#### Date of Award

Winter 2012

#### Project Type

Dissertation

#### Program or Major

Mechanical Engineering

#### Degree Name

Doctor of Philosophy

#### First Advisor

Joseph Klewicki

#### Abstract

The combined roughness-Reynolds number problem is explored from the perspective of ordering of terms in the mean momentum balance. Existing mean velocity and Reynolds shear stress data from zero pressure gradient, rough-wall turbulent boundary layers are used to clarify the nature of the leading order balances across the boundary layer. These existing data are augmented by data from a judiciously chosen set of experiments performed at the University of New Hampshire. These low speed, Laser Doppler velocimetry based experiments were performed over three types of roughnesses. Their purpose is to clarify the trends found in the existing data sets.

By estimating the terms in the un-integrated form of the mean momentum equation (the appropriate mean statement of dynamics), the operative time-averaged balance of forces is revealed. Contrary to the prevalent belief, it is revealed that the mean viscous force retains dominant order, above (often well-above) the roughness crests.

Force balance data are shown to be usefully organized relative to a new intermediate length scale that defines the region from the wall to the point where the leading order mean dynamics are described by a balance between mean advection and the mean effect of turbulent inertia. For a smooth-wall case, this point occurs a little after the peak position of Reynolds shear stress and is a function of Reynolds number. In rough-wall flows, the data indicate that it is not only a function of roughness and the overall scale separation between the inner and outer scales, but also of the scale separation between roughness and the Reynolds stress peak. These results suggest that for any given roughness, with increasing Reynolds number, new dynamical regimes are likely to emerge.

For the existing and recent experiments explored in the present effort, under an intermediate length scale, three regimes emerge that describe the transition to inertially dominated mean flow. These regimes, defined by the ratio of roughness to the Reynolds stress peak position being less than, equal to or greater than order 1, exhibit a Reynolds number invariance. An empirical normalization of this intermediate scale, based on the scale separations between roughness and Reynolds stress peak, results in a solitary length scale that effectively provides a surrogate for the peak position. The normalization of the peak Reynolds stress position by this semi-empirical scale, results in the merging of all the data covered in this study.

#### Recommended Citation

Mehdi, Faraz, "Mean Force Structure and Scaling of Rough-Wall Turbulent Boundary Layers" (2012). *Doctoral Dissertations*. 701.

https://scholars.unh.edu/dissertation/701