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.
Flotation of flexible objects
Consider two plates of infinite width, thickness formula_2, and length formula_3 that are connected by a torsional spring with spring constant per unit width formula_4. Furthermore, let formula_5 be the angle between a plate and the horizontal, and formula_6 the from where the meniscus meets the plate to the horizontal. The distance from the undisturbed water line to the plate's outer edge is formula_7. The density of water is formula_8, the density of air is considered negligible, and the plate density, formula_9, shall be varied. All systems naturally assume a configuration that minimizes total energy. Thus, the goal of this analysis is to identify the configurations (i.e., values of formula_7 and formula_5) that result in a stable equilibrium for a given value of formula_9.