Abstract
Stability of an unsteady channel flow is investigated by incorporating the effect of the base flow change with time and comparing with the optimal growth of the normal mode analysis. The existing literature shows that the modal analysis can be done on the velocity profiles in a quasi-steady manner to study the stability characteristics of unsteady internal flows. But, in the current study, it is shown that the mode obtained from the optimal growth analysis provides higher growth and estimates the structures observed in experiments. Initially, the optimal mode is obtained using Farrell’s analysis, and its energy growth is compared with that of the most unstable eigenmode. Later, to incorporate the base flow change, the optimal mode for maximum growth is obtained by solving the problem with a variational approach. The results are compared to provide justification of Farrell’s analysis, which is quasi-steady, against the requirement of complete study considering the time dependent base flow.
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