Helical instability in pulsatile and oscillatory pipe flows *

Pulsatile pipe flows in the presence of geometric distortions (e.g. bent, constriction) have recently been show to exhibit a nonlinear instability consisting of helical vortices [1]. The instability appears during the deceleration phase, breaks down into turbulence, and eventually returns to the laminar state when the flow accelerates. We track the instability in Reynolds number-Womersley number parameter space, and towards purely oscillatory flows, i.e. flows without mean component. We find that intermediate values of pulsation amplitude 1~<A~<1000 have a stabilizing effect, i.e. the instability threshold Re_δ increases with increasing A. Else Re_δ remains nearly constant.  Here, Re_δ is the Reynolds number based on Stokes layer thickness and A=U_o/U_m; U_o and U_m are oscillatory and mean components of the flow speed, respectively. Increasing Womersley number (i.e. pulsation frequency) on the other hand the instability threshold moves to lower Re_δ. Moreover, we find that streamwise location of the instability in the pipe shifts towards the distortion site (bent section in our case) with increasing Womersley number.  

                       

 

[1] Xu, D., Varshney, A., Ma, X., Song, B., Riedl, M., Avila, M., and Hof, B., Nonlinear hydrodynamic instability and turbulence in pulsatile flow, Proc. Natl. Acad. Sci. U.S.A 117, 11233 (2020).