Wavy wall effects on turbulence production and large-scale modes

We describe how outer flow turbulence phenomena depend on the interaction with the wall. We quantify the influence of highly rough surfaces on turbulence statistics, eigenmodes and spectra of eigenvalues in the outer part of the wall shear layer of an isothermal turbulent flow. Surface geometries with different amplitude-to-wavelength ratios can be regarded as surfaces of defined wall roughness. The wavelength, Λ, and the wave amplitude, 2a, of a water channel are varied by changing the bottom wall in the test section.

We consider three sinusoidal wall profiles defined by the amplitude-to-wavelength ratio α = 2a/Λ = 0.2 (Λ = 30 mm), α = 0.2 (Λ = 15 mm), and α = 0.1 (Λ = 30 mm). Digital particle image velocimetry is performed to examine the spatial variation of the streamwise, spanwise and wall-normal velocity components. Statistical quantities that are determined are the Reynolds stresses, turbulent kinetic energy, and turbulent energy production. Measurements are performed at a Reynolds number of 11200, defined by the half channel height and the bulk velocity. A characteristic length scale in the most dominant eigenmodes can be found that agrees for all wall profiles and is independent of the amplitude-to-wavelength ratio. The turbulence quantities compared at defined streamwise coordinates in wall-normal direction are independent of the wavy wall profile in the outer region when scaled with the friction velocity, u* _w .

Keywords:

• Wall Turbulence
• PIV
• Surface Roughness Effects