Limitations on adiabatic normal modes in range-varying environments

Abstract

Curvilinear coordinates are used to extend adiabatic normal modes to weak range-dependent environments including those with sloping bottoms. Reciprocal vertical wave numbers of a reference mode provide the coordinate scale factors. This approach is valid for negligible horizontal derivatives of intermodal vertical-wave number ratios. Large gradients in the bottom impedance make these ratios large, implying significant mode coupling in oceanic regions spanning both soft and hard terrains. Additionally, a large number of eigenvalues are needed to compute adiabatic normal-mode solutions for high-resolution acoustic fields. The direct solution of eigenvalue problems on a fine grid is often prohibitive. Alternatively, the eigenvalues may be interpolated to the fine grid. This approach usually requires extrapolation toward edges across which the horizontal wave number becomes imaginary at mode cutoff. One choice for an interpolation function is the integrated reciprocal vertical wave number. This function, proportional to water depth, is smooth and real throughout the cutoff region, while causing the horizontal wave number to vanish along the cutoff line. [Work supported by the Office of Naval Research and partially by DOD High Performance Computing facilities at NRL.]