Approximate solutions for an acoustic plane wave propagation in a layer with high sound speed gradient
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The present authors previously obtained an exact solution for propagation of the incident acoustic plane wave in a wind-induced bubbly surface layer where sound speed gradient is high. Based on the solution, the dependence of the grazing angle of the energy flux vector of the incident wave at the surface on the grazing angle of the incident wave at the bottom of the layer was obtained and utilised for calculations of the surface reflection loss. However, the solution in its original formulation is represented via an infinite slowly converging series which makes the use of the solution in practical calculations difficult. In this paper, this solution is simplified with the assumption that the grazing angle at the bottom of the layer as well as some other parameters depending on the frequency and wind speed are small. The convergence of the infinite series is improved using a special technique. Approximate solutions are obtained for the cases where the small parameters can be neglected and where the terms up to the third order with respect to the small parameters are taken into account. Zones of validity are derived for the approximate solutions as well as for the Snell's law of ray acoustics. The results of this paper allow the prediction of the grazing angle at the surface within the zones of validity of the approximate solutions using simple calculations with only the wind speed, the frequency and the equilibrium sound speed as the input parameters. Copyright © (2013) by the Australian Acoustical Society.
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