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.
Shallow water equations
where "u" is the velocity in the "x"-direction, "v" is the velocity in the "y"-direction, "w" is the velocity in the "z"-direction, "t" is time, "p" is the pressure, ρ is the density of water, ν is the kinematic viscosity, and "f" is the body force in the "x"-direction.