Existence of non zero modes in a cylindrical -straight lined duct

Abstract

In an infinitely long cylindrical straight lined duct, carrying a
non-slipping, inviscid, non heat conducting isentropic and
axis-symmetric gas flow, the evolution of mode type initial value perturbation is investigated. Necessary conditions are given for the existence of non zero modes which satisfy the liner-perturbation interaction condition on the duct wall. These conditions are expressed in terms of circumferential wave number $m$ and the pressure regularity on the duct axis. For instance, it is shown that the value of the pressure at the duct axis can be different from zero only when the circumferential wave number $m$ is equal to zero. Numerical investigations are performed for constant gas flow at the central part of the duct and liner-perturbation interaction of mass-spring-damper type. For the considered numerical values and mean flow velocity profile computation reveals the existence of non zero modes for which only the pressure is finite at the duct axis. Some of these modes are attenuated and some of them are
amplified during the evolution.