Empirical Model for Low-Speed Rough-Wall Turbulent Boundary Layer Pressure Spectra

Abstract

An empirical model for estimating surface pressure spectra in high Reynolds number rough-wall turbulent boundary layers in the low-speed regime is presented. The model is based on the low-frequency mean velocity defect scaling [1] and the high-frequency shear friction velocity scaling [2]. This model satisfactorily predicts surface pressure spectra measured over a wide range of roughness configurations in high Reynolds number flows free of transitional effects. These data also provide insights into the characteristics of the turbulent scales which are on the order of the roughness size and comprise the mid-frequency region. The slope of this region is highly dependent on roughness element density and element-relative measurement location. This contradicts the premise of an overlap region with slope . An evanescent pressure decay model provides evidence that the slope changes are due to a roughness-dependent pressure decay within the interstitial flow and suggests that a traditional mid-frequency similarity law may not be possible.