LiNEAE Theories — Viscous 



85 



gress further it is necessary to consider the processes tending to increase or 

 decrease the vorticity of the ocean water. First we shall consider these pro- 

 cesses quahtatively, and then proceed to a mathematical demonstration. 



The vorticity of a vertical column of water^ is taken as positive if counter- 

 clockwise, and negative if clockwise. If the spin is measured in its relation 

 to the earth, we speak of relative vorticity; by adding the CorioHs parameter 

 to the relative vorticity we obtain the absolute vorticity of the column. 

 Unlike the velocity distribution, the vorticity distribution in the ocean may 



Fig. 53. Schematic relation of wind (broken lines) and current (solid lines), 

 with asymmetry. 



be discussed without reference to the pressure field — a fact which greatly 

 simplifies consideration of the quahtative factors. (Formally, the vorticity 

 equation is obtained by elimination of the pressure from the equations of 

 motion by cross-differentiation.) The wind system in fig. 52 is one that 

 would tend to decrease (make negative) the relative vorticity of all the water 

 columns in the ocean. In the steady state of motion which must exist under 

 a prolonged exposure of the ocean to this wind system, the relative vorticity 

 has a fixed value at each point of the ocean independent of time. This 



^ The vorticity of an element of fluid is twice its angular velocity. An element of 

 fluid in a shearing motion is subjected to an instantaneous spin. The qualitative 

 reasoning is done entirely in terms of the total vorticity of a vertical water column — 

 that is, the sum of the vertical components of vorticity of all the elements of a 

 vertical water coliunn. The mathematical definitions of several different kinds of 

 vorticity are given in Chapter VIII, equations (3) and (5). 



