Theoretical study of disturbance evolution in parallel shear flows.
There have been numerous studies on the receptivity, transient growth and nonlinear development of disturbances in shear flows in general and plane Poiseuille flow (PPF) in particular. However, none of these tries to trace the disturbance evolution from the initial linear stage to fairly strong nonlinear stages. Currently we are analysing the disturbance evolutionin PPF due to a localized disturbance source, starting from the linear evolution stage to the secondary disturbance development regime.The analytic solution to the linear evolution problem for PPFshows emergence of a spatial Tollmien- Schlichting wave and a wavepacket, unlike the earlier findings which show only the TS waves.The secondary stability analysis of the new primary stateprovides a new explanation for subcritical instability in PPF as a function of the primary disturbance amplitude.
The initial boundary value problem (IBVP) and the solution methodology are presented in
S. Usha and R. Kidambi, The vibrating ribbon problem in plane Poiseuille flow., PD-CTFD/2017/1004.
The secondary stability analysis for the new base state, comprised of plane Poiseuille flow and wavepackets is presented in
R. Kidambi and S. Usha, Secondary instability of a wavepacket in plane Poiseuille flow., PD-CTFD/2017/1016.