The secondary flow in a twisted curved pipe is studied by using Gelarkin method together with spectral method

and the secondary approximating solution of the velocity profile in the cross - section is given. Based on this velocity profile

the nonlinear mapping between the cross-sections is studied by numerical integration. It is found that the periodic pair-vortex induced from the secondary flow resulted in a chaotic mapping

which stretch and fold the fluid units in an exponential way

and mix the fluid in the pipe efficiently. The result is displayed by numerical simulation and experimental study.