Characterizing Wall Turbulence Reaction to Wavy Deflections via Dynamic Mode Decomposition

Understanding and controlling wall-bounded turbulence remains a critical challenge in fluid mechanics. In this study, we conduct a direct numerical simulation (DNS)-based parametric investigation of turbulent channel flows subjected to dynamic wall deformations in the form of spanwise-traveling waves. Building on prior work, we expand the parameter space by systematically varying spanwise wavenumber, angular frequency, and wave amplitude to evaluate their effects on turbulent structure and skin-friction drag. Dynamic Mode Decomposition (DMD) is employed as a central analysis tool to extract dominant coherent structures from time-resolved flow data. Unlike conventional turbulence metrics, DMD reveals the presence of coherent low-dimensional structures whose alignment and frequency content are strongly dependent on the wall forcing parameters. Particular cases yield substantial drag reduction, which is closely correlated with the suppression of near-wall Reynolds stress and the presence of spanwise-aligned DMD modes. By interpolating the solution domain onto a stationary mesh, we isolate the flow response from wall motion and demonstrate the effectiveness of DMD as a diagnostic tool for flow control strategies. In addition, we explore the performance of DMD in advection-dominated problems with moving grids, assessing its robustness and interpretability under these conditions. This work highlights the ability of wall deformation to reorganize turbulence and reduce drag through targeted modal interactions, and supports the use of modal decomposition techniques in the design and evaluation of active flow control strategies.