The intermittent vibration observed by Reynolds in a cylindrical tube

In a cylindrical tube filled with incompressible fluid, the variable parameter method is applied to solve the vorticity motion equation, and the obtained results are substituted into the Poisson equation satisfied by the energy density. The static distribution of energy density in the tube and the energy density of the flowing fluid after a certain spatial sampling interval are obtained. Further numerical calculations are conducted on the energy density of the flowing fluid, the results show that the intermittent vibration observed by Reynolds 140 years ago can only be obtained with the appropriate spatial sampling interval. The energy density in the tube is proportional to to , where N is an integer It tends to infinity with increasing N.