Structured input–output analysis of compliant wall turbulence

This work employs structured input–output analysis (SIOA) augmented by an eddy viscosity model (SIOA-e) to investigate turbulent flows over rigid and compliant walls. The SIOA-e framework demonstrates the capability in identifying both streamwise and spanwise dominant characteristic wavelengths for rigid wall turbulence. For compliant walls, the SIOA-e method predicts optimal compliant wall parameters associated with positive damping coefficients when minimizing input–output gain for near-wall cycle and very large-scale motions, respectively. The reduction of input–output gain due to the compliant wall is achieved by wall displacement resembling blowing and suction opposite to the wall-normal velocity of dominant streamwise vortices. However, optimized compliant wall parameters based on specific wavenumber–frequency combinations may amplify flow structures for other wavenumber–frequency pairs, potentially leading to an overall drag increase. For example, compliant wall parameters tuned for suppressing large-scale structures can affect both large- and small-scale structures. We also employ input–output analysis to predict convective velocity of wall displacement and pressure for turbulent flow over the compliant wall, and the predicted convective velocity of wall displacement is 0.53 times centreline velocity, which aligns well with recent experimental measurements.