Investigation of the transient growth in plane jet by non-modal stability analysis

Abstract

Linear stability analysis is used to characterize the dynamics of a plane jet by incorporating non-modal stability analysis besides classical global temporal stability analysis. It is explained that similar shapes of different global modes are the result of non-normal characteristics of linearized Navier Stokes equations. Optimal initial disturbances and their eigenfunctions together with transient energy growth are obtained for different time horizons and Reynolds numbers of the jet in the linear unstable configuration. These structures are localized at the upstream of the jet nozzle at the boundary layer. The transient growth of the inlet perturbation in limited time bounds is found in the presence of unstable eigenmodes in the flow. The evolution of optimal initial disturbances yields robust energy growth of more than two orders of magnitude. It is found that by increasing Reynolds number in linear unstable flow framework, the non-modal transient growth can marginally surpass the exponential growth in short times.