NSWC/WOL TR 76-155 



DYNAMICAL MODEL 



2.1 THE SWIM BLADDER . Figure 2.1.1 shows a life-size tracing of 

 a Spot (Leiostonms xanthurus Lacepede) which depicts the swim bladder 

 and the surrounding internal organs. Figure 2.1.2 shows a swim bladder 

 removed from a Spot. In our work we depicted the motion of this organ 

 by that calculated for a spherical bubble of air. The size of this 

 "equivalent spherical bubble" was first estimated by equating its 

 volume to that of the fishes' swim bladder — then later we adjusted 

 the size of the equivalent bubble to optimize the correlation between 

 the calculated motion and the observed injuries. 



Figure 2.1.3 shows a life-size tracing of a White Perch 

 ( Mo rone americana Gmelin) , the other species of fish used in the work 

 reported here. The inset shows the shape of the forward portion of 

 the swim bladder in-place in the fish. 



2.2 PRELIMINARY CALCULATIONS OF BLADDER OSCILLATION . We began 

 this study by making order of magnitude calculations which approxi- 

 mated the explosion pressure field with a step increase followed by a 

 step decrease in pressure. The fishes' swim bladder was approximated 

 by a spherical bubble of air in an infinite body of water — and, we 

 calculated its undamped oscillatory response. These order of magnitude 

 calculations showed that the oscillatory response of the swim bladder 

 was a likely source of the fishes' injuries. They also pointed out a 

 strong resonance which occurs when surface cut-off (the arrival of the 

 rarefaction wave reflected from the water surface) happens at the 

 instant of maximum bladder compression. This work was described in an 

 internal Center report which is reproduced as Appendix A of this report. 



2.3 CURRENT METHOD FOR CALCULATING BLADDER OSCILLATION . The method 

 developed for calculation of the oscillatory response to the changing 

 pressure field generated by an underwater explosion is described in 

 detail in Appendix B. Here, we attempt to give the reader a feel for 

 this computation and its approximate nature. Figure 2.3.1 shows the 

 idealized pressure signature measured on an underwater explosion test 

 together with the calculated pressure inside a fish's swim bladder 



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