A Theoretical Method for the Prediction of Underwater Explosion Pulses at Caustics
Abstract
Our concern [Refs. 1 and 2] is with the effect of refraction on the long range propagation of underwater explosion shock waves.Here, as with acoustic sources, ray tracing can be used to predict refraction effects. From the divergence or convergence of rays, an amplification factor can be calculated. This is defined as the square root of the ratio of the cross sectional area between rays at a given point assuming spherical spreading to the cross sectional area between rays at the same point when the actual sound velocity profile is specified. We can then multiply the pressure history expected at a given point if no refraction occurred by the appropriate amplification factor. This then gives us the pressure history expected at that point when refraction is accounted for. However, the amplification factor is inversely proportional to the square root of the cross sectional area between adjacent rays. So as we approach a caustic, where these rays cross, the amplification factor reaches infinity, and ray theory is invalid. Furthermore, in the shadow zone adjacent to the caustic, ray theory predicts zero energy penetration. This is due to the high frequency nature of the ray theory approximation. So if we are interested in the pressure near a caustic or in an adjacent shadow zone a method other than ray theory must be used. In this paper, I will describe such a method for calculating shockwave pressure histories in and near caustic regions.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1972
- Accession Number
- AD1114346
Entities
People
- I. M. Blatstein
Organizations
- Naval Ordnance Laboratory