0,375 /aqAf 04Ag^. !ii! (7) 



Boussinesque approximation is assaned to be valid sucfi tnat tne only 

 effect of the density stratification is in the gravitational oody force 

 term in the momentum equation (1). Equation (3), a diffusion equation 

 for the temperature perturbation, can be written in terms of the 

 density perturbation. For simplicity, diffusion equation for the 

 salinity perturbation or otner species concentration is not included 

 here. The overbars in the equation denote ensemble-averaged values. 



Many of the right hand side terms in the second-order correlation 

 equations, including the stratification and the rotation terms, are 

 determined precisely and hence did not require any modeling. The last 

 three terms in Equation (M) and the last two terms in Equations (5) and 

 (6) are modeled terms representing the effects of third-order 

 correlation, pressure correlation, and viscous dissipation. Four model 

 coefficients appear in these equations. All the right-hand side terms 

 in Equation (7) had to be modeled. Model constants- are determined from 

 analyzing a wide class of flow situations and remain invariant for any 

 new applications. Boundary conditions required for the above equations 

 will be described later in the specific examples. 



AN OSCILLATORY TURBULENT BOUNDARY LAYER 



Oscillatory turbulent shear flow is encountered in a variety of 

 practical flow situations such as blood flow in arteries, flow past 

 helicopter blades, and oceanic bottom boundary layer under a wave. The 

 important role of wave boundary layer in affecting the suspended 

 sediment concentration in shallow water environments nas been 

 quantitatively demonstrated by Sheng (15). 



Detailed measurements in oscillatory turbulent boundary layers are 

 scarce. Jonsson and Carlsen (7) measured the detailed flow within an 

 oscillating water tunnel with a fixed bottom, while Keiller and Sleath 

 (9) measured the flow near an oscillating wall. Horikawa and irfatanabe 

 (3) measured the bottom boundary layer under a progressive wave in a 

 wave tank. By far, the experiments of Jonsson and Carlsen (I will 

 abbreviate with JC) are still the most comprehensive ones. They 

 considered the more realistic case of a fully turbulent flow over a 

 rough bottom. Jonsson (5) found that flow over a rough bottom becomes 

 fully turbulent when the Reynolds number based on the bottom orbital 

 velocity and the free stream amplitude reaches 10**. 



In JC's experiment (Figure 1), an 8.39 sec wave with a raaximun 

 mean free stream velocity of 2 to 2.22 m/sec and a nearly sinusoidal 

 time variation was imposed on a water depth of 23 cm. Using a 

 micropropeller , they measured the detailed vertical profiles of 

 ensemble-averaged horizontal velocity within tne water tunnel at 15 

 intervals through several wave cycles. 



Due to the lack of quantitative understanding of the turoulent 

 transport processes, all existing theoretical analyses of oscillating 

 turbulent boundary layer are based on some ad-hoc eddy viscosity 



237 



