models. Multi-layered (8) and time-dependent (6) eddy viscosities had 

 to be used to achieve reasonable prediction of certain para;neters. 

 Grant and Madsen (2) predicted the velocity profiles of JC's experiment 

 with reasonable accuracy, but failed to predict the phase relationship 

 accurately. 



OPEN 



SER (a) 



VELOCITIES MEASURED 

 IN THIS LINE 



OSCILLATING 

 PISTON 



A cm 



e em 



C cm 



K cm 



Z-Y cml 



1.7 



6 



0.5 



2.3 



0.25 1 



Fig. 1. Jonsson and Carlsen's oscillatory flow facility: (a) the 

 water tunnel, (b) the bottom roughness elements. 



Using the one-dimensional version of the turbulent transport model 

 described above, we performed a simulation of the oscillatory turoulent 

 boundary layer measured by JC. The computational domain extends 

 vertically from Z=Zq=0.077 cm at the bottom to Z=17 cm at the top. For 

 simplicity, we assume the mean longitudinal velocity at the top to be 

 sinusoidal with an amplitude of 2m/sec. Turbulent correlations at the 

 top are assumed to be negligible. A time-periodic horizontal pressure 

 gradient which balances the time variation of wave orbital velocity at 

 the top boundary, was imposed at all vertical levels. At the lower 

 boundary, all turbulent correlations a re assumed to have a zero 

 gradient, except that the gradient of uw balances tne horizontal 

 pressure gradient. Mean velocities are taken as zero at tne bottom. 

 To avoid the necessity of having to resolve the extremely small 

 turbulence time scales in the immediate vicinity of the bottom, A is 

 assumed to vary linearly with height below a certain height, and is 

 determined from the dynamic equation (7) from there on. The nonlinear 

 inertia terms are neglected, a valid assumption so long as the wave 

 orbital velocity is much smaller than the phase speed of the wave. The 

 model was run for several cycles until the results reached a quasi 

 steady state, i.e., when results do not change from cycle to cycle. 



The mean velocity profiles computed by our model at (j)=0 , 45 t 

 90°, 135°, and 180° are shown in Figure 2. Excellent agreement between 

 our results and JC's data was achieved. At peaK amplitude, our model 

 prediction shows a slightly higher overshoot at the mid-level. It is 

 interesting to note that the velocity profiles at i45 and 135 are 

 quite different. Adverse pressure gradient is imposed on the flow at 

 45°, while favorable pressure gradient is imposed on the flow at 135 . 

 Since the measured free stream velocity is not exactly sinusoidal, the 

 measured velocity profiles have been normalized for comparison witn 

 model results. 



238 



