189 



RADIAL MOTION OF WATER SURROUNDING A SPHERE* OF GAS 

 IN RELATION TO PRESSURE WAVES 



ABSTRACT 



In the study of explosive pressure waves, the theory of a sphere of 

 gas expanding or contracting under water is needed in two connections - in 

 discussing the motion of the gas globe produced by the explosive itself, and 

 in considering the effect of bubbles in the water upon the propagation of 

 pressure waves. The relevant analytical formulas are collected here and dis- 

 cussed. Their deduction is given in an appendix. 



The following topics are treated: 



1 . the period and form of the radial oscillations of a gas globe, and 

 the pressure and impulse thereby generated in the water; 



2. the effect of a pressure wave upon a single gas bubble; 



3. the inverse effect of a layer of bubbles in water upon an incident 

 wave of pressure, which is partially to reflect or scatter the incident wave, 

 and to make the transmitted wave weaker but of longer duration; 



4. an exact treatment for the analytically simple case of weak waves 

 of pressure incident upon water containing bubbles of relatively small size; 



5. scattering by a single bubble. 



INTRODUCTION 



In the study of explosive pressure waves, the theory of the expan- 

 sion and contraction of a sphere of gas under water enters at two points: 

 First, in considering the motion of the gas globe produced by the explosive, 

 which results in secondary impulses of pressure; and second, in considering 

 the effect of bubbles of gas in the water upon an incident pressure wave. 

 Therefore it is proposed to collect and extend the relevant analytical formu- 

 las pertaining to such motion. Only radial motion will be considered here; 

 effects due to gravity or to the presence of obstacles will be reserved for 

 discussion elsewhere. Furthermore, the assumption will usually be made that 

 compression of the water surrounding the gas globe can be neglected. 



The relevant mathematical analysis has for the most part already 

 been published (1) (2) (3),** but it will all be Included for convenience in 

 an appendix. 



In this report a distinction is made between the gas globe formed by the bulk of the gaseous products 

 of an underwater explosion, and gas bubblei. The word fphere applies to either or both. 



Numbers in parentheses indicate references on page 23 of this report. 



