Reynolds number effect on flow structure dominance in transitional boundary layers

Understanding the dominant flow structures that govern the flow physics of transitional boundary layers subject to external forcing is crucial for designing feedback controllers in active flow control applications. Herein, we study the impact of linear and nonlinear mechanisms on the resulting flow structures due to external excitation for a wide range of Reynolds numbers and for three canonical base flows: Couette flow, plane Poiseuille flow, and Blasius flow. To preserve the nonlinearity of the Navier–Stokes equations, we use a structured input-output analysis, where two different uncertainty structures were implemented based on studies of J. Fluid Mech. vol. 927, A25, and Int J Robust Nonlinear Control vol. 34(7): 4881-4897. For each flow case, we track the variation of several modes of interest that have been identified as dominant via linear and nonlinear input-output approaches. We show that streak modes that are predicted via linear input-output analysis lose their dominance when using structured input-output analysis, where for low Reynolds numbers, more modes appear to be similar in strength. We find that amplification trends of these modes vary with the Reynolds number increase, leading to an interchange of mode dominance for different Reynolds numbers.