On the instability of a 3dimensional attachment line boundary layer: Weakly nonlinear theory and a numerical approach
Abstract
The instability of a three dimensional attachment line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time dependent NavierStokes equations for the attachment line flow have been solved using a FourierChebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment line boundary layer is also investigated.
 Publication:

National Aeronautics and Space Administration Report
 Pub Date:
 December 1984
 Bibcode:
 1984nasa.reptV....H
 Keywords:

 Boundary Layer Stability;
 Branching (Mathematics);
 Spectral Methods;
 Three Dimensional Boundary Layer;
 Chebyshev Approximation;
 Finite Difference Theory;
 Fourier Transformation;
 Time Dependence;
 Fluid Mechanics and Heat Transfer