By W. Lauterborn (auth.), Professor Dr. Werner Lauterborn (eds.)
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Extra info for Cavitation and Inhomogeneities in Underwater Acoustics: Proceedings of the First International Conference, Göttingen, Fed. Rep. of Germany, July 9–11, 1979
In this case the following equations to be solved apply to an interface (s =-1) as well as to a solid \~a 11 (s = 1). 0+~0)Rl+~oicos8+l-/a: ao e 1 lim -q,1 = 82 lim 2 ¢1 - sa -a -'r ces8 r ... O Y"700 4 (20) (21) ¢I can be expanded in a series of spherical harmonics. This allows for the expansion of R in a series of LEGENDRE polynomials. Eqs. (19) to (21) then show that: (with the initial conditions Rl=~I=O) ¢I = h(t) CosA _ ;;:2 S a2a 4 r cos8 (22) Substituting in (18), (20) (23) 28 li~e obta in: 9a2~2 + 3a3~ afl + 3afl = ~a - ~a - s - - - - 4 (24) (25) The third equation, necessary to determine the three unknol'Jns f,h and ~~ is obtained by writing that the net pressure thrust on a sphere of radius aB vanishes when B+ O.
4 two shock waves are radiated upon collapse of the aspherical bubble and a grossly distored shape develops after collapse. As frame two shows no sign of a shock wave it must have been taken just before collapse. Of strong interest in cavitation physics is the collapse of cavitation bubbles in the neighborhood of solid boundaries. A knowledge of how bubbles behave near solid boundaries is the key to an understanding of how erosion and destruction of mechanical parts in cavitating liquids come about.
T1igration and shape deformation then intervene simultaneously at order S2. Even if numerical solutions have not already been obtained for this order, we notice that the bubble flattens on one of its sides depending upon the nature of the boundary (solid or free surface). In either case the bubble is attracted or repelled. At order S3 singular points appear on its axis of symmetry. Herring, Columbia Univ. NDRC rep. C-4-sr 20-010 (1941). Cole, Underwater Explosions, Dover Publications (1948). Holt, Ann.