The extension of the theory for two dimensional turbulent boundary layers into three dimensional flows has met with limited success. The failure of the extended models is attributed to the anisotropy of the turbulence. This is seen by the turbulent shear stress angle lagging the flow gradient angle and by the behavior of the Reynolds shear stresses lagging that of the mean flow. Transport equations for the turbulent shear stresses were proposed to be included in a modeling effort capable of accounting for the lags seen in the flow. This study is aimed at developing algebraic relationships between the various Reynolds-averaged terms in these modeling equations. Particular emphasis was placed on the triple products that appear in the transport equations. Eleven existing experimental data sets were acquired from the original authors and re-examined with respect to developed and existing parameters. A variety of flow geometries were collected for comparison. Emphasis was placed on experiments that included all six components of the Reynolds stress tensor and triple products. Parameters involving the triple products are presented that appear to maintain a relatively constant value across regions of the boundary layer. The variation of these parameters from station to station and from flow to flow is discussed. Part of this study was dedicated to parameters that were previously introduced, but never examined with respect to the data that was collected. Results of these parameters are presented and discussed with respect to agreement or disagreement with the previous results. The parameters presented will aid in the modeling of three dimensional turbulent boundary layers especially with models that employ the transport equations for the Reynolds stresses. / Master of Science

This thesis is a study of the effects of distributed roughness elements on a two-dimensional turbulent boundary layer. Measurements were taken on a total of ten rough wall configurations: four involving Gaussian spikes, and six with circular cylindrical posts. Rough wall flows are particularly suited to study with Laser Doppler Velocimetry (LDV) due to the fact that measurements are required near a solid surface, as well has in highly turbulent fluid. The LDV system used in this study is a fine resolution (~50 micron), three-component, fiber optic system. All mean velocities, Reynolds stresses, and triple products are measured. This study is unique in the range and variety of roughness cases for which data was taken. The data show that the flow over a rough wall is characterized by high levels of turbulence near the roughness element peaks at the interface between low-speed, near-wall fluid and the higher speed fluid above. Behind an element, high-momentum fluid sweeps toward the wall, and there is a small region of ejection of low-momentum fluid. Cylindrical elements typically have larger magnitudes of turbulent stresses at their peaks compared to Gaussian elements. Trends in mean velocity profile parameters such as displacement height, roughness effect, and wake parameter are examined with respect to roughness element geometry and spacing. / Master of Science