Resonances in Pulsatile Channel Flow with an Elastic Wall

Interactions between fluids and elastic solids are ubiquitous in applications ranging from aeronautical and civil engineering to physiological flows. Here we study the pulsatile flow through a two-dimensional Starling resistor as a simple model for unsteady flow in elastic vessels. We numerically solve the equations governing the flow and the large-displacement elasticity and show that the system responds as a forced harmonic oscillator with nonconventional damping. We derive an analytical prediction for the amplitude of the oscillatory wall deformation, and thus the conditions under which resonances occur or vanish.