Unsteady flows in pipes with finite curvature

Motivated by the study of blood flow in a curved artery, we consider fluid flow through a curved pipe of uniform curvature, δ, driven by a prescribed oscillatory axial pressure gradient. The curved pipe has finite (as opposed to asymptotically small) curvature, and we determine the effects of both the centrifugal and Coriolis forces on the flow. In addition to δ, the flow is parameterized by the Dean number, D, the Womersley number, α, and a secondary streaming Reynolds number, Rs. Asymptotic solutions are developed for the case when δ " 1, α " 1 and the magnitude of the axial pressure gradient is small, using regular perturbation techniques. For intermediate values of the governing parameters, a pseudospectral code is used to obtain numerical solutions. For flows driven by a sinusoidal pressure gradient (D =0), we identify three distinct classes of stable solutions: 2pi-periodic symmetric, 2pi-periodic asymmetric, and asymmetric solutions that are either quasi-periodic, or periodic with period 2pik for k ∈!. The transition between solutions is dependent on the value of δ; thus pipes with finite curvature may exhibit qualitatively different transitions between the solution classes as the governing parameters are varied from those of curved pipe