Hydraulic jumps in arterial flow: A dynamical systems interpretation of post-stenotic dilation

A spatial dynamical system, derived from cross-sectionally averaged Navier–Stokes equations, investigates hemodynamics in severe arterial stenosis. Utilizing a rigorously justified quasi-steady approximation, we analyze the spatial evolution of vessel area under constant flux. Our analysis reveals a stationary hydraulic jump distal to the stenotic throat, marking the transition from supercritical to subcritical flow. This abrupt expansion provides a mechanistic basis for post-stenotic dilation (PSD). By incorporating viscous diffusion, the hydraulic jump is regularized into a continuous internal layer. Identifying the Shapiro number as the primary bifurcation parameter, this framework predicts PSD onset, highlighting nonlinear wave transitions in vascular pathology.