Stokes eigenfunctions and Galerkin projection of the disturbance equations in plane Poiseuille flow: a systematic analytical approach

In the present paper, the L2-normalized Stokes eigenfunctions for plane Poiseuille flow, which form an orthonormal functional basis for the space of disturbances, are written in a general exponential form. Then, the evolution equations for the disturbances areGalerkin-projected on the considered basis functions, and all the terms of the resulting dynamical system are expressed systematically in analytical form. Finally, a numerical example is given in which the proposed basis functions are used for the simulation of the time evolution of the critical disturbance predicted by the energetic stability theory.