On absolute linear instability analysis of plane Poiseuille flow by a semi-analytical treatment

Abstract

The absolute linear hydrodynamic instability of the plane Poiseuille flow is investigated by solving the Orr–Sommerfeld equation using the semi-analytical treatment of the Adomian decomposition method (ADM). In order to use the ADM, a new zero-order ADM approximation is defined. The results for the spectrum of eigenvalues are obtained using various orders of the ADM approximations and discussed. A comparative study of the results for the first, second and third eigenvalues with the ones from a previously published work is also presented. A monotonic trend of approach of decreasing relative error with the increase of the orders of ADM approximation is indicated. The results for the first, second and third eigenvalues show that they are in good agreement within 1.5 % error with the ones obtained by a previously published work using the Chebyshev spectral method. The results also show that the first eigenvalue is positioned in the unstable zone of the spectrum, while the second and third eigenvalues are located in the stable zone.