54 DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



The corresponding motions in space may be of different kinds. Thus a rolling 

 mass of air (fig. 50 g) will be bounded by a line of convergence and a line of diver- 

 gence parallel to each other. But the most common origin of such lines may be 

 wave-motions.* We shall therefore examine this case separately. 



131. Influence of Wave-Motions on the Aspect of the Lines of Flow. The 

 large-scale waves which can arise in the atmosphere will be of the same nature 

 as long waves in shallow water. During the propagation of the waves the different 

 particles will describe elliptic orbits in vertical planes normal to the wave-ridges. 

 Every ellipse has its long axis horizontal and its short axis vertical. The latter 

 axis will decrease as we go downward, and be zero at the ground. Thus the motion 

 near the ground will consist in rectilinear oscillations. 



Remembering the difference of phase from particle to particle, we can draw 

 arrows representing the simultaneous motion of a set of particles at a given epoch. 

 This distribution of arrows in a vertical plane is shown at the top of fig. 51 A, and 

 the corresponding lines of flow at the top of fig. 51 b. As will be seen, the prop- 

 agation of the waves depends upon a conflux of masses below the front-slope and a 

 corresponding afflux below the back-slope of the waves. In the horizontal projec- 

 tion we shall therefore always get a line of convergence below the front slope and a 

 line of divergence below the back-slope of every wave. These lines will follow the 

 waves in their motion of propagation. 



Fig. 51 a will thus give the instantaneous distribution of motion at the ground 

 in the case of a pure wave-motion. With the system of velocities thus given we 

 shall compose the constant velocity due to a pure translation. 



(1) First let us add a constant velocity which is parallel to the direction of the 

 wave-ridges. Performing the parallelogram-constructions and afterwards drawing 

 the lines of flow, we get the picture of fig. 51 B. The picture shows lines of flow run- 

 ning between a system of parallel and equidistant asymptotic lines, alternately 

 lines of convergence and of divergence. 



(2) To the velocities of fig. 51 a we shall now add a constant velocity which is 

 normal to the direction of the wave-ridges and of smaller intensity than the greatest 

 velocity due to the pure wave-motion. We shall then get the picture of fig. 51c. 

 When we afterwards add the same constant velocity parallel to the direction of the 

 wave-ridges as above, perform the parallelogram-constructions, and draw the lines 

 of flow, we get the picture of fig. 51 d. The picture shows parallel, but no more 

 equidistant, lines of convergence and divergence. 



(3) To the velocities of fig. 51 A we shall again add a constant velocity of direc- 

 tion normal to the wave-ridges, but now of intensity equal to the greatest occurring 

 in the pure wave-motion. We shall then get the velociti s presented by fig. 51 E. 

 When we add in this case the same constant velocity parallel to the wave-ridges as 

 above, perform the parallelogram-constructions, and draw the lines of flow, we shall 

 get the picture of fig. 5 1 F. Here we have a set of wave-formed lines of flow, touching 



*Cf. J. W. Sandstrom: Ueber die Beziehung zwischen Luftdruck und Wind. K. Svenska Vetenskapsakade- 

 miens Handlingar, T. 45, No. 10. 1910. 



