CHAPTER XL 



VERTICAL MOTION IN FREE SPACE-COMPLETE KINEMATIC DIAGNOSIS. 



185. Free Vertical Motion. As the distance from the bounding surface increases, 

 the forced vertical motion produced at this surface will gradually be modified. 

 An additional vertical motion will arise in the free space and conjoin with the 

 forced vertical motion. We shall for the sake of brevity call it the free vertical 

 motion. It can be investigated by the solenoidal condition in space, precisely as 

 the forced vertical motion by the solenoidal surface-condition. 



We have done it already from a qualitative point of view (Chapter V). We had 

 to take the free vertical motion into consideration in order to explain the features 

 of the horizontal motion. The vertical motion existing above centers or lines of 

 convergence and of divergence gives typical examples of this free vertical motion 

 and shows its connection with the horizontal motion. It will therefore be under- 

 stood at once that from a given horizontal motion we can derive the correlated 

 vertical motion by making quantitative use of the solenoidal condition. 



The vector which fulfils the solenoidal condition with the highest degree of 

 approximation is specific momentum. Both in atmosphere and in hydrosphere the 

 field of mass can be considered as stationary in space (section 117). Therefore the 

 mass-transport leading into a stationary volume through one part of the bounding 

 surface will be equal to that leading out of it through other parts of this surface. 

 The solenoidal nature of specific momentum is a consequence of this property of 

 the mass-transport. In the hydrosphere the moving masses can be considered as 

 incompressible. Then the volume-transport obtains the same property as the mass- 

 transport, and even velocity will be a solenoidal vector. But in developing our 

 methods we shall consider only atmospheric motions. Their adaptation to sea- 

 motions will cause no difficulty as soon as the observations to be used are at hand. 



186. Diagnostic Use of the Solenoidal Condition. We shall consider an atmos- 

 pheric sheet limited by two horizontal or quasi-horizontal surfaces, dz will be their 

 vertical distance. The average horizontal motion in this sheet will be represented 

 by the specific momentum V. A chart will be given containing the lines of flow 

 (or the isogons) and curves for equal intensity V = const, of this vector. By 

 using the solenoidal condition we shall derive from this chart the correlated data 

 regarding the vertical motion. We will give three different methods of deriving 

 these data, each leading to a special form for the representation of the vertical 

 motion. 



(A) Areas of equal vertical transport. The simplest plan will be to draw a chart 

 of the horizontal transport T in the sheet. By the solenoidal condition this chart 

 must necessarily give an indirect representation also of the correlated vertical 



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