B. Edward McDonald
Naval Res. Lab., Washington, DC 20375
Similarity solutions developed from the equations of nonlinear acoustics [P. H. Rogers, J. Acoust. Soc. Am. 62, 1412--1419 (1977); B. E. McDonald and J. Ambrosiano, J. Acoust. Soc. Am. 84, 1497--1503 (1988)] have adequately accounted for the range dependence of overpressures in the propagation of underwater spherical shocks, while giving only fair to poor predictions for relaxation time constants at large ranges from the source. The relaxation time discrepancy seems to suggest an anomalously large nonlinearity coefficient at great distances from the source. The effect of minute quantities of entrained air on the shock similarity solution for water is investigated. It is well known that microbubbles can greatly increase the nonlinearity coefficient of water at ambient conditions. At high pressures, however, bubbles may collapse to the point of being dynamically unimportant. The equation of state for water is modified to account for ambient microbubble populations, and the resulting equations solved for self-similar shock profiles. Using air void fraction as a fit parameter, observed relaxation time data are analyzed to yield the levels of entrained air that may have been present in various underwater explosive experiments.