Martian dust) over thestandard power-law relation. In other geophysicaltwo-phase flows, such as suspendedmatter in water, the effects are shown to be negligiblebecause of the small ratio of driftdensity and medium density. Generally, this and otherinteractions between the particlesand the flow should be taken into account to betterunderstand the vertical profile ofsuspended matter in geophysical two-phase flows.