Chapter Three 



THE GEOSTROPHIC 

 RELATIONSHIP 



It is probable that the reader unfamihar with the hterature and conven- 

 tions of meteorology and oceanography will find that the manner in which the 

 hydrod3niamical equations are introduced and abbreviated in this and later 

 chapters is neither sufficiently explained nor fully justified. Because of the 

 speciaUzed nature of the topic of this book it did not seem advisable to me to 

 try to develop the formulation from first principles. The unsatisfied reader 

 is therefore advised to refer to a good treatise on dynamical meteorology, or 

 to Proudman's (1953) textbook on dynamical oceanography, where an 

 adequately detailed exposition can be found. Lamb (1932) gives a concise 

 derivation of the equations of motion referred to a rotating reference frame. 



THE BALANCE OF FORCES IN THE GULF STREAM 



In the ocean there are two sets of forces which are nearly always almost 

 balanced. The first of the near-balances, and perhaps the more obvious, is 

 that in the vertical between gravity force^ and the vertical pressure gradient. 

 We introduce a system of rectangular coordinates in the ocean, with the 

 a;-axis directed toward the east, the y-axis directed toward the north, and 

 the z-axis directed vertically upward. The expression for this hydrostatic 

 balance of forces is 



|=-.P, (1) 



^ Gravity is defined as the vector sum of the gravitational force due to the earth's 

 mass and the centrifugal force due to its rotation. 



