Two-dimensional focusing of evanescent sonic boom noise penetrating an air-water interface

In the late 1960s and early 1970s research on supersonic aircraft determined that sonic boom noise would penetrate the surface of the ocean. It was assumed that the surface of the air-water interface was perfectly flat. Today, sonic boom noise is once again a topic of interest. The present paper concentrates on two-dimensional focusing and defocusing, caused by the curvature of the ocean surface, of the penetrating sonic boom waveform. A finite difference algorithm is used to calculate the pressure levels underwater due to a rounded sonic boom waveform interacting with the water interface. Numerical results are consistent with the predictions of known theories involving 1.) the existence of pressure disturbances underwater and 2.) their penetration depth being a function of the aircraft’s speed. These calculations also indicate that 1.) curvature of the ocean surface focuses and defocuses the waveform with increasing effect as the ocean wave height increases and 2.) the percent change (from a flat ocean interface to a curved ocean interface) in pressure values due to the curvature increases with increasing Mach number.