Horizontal tunneling of sound in three-dimensional idealized curved nonlinear internal wave ducts

Nonlinear internal waves (NIWs) in the ocean can produce substantial effects on acoustic propagation, including three-dimensional reflection, refraction, and diffraction in the sound ducts bounded and formed by individual NIWs. Feature models for analyzing such effects frequently use a well approximation, which neglects the finite width of NIWs. This paper examines consequences of more realistic conditions including finite wave width and curvature. This curved duct model produces acoustic horizontal modes in the radial direction with a distinct characteristic of enhanced horizontal tunneling through the curved NIW that forms the sound duct. Also, because of the proximity of their modal wavenumbers to those of classical horizontal trapped modes, these enhanced tunneling modes are named companion modes. Conditions for the occurrence of these modes can be derived as physically interpretable bounds on acoustic modal wavenumber values. Furthermore, companion modes decay in sufficiently long distances, representing proper mode contributions to the acoustic total field. Theoretical and numerical analyses presented in this paper further suggest that the phenomena of enhanced tunneling is a result of joint wave tunneling and whispering gallery effects.