Minimum description of the onset of pipe turbulence

To demonstrate essentials of the mechanism for the onset of turbulence in a pipe at Re=2000, 48 degrees of freedom are enough. The derivation from the Navier-Stokes equation uses a novel type of modes which guarantee linear stability. For the reduction of the nonlinear interactions, the modes are grouped in 3 blocks. Facilitated by these simplifications the interdependence between linear and nonlinear processes is analysed, however, just for a special example. A phenomenon resembling backflow is identified. Received 20 October 1997