A combined asymptotic and characteristic-based computational framework is developed to investigate unsteady compressible flow response in solid rocket motor (SRM) chambers subjected to exit-plane disturbances and steady sidewall mass injection. The formulation integrates a low-Mach-number asymptotic reduction of the governing equations with a time-accurate numerical solution of the parabolized Navier–Stokes equations, employing characteristic-based boundary conditions to ensure physically consistent wave reflection and transmission at chamber boundaries. Controlled exit-plane pressure forcing is imposed under non-resonant and near-resonant conditions to examine acoustic–vorticity coupling mechanisms within slender SRM geometries. The computational framework is verified and validated against analytical solutions and available experimental measurements for canonical duct configurations, demonstrating accurate pressure wave prediction and stable long-time integration over multiple acoustic cycles. The validated model is subsequently applied to configurations with sidewall mass injection, where interaction between injected flow and acoustic oscillations generates rotational structures that progressively penetrate the chamber cross-section. Parametric investigations reveal strong Reynolds-number dependence of vorticity amplitude, wave penetration depth, and transient flow reversal behavior. Increasing Reynolds number reduces viscous attenuation and promotes sustained wave–vorticity interaction, while weakly nonlinear modulation introduces higher harmonic content in the acoustic response. Despite complex velocity and vorticity structures, transverse pressure gradients remain negligible for slender chamber configurations, consistent with asymptotic predictions.