Acoustic flux formulas for range-dependent ocean ducts.

A concise energy-flux formulation is used to investigate the range- averaged acoustic propagation in ocean ducts. Examples treated have isovelocity, linear, and parabolic sound speed profiles. The results are expressed as the product of a scale factor and, for the latter two examples, a depth factor. The scale factor has a similar form in each case, and remains simple and easy to use even when the profile is asymmetrical and the parameters vary with range. The appropriate solution for transmission from an isovelocity duct to a duct of arbitrary profile is also given. Surprisingly, the depth factor generally has a nominal infinity when receiver depth equals source depth in an unchanging but stratified duct, or when velocity at the receiver equals that at the source, or for scaled depths in a range-dependent duct. These infinites are discussed from the flux, ray, and mode viewpoints and a ray-tracing demonstration is provided. For the special case of axial source and receiver, the character of the infinite is different, and an important point is that it occurs only for velocity minima sharper than that of the parabolic profile. The latter profile has in several respects a critical nature. [ABSTRACT FROM AUTHOR]