Low-frequency normal modes using improved phase integral methods

Abstract

Normal mode (NM) theory provides a solution to sound propagation in an inhomogeneous ocean. Use of NM theory is, however, restricted by the ease with which depth eigenfunctions Φn and eigenvalues λn satisfying d2Φn/dz2 + [w2/c2(z) − λn] Φn = 0, plus boundary conditions, may be computed. Employing generalized Langer transformations, uniform asymptotic expansions to Φn, are obtained in terms of parabolic cylinder functions for realistic sound velocity profiles (SVP). The expansions are valid at turning points, require no connection formulae (unlike WKB), and yield complex eigenvalues. The method is asymptotic to A = (2πfh/c0)2 with f denoting frequency, h the SVP scale depth, and c0 the axial sound speed. For deep ocean A ∼ (2f)2, indicating useability to frequencies as low as 3–5 Hz. Results of calculations for Munk's canonical SVP: c(η) = c0 (1 + ε[e−η + η − 1]), η = (z − z0)/h will be described. Extensions to range-dependent environments and inclusion of arbitrary surface and bottom boundary conditions will be discussed. [Supported in part by Naval Ocean Systems Center.]