A theoretical study of parietal vortex shedding in Taylor-Culick flow via linear stability analysis

In this theoretical study, we use linear stability analysis to investigate the cause of parietal vortex shedding in Taylor-Culick flow, which is representative of the flow in solid rocket motors. We focus on the effects of the lateral-injection Reynolds number and the length-to-radius ratio of the combustion chamber. Through a comparison with pipe flow, we find that flow turning is a major contributor to parietal vortex shedding. We explore the role of amphidromic points and find that they can divide the flow field into two distinct regions, an outer region with strong perturbations and an inner region with weak perturbations. In the outer region, we find that the velocity perturbations develop advection patterns with axial (streamwise) periodicity, while the pressure perturbations induce flow gradients that enhance shear stresses. Collectively, these effects are thought to combine to induce parietal vortex shedding in solid rocket motors.