Therefore, 



K = -^Ua^ 



and for the general case; i. e., r>a 



A model of the polynya circulatory system can be formulated from 

 the idealized case by adaptation of the principles to the bubbling sys- 

 tem. Considering the motion of each ascending bubble to be directed 

 along the positive-downward Z axis, there will be a streamline coinci- 

 dent with the Z axis and a vertical flow of water particles. Ascending 

 motion, represented by a negative vertical velocity, creates divergence 

 at the surface. Approximately midway between bubble streams is a 

 region of convergence with consequent descending motion, clearly dis- 

 cernible in Figure 9« 



Sirrface water beyond the pipe furthest from the pier flows out- 

 ward to a distance determined by the horizontal momentum of the water 

 particles. 



The data show greater density in water brought to the surface by 

 the bubble activity during the pre-freezeup and initial freezeup peri- 

 ods. Consequently, as the higher density surface water flowing outward 

 from the divergence zone above pipe ^ suffers a gradual decrease in 

 the horizontal component of the velocity vector, the vertical component 

 increases. From the point where the horizontal component becomes zero, 

 descending motion extends to depths where divergence directs a horizon- 

 tal component toward the pier. 



The proposed model of the polynya circulatory system is presented 

 in Figure 10. This cross-sectional view shows the eastern ends of the 

 polyethylene pipes; arrows indicate principal paths of the water parti- 

 cles. 



The author is indebted to Dr. Lloyd Simpson of the Ifydrographic 

 Office for advice and assistance in application of iiydrodynamic prin- 

 ciples in development of this idealized model of the bubbling system. 



18 



