Resonant spectral cascade in Womersley flow triggered by arterial geometry

Abstract

Age-related arterial remodeling is dominated by progressive loss of elastic-fiber function and concomitant stiffening, and in many vascular beds it is also accompanied by measurable geometric remodeling (e.g., elongation and tortuosity). These changes are clinically relevant because they modify pulsatile phase relationships, near-wall shear, and axial transport, yet the precise physical mechanisms by which geometry modulates spectral energy redistribution remain insufficiently resolved. While complex geometry is known to increase viscous resistance, its active role in modulating flow dynamics is not fully understood. Here we solve a mathematical model to show that arterial geometry can trigger a resonant transfer of energy to short-wavelength components of the flow. The investigation, conducted over a physiological range of Womersley numbers (Wo, a dimensionless measure of pulsation frequency), reveal a dual dynamic. The global wave energy consistently decays, confirmed by a negative growth rate (G < 0), indicating that the flow does not become exponentially unstable. However, a spectral broadening ratio (R), which quantifies the energy in high-wavenumber versus low-wavenumber modes, exhibits a sharp, non-monotonic peak at an intermediate Wo. This result identifies a resonant frequency at which geometry is maximally efficient at generating spectral complexity, even as the overall flow attenuates. These findings reframe the role of arterial geometry from a passive dissipator to an active modulator of the flow's spectral content, suggesting that spectral diagnostics could provide a sensitive marker for vascular health.