Abstract: An asymmetric nozzle is a type of convergent-divergent nozzle in which the divergent section is terminated by a scarfed cut, endowing it with the capability of generating lateral thrust for propulsion or attitude control. To investigate the flow characteristics of such a nozzle under different navigation speeds in an underwater crossflow environment, three-dimensional unsteady numerical simulations were conducted over a range of crossflow velocities corresponding to Froude numbers Fr = 17.11-42.78. The evolution of the gas-liquid two-phase structures, the time-averaged flow features, and the jet behavior under fully developed conditions were systematically analyzed. Particular emphasis was placed on the spatial distribution of the pressure field, the dynamic evolution of the compressible wave structures, and the influence of crossflow velocity on the time-frequency characteristics of both transient pressure fluctuations and wall pressure loading. Furthermore, the distribution of wave patterns within the jet and its dependence on crossflow velocity were elucidated based on density gradient analysis. The results demonstrate that by modifying the local pressure differential across the gas-liquid interface and the interfacial shear stress exerted by the crossflow, the crossflow velocity induces a transition in the dominant factor governing the flow field. At low crossflow velocities, the jet momentum dominates over the crossflow inertial force, enabling the supersonic jet to penetrate deeply into the liquid crossflow and generate a broad, large-scale plume, accompanied by pronounced interfacial instability and intense mixing. As the crossflow velocity increases, the liquid inertial force becomes dominant; the resulting pressure gradient compresses the jet, transforming its morphology into a thin, wall-attached gaseous channel, while the onset of interfacial instability is substantially postponed. Concurrently, the elevated crossflow velocity increases the back pressure at the nozzle exit, driving a transition from an under-expanded to an over-expanded flow condition. The shear exerted by the supersonic gas jet on the interface leads to continuous gas-liquid entrainment and unsteady oscillations of the internal wave system. These findings reveal the direct modulation of the crossflow on the internal wave structure and operating mode of the asymmetric nozzle, offering new insights into the flow physics of a scarfed nozzle subjected to a liquid crossflow.