Turbulence and Energy Exchange in a High Reynolds Number Boundary Layer over a Compliant Surface

Simultaneous measurements of the 3D time-resolved velocity/pressure field and the wall deformation in a turbulent boundary layer over a compliant surface at Re_τ=3300-8900 are performed by combining tomographic particle tracking velocimetry and Mach Zehnder Interferometry. A previous study has shown that turbulence is advected at the surface wave speed up to the ‘critical layer,’ where the mean velocity is equal to the deformation wave speed, and at the local velocity at higher elevations. The critical height increases with Reynolds number, from y⁺=63 to 193. Here, we examine the critical layer effect on the turbulence and kinetic energy budget. The Reynolds stress profiles scale with inner variables near the wall, and with mixed ones in the outer layer. The velocity and pressure fluctuations are decomposed into the wave-coherent and ‘stochastic’ turbulence using Hilbert projections. The coherent stresses and pressure are smaller than the stochastic counterparts by an order of magnitude, except near the wall. The turbulent kinetic energy (TKE) budget is decomposed into the ‘wave kinetic energy’ (WKE) and stochastic turbulence. Shear production rate of WKE is 6-10% of that of the TKE, and both peak near the wall, well below the critical height. Energy flows from WKE to the stochastic turbulence below the critical layer, but reverses sign at higher elevations. The coherent pressure diffusion is dominated by the p-v correlation, adding energy to WKE below the critical layer, but depleting it at higher elevations.