15 29 



up a local flow in the adjacent water which, in combination with the pressure, 

 acts like a funnel to collect energy from a broad area of the incident wave. 



The non-compressive case also possesses a still wider significance. 

 There exists a continual tendency for the effects of any pressure wave to 

 undergo changes in the direction of non-compressive action. Any sudden im- 

 pulse of pressure produces an increment of motion in the structure according 

 to the laws of local action; but within a time of the order of the diffrac- 

 tion time, diffracted waves act so as to convert this motion at least roughly 

 into the motion that would have been produced by the same pressure impulse 

 acting in incompressible water, except, of course, as the motion may have 

 been further altered by forces arising within the structure. This drift to- 

 ward the non-compressive type of motion has already been mentioned in the 

 discussion of the tension phase on page 9- 



A variety of other cases can be imagined, characterized by various 

 relations among the four time constants. In considering such cases, the fol- 

 lowing general rules, already illustrated in the discussion, will often en- 

 able a step to be taken toward a solution: 



1 . During an initial interval much shorter than the diffraction time 

 Tj, the formulas pertaining to plane waves will be applicable. In special 

 cases, when T, « T^, this interval may cover the whole of the action on the 

 target. 



2. During an initial interval much shorter than the swing time T, , the 

 elements of the target will be accelerated independently. 



3. For a plate or diaphragm, the equation of motion will be approxi- 

 mately as given in Equation [1] during an initial interval that is much 

 shorter than either the diffraction time T^ or the swing time T^. 



CONDITIONS UNDER WHICH CAVITATION MAY OCCUR 



In the consideration of cavitation it may be conducive to clarity 

 if a distinction is made between cavitation due to elastic overshoot and cav- 

 itation due to fluid inertia. 



Cavitation due to inertia is a familiar phenomenon in the non- 

 compressive motion of water. On the back of a propeller blade, for example, 

 cavitation occurs because the inertia of the water prevents it from following 

 the blade. 



Cavitation between a shock wave and a plate, as discussed in a pre- 

 vious section, arises in a different manner and is closely associated with 

 the elasticity of the water. The plate, together with the water in contact 

 with it, is accelerated so rapidly that the water farther away is unable to 



