Potential density
Potential density is a dynamically important property: for static stability potential density must decrease upward. If it doesn't, a fluid parcel displaced upward finds itself lighter than its neighbors, and continues to move upward; similarly, a fluid parcel displaced downward would be heavier than its neighbors. This is true even if the density of the fluid decreases upward. In stable conditions (potential density decreasing upward) motion along surfaces of constant potential density (isopycnals) is energetically favored over flow across these surfaces (diapycnal flow), so most of the motion within a 3-D geophysical fluid takes place along these 2-D surfaces.
Turbidite
Density-based flow, however, occurs when liquefaction of sediment during transport causes a change to the density of the fluid. This is usually achieved by highly turbulent liquids which have a suspended load of fine grained particles forming a slurry. In this case, larger fragments of rock can be transported at water velocities too low to otherwise do so because of the lower density contrast (that is, the water plus sediment has a higher density than the water and is therefore closer to the density of the rock).