The turbulent shear stress -uw computed by our model is also 

 compared with JC's data. As shown in Figure 3, tne agreejnent is very 

 good at ({i=l80°. However, the agreement is not as good at otner 41's. 

 Johnson and Carlsen did not measure the shear stresses directly, out 

 instead computed them indirectly from the momentum equation. Due to 

 the relatively coarse time resolution (A(})=15°), errors could be 

 introduced in determining the time derivative of the mean velocities. 

 The computed bottom shear stress does indicate a phase lead of 

 approximately 25° over the free-stream velocity, which was also 

 measured by JC. Although our model also computes all the other 

 second-order turbulent correlations, no comparison with data could be 

 made since they were not measured. 



180' 



Fig. 2. Velocities vs. height measured from top of roughness 

 element ( model result, >< ova JC's data). 



The 

 o 



The phase lags of horizontal velocities at various levels computed 

 with our model compare very well with JC's data (Figure 14) 



horizontal velocity near the bottom shows a phase lead of about 25 

 Grant and Madsen's eddy viscosity model predicted a much worse phase 

 relationship. As shown in Figure H, their computed phase lead is 

 actually off by more than 25% near the bottom. 



In slowly-varying turbulent boundary layers, there exists a thin 

 layer near the bottom within which the turbulence is at equilibrium 

 with the mean flow gradients and the mean flow variables vary 

 logarithmically with height. This so-called logarithmic layer was also 

 detected in JC's experiment on an oscillatory turbulent boundary layer. 

 However, none of the previously mentioned theoretical analyses were 

 able to predict the thickness of this layer and its variation with 

 time. Figure 5 shows the variation of the log-layer thickness within 



239 



