Influence of the Direction of Sources on the Phase Invariants of Vector–Scalar Fields in a Shallow Sea

For the first time, the properties of the phase invariant of sound to vector–scalar fields formed in a waveguide by directional multipole sources are studied. It is shown that, when even such complex sources are used, the phase invariant is valid for sound pressure and for projections of the vibrational velocity vector. It practically does not depend on the directivity and frequency of the source, the distance between the receiver and the source, or on the parameters of the waveguide.