Articles | Volume 18, issue 2
Nonlin. Processes Geophys., 18, 171–178, 2011

Special issue: Complexity and extreme events in geosciences

Nonlin. Processes Geophys., 18, 171–178, 2011

Research article 08 Mar 2011

Research article | 08 Mar 2011

Chaotic behavior in the flow along a wedge modeled by the Blasius equation

B. Basu1, E. Foufoula-Georgiou1, and A. S. Sharma2 B. Basu et al.
  • 1Department of Civil Engineering, University of Minnesota, Minneapolis, MN 55414, USA
  • 2Department of Astronomy, University of Maryland, College Park, MD 20742, USA

Abstract. The Blasius equation describes the properties of steady-state two dimensional boundary layer forming over a semi-infinite plate parallel to a unidirectional flow field. The flow is governed by a modified Blasius equation when the surface is aligned along the flow. In this paper, we demonstrate using numerical solution, that as the wedge angle increases, bifurcation occurs in the nonlinear Blasius equation and the dynamics becomes chaotic leading to non-convergence of the solution once the angle exceeds a critical value of 22°. This critical value is found to be in agreement with experimental results showing the development of shock waves in the medium and also with analytical results showing multiple solutions for wedge angles exceeding a critical value. Finally, we provide a derivation of the equation governing the boundary layer flow for wedge angles exceeding the critical angle at the onset of chaos.