Wave-Current Induced Bottom Shear Stress 



Slowly-varying currents and wave orbital velocities generally both 

 contribute to the generation of bottom shear stress in shallow waters. Eddy 

 viscosity models have been used by Grant and Madsen (1979) and Smith and 

 McLean (1977) to investigate this process. Based on certain assumed eddy 

 viscosity profiles and a constant thickness of wave boundary layer, their 

 models showed that the presence of the wave enhances the bottom shear stress 

 induced by the mean currents. While relatively inexpensive to use on a 

 computer, the eddy viscosity model necessarily requires more effort in 

 parameter tuning and is also not expected to be valid under all varieties of 

 turbulent flow situations. To remove the empiricism from the model 

 simulation, we have used a dynamic turbulent model to predict the wave-current 

 interaction within the bottom boundary layer. In the following, we present 

 our model simulation of some data collected during the CODE-1 (Coastal Ocean 

 Dynamics Experiment) program. 



The data were collected at a 90 m site (C3) about 1 km off the California 

 coast. Both the USGS tripod (Geoprobe) and the WHOI tripod (Bayshore and 

 El Camino) were deployed at the site during various time periods. For this 

 preliminary simulation, data from the WHOI tripod (samples at 30, 50, 100, and 

 200 cm above bottom) are used. Due to the relatively long fetch from the 

 north, high seas (6-8 feet) were typical, and wavelengths were sufficiently 

 long for the wave to feel the bottom. 



Velocity profiles (averaged over 6 minute intervals) at this site show 

 typical logarithmic variation with height above the bottom. The values of u* 

 are typically between .22 and .66 cm/sec. Using the reference velocities at 

 1 m, these u* values correspond to drag coefficients of 0.019 and 0.026, 

 respectively. Values of the effective Zq in the presence of the wave are 1.3 

 and 3 cm, an order of magnitude greater than the Zq based on physical 

 roughness alone. 



Without parameter tuning, our model was able to simulate the increase in 

 u*. and Zq due to the presence of the wave. Data provided to us for one 

 6-minute period at 100 cm above the above, show a mean velocity (Ujqq) of 

 10.21 cm/sec, a wave orbital velocity (u^,) of 6.09 cm/sec, a period (T) of 



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