Abstract
To know the nonlinear characteristics of pipe flow, we simulate the flow as a superposition of many vortex rings. As a first step, we investigated the nonlinear interaction among vortex rings whose number is three at most. The pipe wall is replaced by many bound vortices. A free vortex ring moves forward or backward according to the radius, and that of a particular radius keeps its initial position. Two vortices of equal radii always show an overtaking process repeatedly, i.e., the backward ring increases the velocity due to the forward ring while the forward one is decreased by the induced velocity due to the vortex behind it. In the case of three vortices, there appears a wide variety of behavior. For certain combinations of the radii and the axial spaces among them, the motion seems to be very complex. It is expected that our result will give a clear sight for seeking the nonlinear behavior of many vortices.
