poor agreement for tests carried out with one half pound charges, but somewhat better 

 agreement for the tests with 25 lb. and 50 lb. charges. 



The reason for this disagreement may be either inaccurate experimental data 

 or an unrealistic assumption for the derivation of this formula. 



The asymptotic law was obtained from the Rankine-Hugoniot conditions for 

 the shockfront and the equations of inviscid fluid motion behind the shockfront. This 

 means that outside the discontinuity all dissipative effects are ignored and that the 

 asymptotic equation is based on a wave profile as illustrated in Fig. 3 by the solidly 

 drawn curve. Actually, weak Shockwaves have a profile as sketched in Fig. 3 by the 

 dotted curve: The front shows a steep but steady rise and the peak is rounded off by 

 the effect of viscosity. The question has been raised [7, 8] as to whether the equation 

 shown in Fig. 3 would still hold for such conditions. Arons [7] has attacked this prob- 

 lem by means of an approximate calculation and found a decay stronger than that 

 given by this equation. In this calculation an acoustic treatment is used to account for 

 the viscous effects and afterwards a correction is applied for the cumulative effects of 

 the non-acoustic contributions. Although the results are probably qualitatively correct, 

 it is not clear whether the accuracy of the calculation is sufficient to demonstrate a 

 valid deviation from the asymptotic law.* On the other hand Aron's calculations agree 

 very well with the experimental points shown in Fig. 3. This brings us to the question 

 of the accuracy of the experimental results. To measure such low pressures with 

 electronic equipment, very sensitive and therefore very large gages are necessary. The 

 presence of such a large gage in the water distorts the incident wave so that a true 

 pressure measurement is in principal not possible. 



The data of the graphs in Fig. 3 are corrected for finite gage size assuming 

 that the response-time of the gage is equal to the transit-time of the wave; hence, the 

 hydrodynamic distortion of the pressure field is neglected. It is not known today 

 how large this effect is. Unfinished and unconfirmed studies of Slifko at NOL have 

 resulted in response times which are about twice the transit time. The use of such 

 a large response time would move the experimental points in Fig. 3 — in particular 

 those for the Vi lb. charges-upward. This would improve the agreement with the 

 asymptotic relation. 



Surface Reflection 



When the shockwave emitted from an explosion (Fig. 4), hits the free water 

 surface, the pressure in the water at this interface must be equal to that of the air. 

 It is well known that this leads to the formation of a rarefaction wave, which — if we 

 use the acoustic approximation — is seemingly emitted from the image of the point of 

 the explosion. This yields the dashed pressure-time-curve for the point P. Considering 

 the high pressures of Shockwaves, it appears that the negative phase shown will not 

 occur in actuality. Only highly purified water can sustain a substantial tension without 

 beginning to cavitate. Sea water contains numerous cavitation nuclei and cavitates as 

 soon as the pressure drops below a certain level usually somewhat above the vapor 

 pressure [7]. This results in the solidly drawn pressure curve: — the tail of the wave 

 is cut off. At the pressure scale of such a record no distinction between cavitation 

 pressure and the pressure of the undisturbed medium can be made. 



This cavitation of an elastic liquid is called bulk cavitation. Kennard [9] has 

 given the basic laws of this phenomenon, but very little more has been done. Kennard 

 [10] and Arons [7] have calculated the extent of the cavitated region. It is a surprisingly 

 thin layer which extends far to the side, Fig. 4. Nobody has so far attempted to 



* In a recent publication [23] LIGHTHILL has derived the asymptotic formula, Fig. 3, 

 from the "Burgers" equation which includes dissipation at all points of the wave profile. This 

 theory will go far towards dispersing the above mentioned objections against the asymptotic 

 equation. 



330 



