254 



DEPARTMENT OF THE NAVAL SERVICE 



As a rule, the friction has a retarding effect upon the currents in the sea, so that 

 the diagrams of velocity through these are generally convex. Let us suppose that all 

 the water i)article3 in one and the same current are retarded with the same fore^. 

 The difference between the velocity of one water particle and the mean velocities 

 above and below will then be constant for all water particles throughout the currei\t 

 A diagram of velocity answering to these conditions is easily drawn, the figure being 

 in this case a parabola (fig. 39). 



Fig. 39. — Diagram of velocity for a current 

 with constant frictional resistance. 



If the equation for this parabola be 



u = az' (3a) 



then the force with which the friction retards each ccm. of the current will be 



f = -2ak (3&) 



where A; is the coefficient of friction. The more acute the parabola, the greater will be 

 the check exerted upon the current by friction. In currents where the water flows at a 

 great velocity in a thin layer, the retarding force is therefore very great, whereas in 

 currents of great volume such as the Gulf Stream, it is insignificant. 



In any current, where stationary conditions have been arrived at, the frictional 

 resistance in the longitudinal direction of the current is nearly equal to, albeit 

 naturally in an opposite direction to the force by which the current is impelled, and 

 we can therefore, from the diagram of velocity, directly ascertain this force. If such 

 a stationary current be disturbed by external influences, as for instance by that of the 

 wind, the appearance of the diagram of velocity is at once changed, and we may, from 

 the deformation occasioned therein, ascertain the magnitude and extent of the effect 

 produced by the disturbing force upon the current. A diagram of velocity is therefore 

 the best means we have of studying in detail the dynamic conditions of the ocean 

 currents. 



This analysis of the diagram of velocity is best carried out by dividing the curve 

 into so small portions that each can be regarded as a parabolic curve with horizontal 

 axis. For each such curve,, we then determine a and fj according to equations 3 a 

 and 3 b. 



Let us, for instance, consider the effect of the wind upon a surface current in the 

 sea. The diag'ram of velocity for such a current normally takes the form of a para- 

 bola, the point of which lies immediately under the surface of the water, vide fig. 40 a, 

 with a wind blowing across the sea in the same direction as the current, the diagram 

 will assume the form shown in fig. 40 b, i.e. its upper portion will become concave, while 

 the remaining parts will still continue convex. The upper portion of the current is 

 thus accelerated by the friction. The effect of the wind extends down as far as the 



