Laboratory experiments were conducted to investigate the effect of low relative depth and high Froude number on the dimensionless critical shear stress (Shields parameter). Spherical particles of four different densities and an 8mm diameter were used as movable test material. The relative depth ranged from 2 to 12 and the Froude number ranged from 0.36 to 1.29. The results show that the traditional Shields diagram cannot be used to predict the incipient motion of coarse sediment particles when the relative depth is below 10 and the Froude number is above 0.5, approximately. Experiments using glass balls, whose density is almost identical to that of natural gravel, show that the Shields parameter can be twice as large in shallow flows than in deep flows. The results also show that the Shields parameter is dependent on the density of the particles. Data obtained from other studies support the findings of the present work. These findings can result in significant cost savings for riprap. Additionally, velocity profiles using a laser-Doppler velocimeter (LDV) were taken for the glass ball incipient motion experiments. The purpose of this was to study possible changes in the velocity distribution with decreasing relative depth and increasing Froude number. The results show that the von Karman and integral constants in the law of the wall do not change in the range of relative depths and Froude numbers tested. / Master of Science

The pressure fluctuations under a high Reynolds Number, rough-wall, turbulent, boundary layer have been studied in the Virginia Tech Stability Wind Tunnel. Rough surfaces of varying element height (1-mm, 3-mm), shape (hemispheres, cylinders) and spacing (5.5-mm, 10.4-mm, 16.5-mm) were investigated in order to ascertain how the turbulent pressure fluctuations change with changes in roughness geometry. Rough surfaces which contain two types of elements are investigated and relationships between the combination surface and the individual surfaces have been uncovered. Measurements of the wall pressure fluctuations were made using pinhole microphones and hotwire measurements were made to obtain the velocity and turbulence field. Among the principal findings is the development of two scaling laws for the low frequency pressure fluctuations. Both of these are based on the idea that the defect between the edge velocity and some local boundary layer velocity sustains the pressure fluctuations in the outer regions of the flow. The first scaling uses the broadband convection velocity as the local velocity of the large scale pressure fluctuations. The second scaling uses the mean boundary layer velocity. Both these scalings appear more robust than the previously proposed scalings for the low frequency region and are able to scale the pressure spectra of all the data to within 3.5-dB. In addition, it was proven that the high frequency shear friction velocity scaling of Meyers et al. (2015) is universal to rough surfaces of different element shape and density. Physical insights into the shear friction velocity, on which this scaling is based, have been revealed. This includes an empirical formula which estimates the element pressure drag coefficient from the roughness density and the Reynolds number. The slopes in the mid-frequency region were found to vary with element density and microphone location such that a useful scaling could not be determined for this region. The possibility of an overlap region is explored and the expectation of a -1 slope is disproved. It is hypothesised that an evanescent decay of the mid-frequency pressure fluctuations occurs between their actual location and the wall where they are measured. A method for accounting for this decay is presented in order to scale the pressure fluctuations in this region. Lastly, a piecewise interpolation function for the pressure spectrum of rough wall turbulent boundary layers was proposed. This analytical function is based on the low frequency scaling on mean velocity and the high frequency scaling of Meyers et al. (2015) The mid-frequency is estimated by a spline interpolation between these two regions. / Ph. D.