| Popis: |
A method for eliminating the branch cuts and branch line integrals from the normal mode solution to the range‐invariant acoustoelastic wave equation has been developed and implemented. In the usual normal mode formulation, evaluation of the vertical wave number in the ocean waveguide’s lower half‐space involves a square‐root operation and gives rise to a branch point at the critical angle. When the Pekeris cut is chosen, energy steeper than the critical angle is represented by leaky modes, and lateral‐wave energy near the critical angle is represented by the branch line integral. When a mode lies near the branch cut, the branch line integral can be significant at all ranges. Branch line integrals are cumbersome to compute, and, for range‐dependent problems, cannot be included in adiabatic and coupled‐mode algorithms. By inserting a (small) positive attenuation gradient in the lower half‐space, the plane wave solution is replaced by a complex‐valued Airy function solution, the branch point is eliminated, the Pekeris branch cut is replaced by a series of modes, and the leaky modes become bounded at infinite depth. Implementation and applications of this approach using the normal mode model ORCA are given. [Work supported by ONR 321OA.] |
