The spatial structure of an acoustic wave propagating through a layer with high sound speed gradient

A plane acoustic wave propagating through a high sound speed gradient layer in a liquid near a pressure-release surface is considered in detail. Analogously to the solution for the refraction of the incident plane wave obtained previously, equations describing the refraction of the reflected wave are derived. For the total acoustic field in the layer, dependencies of the pressure and the vertical particle velocity on the depth and frequency are calculated for several incident grazing angle values. It is shown that these dependencies have distinct features close to the acoustic duct cut-on frequencies. Near these cut-on frequencies, both pressure and vertical velocity have strong maxima along the frequency axis, whereas along the vertical spatial axis the two variables have alternate minima and maxima, the number of which increases with frequency. It is suggested that the maxima in the vertical velocity near the surface at the cut-on frequencies are responsible for the sharp maxima in the grazing angle at the surface in the incident wave. The latter maxima were demonstrated previously. The presence of the pressure maxima and minima within the layer is confirmed by calculations using the RAMSurf parabolic equation simulation code.