General Theory of Ocean Currents in a Homogeneous Sea 



431 



more difficult. Instead of determining curl U, Ekman in his older theory (1923) 

 investigated a quantity W, termed the "quasi-vortex". It is strictly not identical with 

 curl U but in most cases agrees with it in sign and magnitude. This quantity W is the 

 sum of thiee terms 



W 



(XIII.59 a) 



The first term depends only on the wind and is directly proportional to the vorticity 

 of the wind {anemogenic vortex effect), Wa depends on the slope of the bottom topo- 

 graphy but not on the total depth {topographic vortex effect), W^ depends only on the 

 curvature of the Earth {planetary vortex effect). The two latter effects are the most 

 important ; their mode of action has been illustrated in the examples previously dis- 

 cussed. When a current flows across the isobaths of the sea bottom, even quite small 



d{ 



Fig. 184. Deep current influenced by a wave-form sea bottom profile. Lower picture: 

 vertical cross-section parallel to the coast. Upper picture: horizontal section through the 



current field. 



slopes can affect the deep current and usually give it quite a different appearance. On 

 the other hand, the curvature of the Earth so strongly resists forced meridional water 

 movements that in the lower latitudes almost only zonal currents are possible. For the 

 combined topographic and planetary vortex effect Ekman obtained the same results 

 as were derived earlier for frictionless gradient currents (see p. 386). This suggests that 

 the simplifications introduced for their calculation eliminate the frictional effect to 

 such a degree that only the part for frictionless currents remains. 



In a new theory Ekman (1932) extended his investigations, in which he still deals 

 only with steady currents. But previously these currents were also subject to the 

 condition of no acceleration dujdt = dvjdt = 0, while for a steady current only the 

 condition cujdt — dvjdt = is required. Accelerations are thus possible due to the 

 circumstance that water elements are subjected to velocity change when changing their 

 position. These accelerations give rise to changes in the form of the current which may 

 be quite large. For example, the case discussed previously of a current over a wave- 

 shaped sea bottom (Fig. 184) would show two types of change: First, the amplitude 



