6.7 Bottom Boundary Layer Dynamics 



Current-Induced Bottom Shear Stress 



For fully rough turbulent flow over a flat bottom in the absence of 

 wave-induced orbital currents, the near-bottom currents are relatively steady 

 and follow the logarithmic variation with depth: 



u* 

 T 



S,n 



t^Mr 



(6.4) 



where u* is the friction velocity, k is the von Karman constant, zo is the 

 roughness height, 'i>^ is a stability function and L is the Monin-Obukhov 

 similarity length scale. Under neutral stability, L="', '^^-0, and the velocity 

 follows a simple logarithmic relationship. Within the bottom boundary layer, 

 the shear stress remains relatively constant. With velocity measurements at 

 two or more points, the shear stress and the roughness height could be 

 determined. The above equation is the basis for deriving the drag coefficient 

 formulation shown in Eq. (2.20). In shallow coastal waters, the depth of the 

 constant flux region is on the order of a meter. 



In shallow coastal waters, wind waves are generally present and their 

 effect can reach the bottom. The wind waves induce orbital currents which 

 gradually decrease with the depth. Nearly-sinusoidal motion exists in the 

 vicinity of the bottom. The boundary layer associated with this wave-induced 

 oscillatory motion is generally much thinner than that induced by the mean 

 currents. Consequently, for an orbital current comparable in magnitude to the 

 mean current, wave-induced bottom shear stress is generally much stronger than 

 the current-induced stress. 



Wave-Induced Bottom Shear Stress 



Detailed flow measurements within the wave boundary layer are scarce. 



Comprehensive data in a coastal environment is even more scarce. Based on 



limited laboratory studies (e.g., Jonsson and Carlsen, 1976), empirical 



formulae for estimating the bottom shear stress have been developed based on 



ad-hoc, eddy-viscosity models. Grant and Madsen (1978) were able to obtain 



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