The transition to turbulence of a laminar boundary layer can be affected by free-stream turbulence
(FST). High levels of FST can cause the exponentially growing Tollmien-Schlichting wave to
be replaced by algebraically growing streaks. Transient growth theory successfully identified
counter-rotating, streamwise-oriented vortices as optimal flow configuration for maximum streaks’
amplification.
The introduction of a wall film can significantly alter the amplification and evolution of
streaks, influencing the penetration of FST inside the boundary layers, and its effects on modal
and non-modal stability are yet to be addressed within the appropriate spatially-developing
framework.
In this work, the outcome of the introduction of a wall film on spatial transient amplification
is analysed. Under base flow parallelism, optimal disturbances are computed by solving an
optimal evolution problem. This study demonstrates that decreasing the viscosity of the film
has a direct impact on the efficacy of the vortex tilting mechanism, leading to transient growth
reduction.
The different spreading rates of the boundary layer edge and the interface height imply
that the effects of stratification vary in the streamwise direction. The assumption of base flow
parallelism is therefore relaxed and a framework for the determination of optimal disturbances
and spatial transient amplification in two-phase spreading boundary layers is presented, using
adjoint optimization techniques. It is shown that spreading effects can alter the prediction of
linear stability on streaks amplification.
Beyond the early linear stage, the amplitude of the instability waves and interface deformation
become appreciable and nonlinear effects cannot be neglected. As a result, an accurate
description of the evolution of disturbances in two-fluid boundary layers must account for nonlinear
interactions and mean flow distortion. Direct Numerical Simulation (DNS) with interface
tracking is used to study the nonlinear evolution of the optimal disturbances in the two-fluid
flow.