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MIGRATION OF UNDERWATER GAS GLOBES DUE TO 

 GRAVITY AND NEIGHBORING SURFACES 



ABSTRACT 



Approximate formulas are assembled, and Illustrated by curves, for 

 the migration of gas globes under water due to the action of gravity and of 

 neighboring surfaces. In addition to the effect of a single surface, rigid 

 or free, consideration is given to the combination of a free surface with a 

 rigid bottom or a vertical wall. The general' analytical procedure by which 

 the formulas were obtained is described but most of the details are omitted. 



INTRODUCTION 



The gas globe formed by an underwater explosion not only pulsates 

 in size but also usually changes position as each pulsation occurs (1).* 

 This migration may be of importance because the first recompression or con- 

 traction of the globe thereby comes to be centered at a point different from 

 that of the initial detonation, and the location of the point of recompres- 

 sion influences the damage that may be done by the associated secondary pulse 

 of pressure. Measurements of the migration will be reported separately but a 

 number of analytical results have been obtained, and these results will be 

 assembled here for convenience of reference. Deductions of the formulas may 

 be found elsewhere (2). 



The motion of the water around the pulsating gas globe is suffi- 

 ciently slow so that compression of the water can be neglected. Furthermore, 

 good experimental support exists for the assumption that the globe remains 

 approximately spherical during the larger part of the first cycle at least. 

 For these reasons certain aspects of the migration are adequately covered by 

 old investigations on the motion of spheres, which are summarized in Lamb's 

 Hydrodynamics, Section TOO (3). 



A thorough survey of the problem has been given recently by Herring 

 (4) and numerical studies have been made, especially of the gravitational 

 displacement, by Taylor and others in England (5) (6) (7) (8). Calculations 

 by an approximate method have been made under the author's supervision at 

 the David Taylor Model Basin. More extended calculations are in progress 

 under the direction of Professor R. Courant of New York University; these 

 will be described in a later report. 



Numbers in parentheses indicate references on page 33 of this report. 



