Temporal stability of asymptotic suction boundary layer with spectral collocation method

In this paper, the linear stability theory of an incompressible asymptotic suction boundary layer was studied. A small disturbance was introduced spatially in a streamwise direction to the laminar base flow with various wavenumber $\alpha = 0.01 - 0.3$ to investigate its temporal stability. A spectral collocation method was used to solve the fourth-order ordinary differential equation (ODE) of the generalized eigenvalues problem. From the neutral stability curve, the result showed that the critical Reynolds number occurred at $Re_{c}= 47145$ for $\alpha=0.161$. By taking into account that the disturbance traveled in spanwise direction, the transition can be delayed.