  The non-modal transient growth of perturbations in horizontal and inclined
channel flows of two immiscible fluids is studied. 3D perturbations are
examined in order to find the optimal perturbations that attain the maximum
amplification of perturbation energy at relatively short times. Definition of
the energy norm is extended to account for the gravitational potential energy
along with the kinetic energy and interfacial capillary energy. Contrarily to
the fastest exponential growth, which is reached by essentially 2D
perturbations, the maximal non-modal energy growth is attained mostly by
three-dimensional spanwise perturbations. Significant transient energy growth
is found to occur in linearly stable flow configurations, which, similarly to
single phase shear flows, may trigger non-linear destabilizing mechanisms
within one of the phases. It is shown that the transient energy growth in
linearly stable cases can be accompanied by noticeable interface deformations.
Therefore, flow pattern transition due to non-modal transient growth and
reduction of the range of operational conditions for which stratified-smooth
flow remains stable cannot be ruled out.
