Mathematical model of spiral waves propagating in the aorta

The spiral waves in the viscous incompressible fluid flow within an arterial vessel modeled by a thin elastic isotropic shell are studied. Asymptotic expansions are constructed for two types of spiral waves. The first type is spiral long wall waves generated (owing to the viscous fluid no-slip at the inner shell wall) by the longitudinal and twist harmonic waves that propagate along the wall. For these waves the amplitude distribution over the vessel cross-section has the form of a boundary layer localized near the inner shell surface. The second is short small-amplitude waves that practically fill the entire vessel cross-section. It is shown that for the short waves the transfer mechanismis the steady-state flow, the role of the longitudinal wall waves and the elastic characteristics of the shell being in this case insignificant.