Phase Invariants of Vector–Scalar Fields Excited in the Shallow Sea by Multipole Sources

The concept of a phase invariant (PI), introduced in our previous studies, is used to describe the sound-field phase distribution in an underwater waveguide in the distance–frequency plane. This concept is similar to the classical waveguide Chuprov invariant (ChI), which specifies the slopes of constant-field intensity lines in the same plane. The PIs of vector–scalar fields excited by multipole sources are investigated for the first time in this paper. It is shown that, as well as in the case of a monopole source, PI is a stable characteristic of a sound field. It is demonstrated by numerical simulation that the PI value in shallow water barely depends on the source directional pattern, the path length, the frequency of emitted signal, and the waveguide characteristics. Significant deviations of PI from its basic value (–1) are observed only in the vicinity of interference minima (in the phase-dislocation zones).