Wave-turbulence interactions in flow over compliant wall

Direct numerical simulations of turbulent channel flows with one rigid and one compliant wall were performed. We adopt an Euler-Euler approach with a level-set method to simulate the incompressible turbulent flow interacting with an incompressible viscous hyper-elastic wall. The compliant wall sustains the propagation of Rayleigh waves whose phase speed depends on the shear modulus of elasticity and whose dominant wavelength depends on the compliant layer thickness. When the phase speed of Rayleigh waves is commensurate with the advection speed of near-wall pressure fluctuations, strong two-way coupling between the surface and the flow is established. Inflectional instabilities and shear-layer detachment downstream of the surface waves leads to a sharp phase difference between the deformation and pressure. The instabilities are due to the inflectional velocity profiles near the troughs, and are controlled by the net vorticity flux at the elastic surface. This flux is due to pressure gradient at the wave surface and an additional contribution due to an out-of-phase surface acceleration. We will discuss how the choice of material properties affects the balance between these two contributions, and how it will in turn impact the location and intensity of instabilities above the surface.