Onset of chaos in some hydrodynamic model systems of equations

Model computational results are reported on the transition to turbulence in the Taylor-Couette flow between two concentric cylinders and the Rayleigh-Benard convection between two horizontal parallel plates. An attempt is made to elucidate mechanisms operative during the transition process, using several model systems of truncated ordinary differential equations for the flow mode variables. A small model system is used for each case, consisting of no more than several dozen mode variables, to describe some characteristic aspects of the fluid motion near the onset of turbulence under the condition that the overall spatial structure of the flow is coarsely determined by the Galerkin basis functions.