Jacob Page

Disturbance amplification in boundary layers over thin wall films

In single-fluid boundary layers, streaks can amplify at sub-critical Reynolds numbers and initiate early transition to turbulence. Introducing a wall film of different viscosities can appreciably alter the stability of the base flow and, in particular, the transient growth of the perturbation streaks. The formalism of seminorms is used to identify optimal disturbances which maximize the kinetic energy in the two-fluid flow. An examination of optimal growth over a range of viscosity ratios of the film relative to the outer flow reveals three distinct regimes of amplification, each associated with a particular combination of the eigenfunctions. In order to elucidate the underlying amplification mechanisms, a model problem is formulated: An initial value problem is solved using an eigenfunction expansion and is used to compute the evolution of pairs of eigenfunctions. By appropriately selecting the pair, the initial value problem qualitatively reproduces the temporal evolution of the optimal disturbance, and...