Low-frequency sound transmission through rough bubbly air–water interface at the sea surface

Abstract

Transmission of a sound generated by a localized point source in the air through a realistic sea surface is studied by the use of the Kirchhoff-Helmholtz integral. An earlier approach had been based on the Kirchhoff-Helmholtz integral which only considered the effects of rough surface. In the current study, not only the effect of the rough surface is taken into account but also the effects of subsurface bubbles are included in modeling the real phenomenon more accurately. In order to include the effects of subsurface bubble population, the classic relations of the Kirchhoff-Helmholtz integral are reformulated. Accordingly, a three-phase region of air, water, and bubbly water at the sea surface is analyzed, and the rough interface of bubbly water–air is discretized. Through considering an element area Ai, the transmission coefficient [Formula: see text], incident angle [Formula: see text], transmitted angle [Formula: see text], and local surface acoustical roughness Ri are investigated for each individual element. Also, the effects of subsurface bubbles, transmission change as a function of frequency f, wind speed W, incident angle [Formula: see text], source/receiver position ratio (D/H), surface acoustical roughness, and subsurface bubble population are examined. Results of the modified Kirchhoff-Helmholtz integral method display good agreement against available experimental data.