The Geosteophic Relationship 17 



where p is pressure, g is the acceleration due to gravity, and p is the 

 density of the ocean water. In general, the order of magnitude of each of 

 these two terms is 10^ dynes/cm.^. Under surface waves, where there are 

 vertical accelerations, terms up to the order of magnitude of 10^ dynes/cm.^ 

 may be expected, but these are important only in the upper 100 m. The 

 acceleration term for ocean tides is much less, perhaps of the order of 

 magnitude of 10~® dynes/cm.^. The vertical CorioUs force due to horizontal 

 motions is not likely to exceed 10~^ dynes/cm.^ anywhere in the ocean ; 

 and, because large-scale vertical motions are so small, this force may be 

 neglected for practical purposes, such as in the computation of depth in 

 terms of measured pressures. The balance of forces expressed by this 

 equation is therefore correct to a very high order of approximation for 

 most large-scale oceanic phenomena. 



The horizontal equations of motion for large-scale oceanic features 

 exhibit a similar balance between two large forces compared to which most 

 other terms in the equations of motion are often small. In order to illus- 

 trate this, we shall first write the two equations of motion including only 

 these two forces (the so-called geostrophic equations) : 



The symbols u and v are the x and y components of velocity, and / is a 

 quantity called the Coriohs parameter /=2w sin (j), where w is the angular 

 velocity of the earth and is the geographic latitude. In mid-latitudes the 

 value of /is approximately 10~*/sec. The maximum current velocities in 

 the Gulf Stream range from 100 to 250 cm. /sec, and hence the CorioHs 

 force, acting at right angles to the Stream, is of the order of 10-^ dynes/cm.^. 

 This CorioHs force is nearly balanced by horizontal pressure gradients 

 due to the density distribution in the ocean, as shown in equations (2) 

 and (3). 



It is interesting to compare the order of magnitude of these terms with 

 that of other terms in the equations of motion. If there is a local ac- 

 celeration of the ocean currents at a particular locahty such that a 

 250 cm. /sec. current is diminished to zero in the course of a week, the local 

 acceleration term is of the order of magnitude of 4 x 10"^ dynes/cm. 3. 



If the current happens to be flowing in a curvihnear path, with a radius 

 of curvature of M, the inertial terms will be of the order of magnitude of 

 u^lM. For example, if the radius of curvature of the streamUnes is 200 km., 

 and the current velocity is 200 cm. /sec, the inertial terms in the equations 



