Direct numerical simulation of a turbulent boundary layer over an anisotropic compliant wall

Direct numerical simulation of a spatially developing turbulent boundary layer over a compliant wall with anisotropic wall material properties is performed. The Reynolds number varies from 300 to approximately 860 along the streamwise direction, based on the external flow velocity and the momentum thickness. Eight typical cases are selected for numerical investigation under the guidance of monoharmonic analysis. The instantaneous flow fields exhibit a traveling wavy motion of the compliant wall, and the frequency-wavenumber power spectrum of wall pressure fluctuation is computed to quantify the mutual influence of the wall compliance and the turbulent flow at different wave numbers. It is shown that the Reynolds shear stress and the pressure fluctuation are generally enhanced by the wall compliance with the parameters considered in the present study. A dynamical decomposition of the skin-friction coefficient is derived, and a new term (C_W) appears due to the wall-induced Reynolds shear stress. The influence of the anisotropic compliant wall motion on the turbulent boundary layer through the wall-induced negative Reynolds shear stress is discussed. To elucidate the underlying mechanism, the budget analysis of the Reynolds stress transportation is further carried out. The impact of the wall compliance on the turbulent flow is disclosed by examining the variations of the diffusion and velocity–pressure correlation terms. It is shown that an increase of the Reynolds stress inside the flow domain is caused by enhancement of the velocity–pressure correlation term, possibly through the long-range influence of the wall compliance on the pressure field, rather than diffusion of the wall-induced Reynolds shear stress into the fluid flow.