Structured input-output analysis of oblique laminar-turbulent patterns in plane Couette-Poiseuille flow?

In this work, we employ structured input-output analysis to study the flow patterns in transitional plane Couette-Poiseuille flow (CPF). First, we focus on the well-studied intermediate laminar profile, which balances the shear and pressure effects. We show that the highest structured gain corresponds to perturbations with wavelengths associated with the oblique turbulent bands observed in experiments. In addition, the inclination angles of these structures show a Reynolds number dependence consistent with experimentally observed trends. We then examine the Reynolds number scaling of the maximal structured frequency response as the velocity profile is varied from plane Couette to Poiseuille flow. Our results demonstrate that, as expected, the scaling exponent increases over this range, but this increase is not monotonic. We attribute the variation in the shape of the scaling exponent curve as a function of the velocity profile shape to changes in flow patterns that dominate each associated flow regime. We then focus on the particular case of plane Couette flow and compute the structured response modes. Their behavior and structural features are consistent with results obtained through direct numerical simulation (DNS) studies. Finally, we employ the structured analysis framework to examine the temporal evolution of the dominant structures. For the well-studied cases of plane Couette and plane Poiseuille flows, the computed advection speeds of the oblique structures are consistent with those predicted through DNS.