On temporal stability of the Poiseuille flow in a channel of elliptic cross-section

A numerical model for the temporal stability analysis of the Poiseuille flow in a channel of constant elliptic cross-section is described. In particular, an algorithm for computing the maximum possible amplification of the average kinetic energy density of disturbances with the use of a spectral reduction is described. This reduction allows us to significantly reduce the computational costs as well as to eliminate artefact disturbances appearing because of the approximation errors. The maximum amplification of the average kinetic energy density of disturbances is computed for channels with round and elliptic cross-sections. It is shown that its absolute maximum in the case of the round and elliptic channel cross-sections is attained on disturbances which possess different symmetries.