Structured Input-Output Analysis of Oblique Laminar-Turbulent Flow Patterns in Transitional Plane Couette-Poiseuille Flow

In this work, we apply structured input-output analysis to study laminar-turbulent patterns in transitional plane Couette-Poiseuille flow. The results demonstrate that this approach predicts the high structured gain of perturbations with wavelengths corresponding to the oblique turbulent bands observed in experiments. The inclination angles of these structures and their Reynolds number dependence are also consistent with previously observed trends. Reynolds number scalings of the maximally amplified structures for an intermediate laminar profile that is equally balanced between plane Couette and Poiseuille flow show an exponent that is at the midpoint of previously computed values for these two flows. However, the dependence of these scaling exponents on the shape of the laminar profile as the relative contribution moves from predominately plane Couette to Poiseuille flow is not monotonic and our analysis indicates the emergence of different optimal perturbation structures over the parameter regime. Finally we perform spectral analysis on the frequency response operator to obtain its principal singular vectors, which provide insights regarding the wall-normal structures of velocity fluctuation modes with the largest structured gain.