The form of the normal mode that ensures escape with certainty from a surface channel

Abstract

Surface channels trap those rays that are reflected internally before reaching a deep sound channel according to classical geometric ray tracing. In the wave representation, some leakage of trapped normal modes does occur. Recent advances in wave propagation [E. R. Floyd, Anal. Fond. L. Broglie 20, 263–279 (1995)] have shown that a wave function having subbarrier energy but with a particular compound modulation in amplitude and wave number does tunnel through a barrier with certainty and without reflection. Herein, a normal mode with a particular compound modulation is shown to escape from a surface channel with certainty and without reflection. These normal modes with compound modulations, which may be unfamiliar to many workers, are solutions to the wave equation. The investigation considers a bottomless sound velocity profile, C(z), whose reciprocal square, C−2(z), forms a surface channel over the deep sound channel by two piecewise-continuous linear segments. The findings are generalized to include various surface and deep sound channels. While the quantum tunneling problem was originally solved in a trajectory representation [analogous to rigorous ray tracing, cf. E. R. Floyd, J. Acoust. Soc. Am. 80, 877–887 (1986)], herein a wave representation is used.