13.79 sec, and a physical roughness (Zq) of 0.2 cm. Using these data as 

 boundary conditions to our model, the mean velocity profile in the absence of 

 wave exhibits logarithmic variation with height (Fig. 6.6). Ursell number was 

 much smaller than 1, thus justifying a linear wave boundary condition at 1 m. 

 The wave orbital velocity which varies sinusoidally with time was then imposed 

 at the boundary, and the model was allowed to run until the solutions repeated 

 themselves from cycle to cycle, i.e., a quasi-steady state was reached. The 

 velocity profile averaged over a complete wave cycle, as shown in 

 Figure 6.6(a), indicates an increase in Zq to 0.5 cm. As shown in 



2 



Figures 6.6(b), turbulent kinetic energy (q ) and Reynolds stress (-u'w') have 



also increased due to the presence of the wave. Fig. 6.6(c) indicates 



1/2 

 u* (-u'w'/p) has increased from 0.6 cm/sec to 0.71 cm/sec. The estimated 



values of u* and Zq are less than those estimated by Grant and Madsen 



(0.9 cm/sec and 0.9 cm, respectively), which were higher than the values 



determined from the logarithmic profiles. 



If one uses the empirical formula of Kajiura (1968) or Jonsson and 



Carl sen (1976), the wave-induced bottom shear stress averaged over the wave 



2 

 cycle is on the order of 1.3 dyne/cm for the present case. Adding the 



2 

 current-induced stress onto it, the total bottom stress would be 1.6 dyne/cm , 



much higher than the measured value and our model estimate. 



The success of the above simulation is not to be interpreted as having 

 resolved all the problems surrounding the current and wave interaction within 

 the boundary layer. In fact, further applications of our model to simulate 

 the turbulent boundary layer under combined current and wave actions indicate 

 the wave modulation may either enhance or reduce the turbulence due to the 

 mean currents, depending on the quasi-steady turbulence level, the relative 

 strength of wave vs. current, and the period of the waves (Sheng and Lewellen, 

 1982). A laboratory study by van Hoften and Karaki (1976) found that the 

 Reynolds stress was reduced due to the presence of the wave. 



142 



