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.
Viscosity
In general, the viscosity of a system depends in detail on how the molecules constituting the system interact. There are no simple but correct expressions for the viscosity of a fluid. The simplest exact expressions are the Green–Kubo relations for the linear shear viscosity or the "transient time correlation function" expressions derived by Evans and Morriss in 1985. Although these expressions are each exact, calculating the viscosity of a dense fluid using these relations currently requires the use of molecular dynamics computer simulations. On the other hand, much more progress can be made for a dilute gas. Even elementary assumptions about how gas molecules move and interact lead to a basic understanding of the molecular origins of viscosity. More sophisticated treatments can be constructed by systematically coarse-graining the equations of motion of the gas molecules. An example of such a treatment is Chapman–Enskog theory, which derives expressions for the viscosity of a dilute gas from the Boltzmann equation.