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3.9 Gravity and the Buoyancy Force 35in the Cartesian coordinate system and has vector components (0, 0, −g), where g =9.81 m/s 2 is called acceleration due to gravity.If an object of a certain mass M obj and volume V obj is released in the water column,instead of the full gravity force, it will experience only a reduced gravity force,called buoyancy force, that makes it sink at a slower rate or even rise in dependenceof the density of the ambient medium. Imagine an air-fille plastic ball that will popup if released in water.According to Archimedes’ Principle, the resultant buoyancy force is proportionalto the difference between the object’s mass with the mass of the flui replaced by theobject’s volume. See Stein (1999) for a biography of Archimedes. The constant ofproportionality is acceleration due to gravity. Accordingly, the resultant buoyancyforce (per unit mass of the object) is given by:Buoyancy force =−g (M obj − M amb )M objwhere M amb is the mass of the ambient flui replaced by the object. After a fewmanipulations, this formula can be expressed in terms of densities, yielding:Buoyancy force =−g (ρ obj − ρ amb )ρ obj(3.14)where ρ amb is the density of the ambient fluid Note that the buoyancy force has anegative sign and is directed downward if the object’s density exceeds that of thesurrounding fluid Now it will be not that difficul for the reader to tell why shipsmade from steel usually stay at the sea surface (unless capsizing).3.9.2 Reduced GravityIn physical oceanography, the negative of the buoyancy force (per unit mass) iscommonly termed reduced gravity. This quantity carries the symbol g ′ and is givenby:g ′ = g (ρ obj − ρ amb )ρ obj(3.15)It should be noted that buoyancy is not only restricted to objects of a solid skin.The object of interest can be a flui parcel itself.3.9.3 Stability FrequencyVertical density gradients can be expressed in terms of the stability frequency N,traditionally called Brunt – Väisälä frequency with appreciation of early works by