Transient disturbance growth in a corrugated channel

Transient growth of small disturbances may lead to the initiation of the laminar-turbulent transition process. Such growth in a two-dimensional laminar flow in a channel with a corrugated wall is analysed. The corrugation has a wavy form that is completely characterized by its wavenumber and amplitude. The maximum possible growth and the form of the initial disturbance that leads to such growth have been identified for each form of the corrugation. The form that leads to the largest growth for a given corrugation amplitude, i.e. the optimal corrugation, has been found. It is shown that the corrugation acts as an amplifier for disturbances that are approximately optimal in the smooth channel case but has little effect in the other cases. The interplay between the modal (asymptotic) instability and the transient growth, and the use of the variable corrugation for modulation of the growth are discussed.