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.
Annular velocity
The other major variable is the rheology of the drilling fluid. Rheology is sometimes thought of as viscosity to the uninitiated, though improperly. Viscosity (sometimes thought of as its thickness) is a very basic measurement of the fluids resistance to change in movement or flow. The viscosity of a fluid can be measured with a Marsh Funnel. Rheology is the study of viscosity and requires more precise and complicated procedures and equipment for its determination. For drilling fluid applications a rheometer is used.