Low-dimensional dynamical model of a turbulent boundary layer over a compliant surface: Preliminary results

In this paper we are reporting preliminary results of an ongoing research project that aims at getting an improved understanding of the interaction between wall-generated turbulence and compliant surface coatings. We axe pursuing an integrated approach using analysis, low-dimensional modeling, and direct numerical simulations, with a view towards the reduction of turbulent sound production and turbulent drag. By Galerkin projection of the Navier-Stokes equations onto special sets of basis functions that describe the structure of the near-wall flow, we have constructed low-dimensional models for the dynamics of the flow. The resulting flow equations axe coupled to sets of linear oscillators describing damped mass-spring systems that represent the dynamics of the wall in Fourier space. First results from an investigation of these models show a reduction in bursting frequency which is strong evidence for turbulent drag reduction, in agreement with experimental results from other groups.