  Laminar as well as turbulent oscillatory pipe flows occur in many fields of
biomedical science and engineering. Pulmonary air flow and vascular blood flow
are usually laminar, because shear forces acting on the physiological system
ought to be small. However, frictional losses and shear stresses vary
considerably with transition to turbulence. This plays an important role in
cases of e.g. artificial respiration or stenosis. On the other hand, in piston
engines and reciprocating thermal/chemical process devices, turbulent or
transitional oscillatory flows affect mixing properties, and also mass and heat
transfer. In contrast to the extensively investigated statistically steady wall
bounded shear flows, rather little work has been devoted to the onset,
amplification and decay of turbulence in pipe flows driven by an unsteady
external force. Experiments [1, 3, 6] indicate that transition to turbulence
depends on only one parameter, i.e. Re_{\delta} \sim Re/Wo with a critical
value of about 550, at least for Womersley numbers Wo > 7. We perform direct
numerical simulations (DNS) of oscillatory pipe flows at several combinations
of Re and Wo to extend the validity of this critical value to higher Wo. To
better understand the physical mechanisms involved during decay and
amplification of the turbulent flow, we further analyse the turbulent kinetic
energy distribution and its budgets terms.
