48 DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



asymmetric figures, we get pictures of the singularities and of the field surrounding 

 them as they will appear in the case of concrete motions. In this manner we get the 

 schemes of singularities presented by the different diagrams of fig. 48. The following 

 remarks regarding each of them will easily be understood by a comparison with the 

 results obtained analytically in sections 120, 122, 123 of the preceding chapter. 



I. Neutral Points. Points of this description appear when opposite currents 

 meet each other and bend off against each other without producing any motion 

 normal to the sheet (section 120). In the singular point two lines of flow will 

 intersect each other. Points of higher order, in which a greater but still finite 

 number of lines of flow intersect each other under finite angles, are also theoretically 

 possible (fig. 38), though they will occur rarely. 



II. Points of divergence and of convergence. Let a field in space as that of fig. 

 42 (p. 37) be given. The corresponding two-dimensional field contained in a 

 horizontal plane is represented by fig. 43 d. It contains a point in which an 

 infinite number of lines of flow intersect each other. A tangential motion of this 

 kind in a sheet always depends upon the existence of a motion normal to the sheet, 

 leading masses into it or taking masses away from it. In the atmospheric sheet 

 near the ground a point of divergence will appear where there is a descending current 

 (centre of anticyclone) and a point of convergence where there is an ascending 

 current (center of cyclone). The lines of flow are drawn in diagrams B-E of fig. 48, 

 with the common spiral-formed curvature due to the earth's rotation, which is 

 so well known from the air-motions near the centers of cyclones or anticyclones. 

 In the sheet of water near the sea's surface a point of divergence will depend upon an 

 ascending motion and a point of convergence upon a descending motion of the 

 water masses below. When the sheet is situated at a greater distance from the 

 bounding surfaces, divergence in the tangential motion shows that the normal 

 motion brings greater masses into the sheet on one side than it brings out on the 

 other, and vice versa for convergence in the tangential motion. But no definite 

 conclusion can be drawn regarding the general direction of this normal motion, 

 which may even have opposite directions on the two sides of the sheet. 



III. Lines of divergence and of convergence. Let a field in space, as that de- 

 scribed in section 123, be given. Fig. 45 d shows that the two-dimensional field in a 

 horizontal plane will contain a singular line of flow from which an infinite number 

 of other lines of flow diverge out asymptotically (fig. 48 p) . Reversing the direction 

 of the motion, we get a similar line toward which an infinite number of lines of 

 flow converge asymptotically (fig. 48 g). Evidently the lines of divergence and 

 convergence are in precisely the same relation to the normal motion as the points of 

 convergence and of divergence. In the case of rapid convergence, the designer can 

 make no difference between common and asymptotical touching. When the singu- 

 lar line is represented by a stroke of finite breadth, it will completely absorb the 

 lines converging toward it. The case of an infinitely rapid convergence arises when 

 the lines go normally into the singular line, the case ^4j, = oor& = o in the example 

 of section 123. In this case the asymptotic line ceases to be a line of flow and is 

 reduced to be a line for zero numerical value of the vector. 



