An experimental investigation of the turbulent boundary layer over a wavy wall

An experimental investigation of turbulent boundary layer flow over wavy surfaces was conducted at low speed. Two models with the ratio of the amplitude to the wave length a/λ = 0.03 and wave lengths λ = 6" and 12" were tested in an open-circuit wind tunnel. The free stream velocity was 15.4 m/sec, giving Reynolds number Re = 2.54 X 10^4 per inch. Boundary-layer thickness varied from δ = 1.5" to δ = 4. 1" by means of boundary-layer trips of various height, in order to change the ratio λ/6. The following measurements were taken: * Wall pressure distribution * Average velocity and turbulence level, using a single element hot-wire probe * Wall stress distribution, using Preston's tube * Static and total pressures * Turbulence intensities and shear stress using X-array hot-wire probe. An appreciable modulation of all the flow quantities, imposed by the wavy boundary, is observed throughout the investigation. Wall pressure is much lower than predicted by uniform, inviscid theory and is slightly non-symmetric. Wall stress distribution has a peak with C_f/C_fo = 1.2 upstream of the crest and a dip of C_f/C_fo = 0. 6 upstream of the trough. Static pressure decays exponentially in the outer layer while its gradient is decreased toward the surface in the wall layer. The turbulence intensities and shear stress distributions near the wall show oscillatory modulation superimposed on the reference flat plate profiles. The amplitude of the oscillations decay exponentially toward the edge of the layer, so that in the outer part of the layer the turbulence quantities are practically independent of the longitudinal position. It was found that Coles' Law of the Wall does not apply in the present situation because of the modulation of the slope of the semi-logarithmic portion of the velocity profiles. A presentation of velocity profiles is suggested through the use of total velocity defined by U^t = (U^2 + 2(p–p_∞)/p)^(1/2). This quantity obeys the Law of the Wake. Mixing length and eddy viscosity profiles based on the derivative ∂U^t/∂y are reduced into one curve which is the reference flat plate distribution