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INVESTIGATION OF OUTER LAYER SIMILARITY FOR ROUGH WALL BOUNDARY LAYERS

Karen A. Flack
Department of Mechanical Engineering United States Naval Academy Annapolis, MD 21402 USA

Michael P. Schultz
Department of Naval Architecture and Ocean Engineering United States Naval Academy Annapolis, Maryland 21402 USA

Jonathan S. Connelly
Department of Ocean Engineering U.S. Naval Academy, Annapolis, MD, USA

Abstract

Based upon literature reviews, the papers of Jimenez (2004) and Flack et al. (2005) have concluded that changes to the turbulence structure across the boundary layer can be expected in rough wall flows where the boundary layer thickness (δ) is not much larger than the roughness height (k) or equivalent sand roughness height (ks). The two studies state that outer layer similarity in the turbulence may cease to exist in cases where δ/k ≤ 50 or δ/ks ≤ 40, respectively. In order to explore a limiting roughness height for boundary layer similarity, an experimental investigation was carried out on six rough surfaces representing two types of three dimensional roughness (sandpaper and woven mesh) in which 16 ≤ δ/k ≤ 110 and 6 ≤ δ/ks ≤ 91. The measurements were conducted in a closed return water tunnel, over a momentum thickness Reynolds number (Reθ) range of 6,100 to 13,000, using a two-component, laser Doppler velocimeter (LDV). The present results indicate that the mean velocity defect profiles for both the smooth and rough surfaces collapse well in both classic scaling and using the velocity scale of Zagarola & Smits (1998). The Reynolds stresses for all the surfaces collapse with smooth wall results outside of 3-4ks. These results indicate that turbulence similarity in the outer layer may be more robust than previously thought.