| Summary: | In modelling the reflection of sound from an ocean surface, it is necessary to include the refractive effects of near-surface bubbles generated by wind action for certain frequencies. The vertical sound speed gradient in the near-surface region is, however, so extreme that ray acoustics cannot be applied, and thus a wave approach is necessary. This paper describes the nature, and application, of a suitable wave-based description of the refraction of the intensity vector in this region of very high sound speed gradient. It is shown that the sound speed profile in the high-gradient layer can be well approximated by the sound speed profile in the "transitional" layer described by Brekhovskikh (Waves in Layered Media, Academic Press 1960). This exact solution of the wave equation is used to calculate the depth dependence of the acoustic pressure amplitude of the incident plane wave. The fluid particle velocity vector at the surface is also calculated and, together with the pressure amplitude, is used to obtain the intensity vector. Results show that, close to the resonance frequencies, the grazing angle at the surface is significantly larger than that predicted by the laws of geometrical acoustics. It is also shown that these resonance-like phenomena are characteristic not only of sound speed gradients typical of near-surface bubbles, but also of the less-severe gradient typical of conventional isothermal conditions.
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