VAXADIAX Fl.SBERIES EXPEDITIOX, IDl'rlo 



253 



9. INFLUENCE OF FKICTIOX UPON THE MOVEMENT OF SEA-WATER. 



Internal friction exerts a powerful regulating influcMico uixju the movement of 

 the water in an ocean current. In order to compreliend this, it will be necessary to 

 consider the forces acting upon the water through friction. And it will simplify 

 matters if we here disregard the insignificant vertical velocities in the water. Let 

 us suppose that the water particle a has a velocity inferier both to that of the water 

 above and of that below, vide fig. 38 a. The velocity of a wiU then be accelerated by 

 friction with both these layers, until finally it attains their velocity. In this instance, 

 then, the velocity of the water particle is accelerated by internal friction. 



Fig. 38. — Frictional force as indicated by the 

 iiiovemwit of the watei in a current. 



If, on the other hand, the water particle a is of greater velocity than the water 

 above and below (fig. 38 b), it will be retarded until its velocity is equal to theirs. In 

 this instance, the friction acts as a check upon the movement of a. 



Again, if the velocity of a be equal to mean of the two values for velocity of the 

 Layer above and of that below, (fig. 38 c), then the retarding effect of the one will be 

 equal to the accelerating influence of the other; i.e., the resultant value of the forces 

 acting upon a through internal friction will be nil. 



If the velocity of the particle a be not equal to the mean of the velocities above 

 ar.d below (fig. 38 d), then the friction in a will be the greater between it and the layer 

 having the greater divergence in point of velocity from the particle a. The result of 

 tiiis will be that the velocity of a is finally brought, through friction, to a value equal 

 to the mean of the two velocities in the water above and below it. 



Where the current has a screwing movement, so that the vectors \\ and \u (in fig. 

 38 d), do not lie in the same plane, or take opposite directions, then the vector repre- 

 senting a will constantly endeavour to attain a velocity and direction equal to the 

 mean values for those of the ve-ctors v\ and V2. 



If we measure the velocity of the water at a great number of points in a vertical 

 down through the sea, and draw up from these a co-ordinate system with the velocities 

 as abscisses and depths as ordinates, then we obtain a diagram of velocity for the 

 vertical in question. Where the resulting diagram is convex, as in fig. 38 e, then 

 the velocity of each particle will be greater than the mean value of those immediately 

 above and beneath; the current is then retarded by internal friction. If, on the other 

 hand, the diagram presents a concave figiu-e (fig. 38 f). then the velocity of each 

 particle is less than the mean value of the velocities in the layers immediately above 

 and below, wherefore the current will be accelerated by internal friction. 



