Underwater acoustic communications are limited by low information capacity and data rate[1]. While orbital-angular-momentum (OAM) multiplexing can address these issues[2], conventional OAM beams scale poorly in realistic ocean environments over long distances because their beam diameter increases with topological charge [3,4], amplifying crosstalk and alignment sensitivity over range. We address these challenges by introducing acoustic iso-propagation vortices (IPVs), engineered superpositions of OAM modes whose far-field envelope is effectively independent of the OAM topological charge, thus preserving a fixed spatial profile while retaining an orthogonal set of OAM states for multiplexing. The design leverages recent optical IPV theory in acoustics and is compatible with the existing transducer arrays used in previous studies [4]. We evaluate the wave propagation characteristics and modal-domain demultiplexing performance of multiplexed IPV channels in shallow-water channels using the BELLHOP ray-tracing framework with representative sound-speed profiles and surface roughness to simulate real ocean environments. Our theoretical study shows that, compared with conventional OAM beams, IPVs (i) maintain near-constant beam width across OAM topological charges, (ii) increase robustness by reducing modal coupling under turbulence and multipath propagation, and (iii) improve demultiplexing fidelity without increasing Receiver array aperture size or transmit power. These results indicate that, rather than OAM serving only as a fragile information-encoding capacity booster, acoustic IPVs have the potential to become a scalable physical-layer primitive for long-range, highly reliable underwater communication, and suggest immediate extensions to resilient MIMO-based underwater wireless communications and wide-aperture sonar.