Absence of turbulence in a unidimensional model of fluid motion /Burgers model/
Abstract
The Burgers unidimensional model of fluid motion, consisting of a parabolic quasilinear 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 HopfCole 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.
 Publication:

Meccanica
 Pub Date:
 March 1977
 Bibcode:
 1977Mecc...12...15B
 Keywords:

 Burger Equation;
 Flow Theory;
 Fluid Flow;
 Mathematical Models;
 Turbulent Flow;
 Boundary Conditions;
 Boundary Value Problems;
 Linear Equations;
 NavierStokes Equation;
 Parabolic Differential Equations;
 Partial Differential Equations;
 Reynolds Number;
 Viscous Flow;
 Fluid Mechanics and Heat Transfer