behaviors were due to differences between the properties of 

 sea water and the water in the model basins, just the opposite 

 effects might have been expected since, even for similar 

 pressure distributions, sea water with its high air content 

 would cavitate sooner than the model. Thus, it appears that 

 rudder breakdown is associated primarily with separation 

 (which on such thin lifting surfaces is delayed as the Reynolds 

 number is increased) rather than with cavitation itself. 



The writer is very grateful to Dr. Plesset for his very 

 kind remarks regarding the review reports^ particularly in 

 view of Dro Plesset 's many personal contributions to the 

 subject and the stimulus he has provided for research in 

 this field among his students and colleagues at the California 

 Institute of Technology., 



The preliminary copy of the report available to Dr. Plesset 

 did not contain the observations on hysteresis included in the 

 final copy, and further comments on this phenomenon need not 

 be included here. The question of stability of collapsing 

 bubbles is particularly important in connection with the 

 pressures that will be developed during this phase of the 

 motion, a distorted bubble evidently producing lower pres- 

 sures than a spherical bubble. 



At least two mechanisms, in addition to the wall effects 

 mentioned previously, can be distinguished as leading to 

 deformations of an initially spherical bubble o One is 

 "Taylor instability", ioe,, the instability of an interface 

 between light and heavy fluids accelerated one toward the 

 other*, and the other is the deformation produced by the 

 pressure gradients in the field in which the bubble is 

 moving. The question of stability in the above sense has 

 been investigated by Binnle** for spherical surfaces as an 

 extension of Taylor's plane caseo He concludes that if 

 surface tension is neglected, the interface is stable if the 

 acceleration is directed toward the lighter fluid and unstable 

 if the acceleration is directed toward the denser fluid. For 

 the Rayleigh empty cavity, this implies that the motion is 

 always stable. However, in an actual case in which the gas 

 phase is compressed to high pressures, both the collapse in the 

 very last stages and the early stages of the subsequent growth 

 would be unstable. Binnle also found that surface tension has 

 a strong stabilizing effects 



♦Taylor, Sir Geoffrey, "The Instability of Liquid Surfaces 

 when Accelerated in a Direction Perpendicular to their Planes", 

 Proc, Roy. Soc. Lond., Ser. A, Vol. 201, 23 May 1950, 

 pp. 192-196. 



**Binnle, A. M. , "The Stability of the Surface of a Cavitation 

 Bubble" , Pro( ' . ^ . - .- 



pp. 151"l55o 



Bubble", Proc.'Cambo Phil. Soc, Vol, ^9? pto 1, Jan 1953 ■ 



12 



