A Spectral-Grid Method for the Stability Analysis of the Blasius Boundary Layer and the Dynamics of the Velocity Vector

This study investigates the longitudinal and transverse components of linear perturbations in the Blasius boundary layer within the framework of local hydrodynamic stability analysis. The base-flow profile is determined from the Falkner–Skan equation, after which the linearized equations of motion are reduced to the Orr–Sommerfeld spectral problem. For its numerical solution, a spectral-grid method is employed, based on dividing the computational domain into elements and representing the solution on each element by a finite series of Chebyshev polynomials. The resulting generalized eigenvalue problem is reduced to a lower-dimensional system, followed by reconstruction of the eigenvector of the original system and the corresponding eigenfunction. Based on a selected physically relevant mode, the components of the perturbed velocity field are determined. For the test case, the computed eigenvalue is compared with a published reference numerical result; the influence of the distribution of the number of polynomials among the elements of the computational domain is also investigated. The obtained results confirm the applicability of the proposed computational procedure to the analysis of linear perturbations in the Blasius boundary layer.