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
where formula_58 is the Boltzmann constant, formula_59 the molecular mass, and formula_60 a numerical constant on the order of formula_61. The quantity formula_62, the mean free path, measures the average distance a molecule travels between collisions. Even without "a priori" knowledge of formula_60, this expression has interesting implications. In particular, since formula_62 is typically inversely proportional to density and increases with temperature, formula_10 itself should increase with temperature and be "independent" of density at fixed temperature. In fact, both of these predictions persist in more sophisticated treatments, and accurately describe experimental observations. Note that this behavior runs counter to common intuition regarding liquids, for which viscosity typically "decreases" with temperature.