Direct numerical simulations of turbulence over compliant walls

The interaction of turbulence with compliant walls leads to the generation of Rayleigh waves in the material and qualitative changes in the flow in the near-wall region (Esteghamatian et al., J. Fluid Mech. 942, A35, 2022). The Rayleigh wave speed sets the height of a critical layer whose role will be examined using data from direct numerical simulations. The computations adopt an Eulerian-Eulerian approach with a level-set method that distinguishes the fluid and compliant wall, and the results are analyzed in a wave-fitted coordinate in order to highlight the influence of the wave motion. Our findings are consistent with and supplement recent observations from experiments by Katz and co-workers. Even when the wall deformation is on the order of a few viscous units, the flow dynamics between the critical layer and the wall are qualitatively altered compared to rigid-wall turbulence, in particular the vorticity flux and the phase speed of propagation of perturbations. The analogy to wind-wave interaction is explored, specifically by evaluating the validity of Lighthill's theory on the role of the critical layer in the energy exchange between the wave motion and the flow above it.