Absence of turbulence in a unidimensional model of fluid motion /Burgers model/

The Burgers unidimensional model of fluid motion, consisting of a parabolic quasi-linear partial differential equation, is studied with the aim of finding whether the model equation possesses turbulent features. In particular, the ability of the Burgers model to show a transition from a simple to a complex behavior at a critical Reynolds number is examined. An explicit solution of the Burgers equation is obtained for the case of stationary boundary conditions with no external force by use of the Hopf-Cole transformation; the case involving presence of a force is then treated. The stationary solution proves to be attractive for all viscosity values, whether or not an external force is present.