Sonic-boom noise penetration under a wavy ocean: theory

Abstract

Sonic-boom noise penetrating under a deep ocean is affected by its time-dependent interaction with the surface waves, which can significantly influence the perceived sound pressure level and tonal content of the disturbances at depth far greater than expected from the flat-ocean (Sawyers) model. The present theory assumes a small surface slope and a high water-to-air density ratio; the ocean surface in the analysis is modelled by a sinusoidal surface-wave train. The analysis shows that a distinct acoustic wave mode in the form of a packet of wavelets emerges in the sound field far below the surface and attenuates with increasing distance in a manner similar to the cylindrical spreading of monochromatic waves. The latter feature renders the surface waviness influence an effect of first-order importance, overwhelming the primary noise field at large depth. Detailed properties of the deep-water wave fields are examined and illustrated for the case of an incident N-wave, for which an explicit, analytic solution is obtained. The result reveals a similarity structure of the wave field with two distinct time scales and the invariance characteristics of the cylindrically spreading waves, in accord with the group-velocity concept of dispersive waves. An example is given of the interaction, illustrating the underwater waveform, sound-pressure and frequency levels.

Sonic-boom generated sound field under a wavy air–water interface: Analyses for incident N waves

“…The velocity U is assumed to be constant and much greater in magnitude than the surface-wave speed c. Following Ref. 8, all length and time scales are to be made dimensionless with the signature length LЈ and LЈ / U, respectively. As shown in Fig.…”

“…8, this paper addresses problems in which the underwater wave fields remain subsonic, corresponding to a requirement on the Mach number above the water M A ϵ U / a A Ͻ 4.53 under standard conditions. Another requirement is that the aspect ratio of the sonic-boom impact zone be very high, corresponding to LЈ being very small compared to the lateral extent of the impact zone ͑cf.…”

“…6,7 The more recent work of Ref. 8 revealed, however, that the interaction of surface waves with a sonic boom, even though a secondary effect near the water surface, can produce signals at depths that are distinctly different from, and more intense than, those given by the flatocean model. This paper will present a study of the wavysurface influence based on the theory established in Refs.…”

“…To be presented are computational results in parameter domains of relevance to studies of the audibility issue; also explained are the analysis procedures and interpretations not adequately documented in published works. The investigation will focus on examples with incident N waves, for which analytical solution details are available 8,9 to aid assessing computation accuracy and understanding. A concurrent laboratory study has been carried out by Fincham and Maxworthy; 10 several major features that support the theoretical predictions were identified therein.…”

Numerical investigation of transmission of low frequency sound through a smooth air-water interface

“…Viewed from the air, the same surface would be called acoustically "hard" (Medwin and Clay, 1998). There have been many theoretical (Kazandjian and Leviandier, 1994;Brokesova, 2001;Carey et al, 2006;Ravazzoli, 2001;Buckingham, 2001;Komissarova, 2001;Desharnais and Chapman, 2002;Sparrow, 2002;Buckingham et al, 2002;Cheng and Lee, 2004;Buckingham and Garcés, 2001) and experimental (Lubard and Hurdle, 1976;Gordienko et al, 1993;Ferguson, 1993;Richardson et al, 1995;Sohn et al, 2000) approaches for studying sound transmission through water-air interface which focus on the acoustic field in water due to the existence of powerful airborne noise sources. These noise sources include helicopters (Gordienko et al, 1993;Richardson et al, 1995), propeller-driven aircraft (Buckingham and Garcés, 2001;Buckingham, 2001;Buckingham et al, 2002;Cheng and Lee, 2004) and supersonic transport (Buckingham et al, 2002;Sparrow, 2002).…”