Bottom Boundary Condition 



The bottom stress terms xbx ^"^ '^by appearing in the above external mode 

 equations are computed from the vertical velocity profiles, available from the 

 internal mode computations, and the quadratic stress law (2.32). Conventional 

 vertically-integrated models, however, compute the bottom stresses based on 

 the vertically-integrated velocities through the following dimensional 

 formula: 



Ubx' -cby) --f- (U'+V^) ' " (U,V) (2.40) 



C(.H 



where C^ is the Chezy coefficient derived from analysis on one-dimensional 

 pipe flows: 



C^ - 8.21 H ^ Vn [cm/sec] (2.41) 



where n is the Manning's n in u.iits of (cm) . Values of Manning's n have 

 been suggested for a variety of surface materials (e.g., Pao, 1967) in open 

 channel flows. When such a formula is used to compute coastal currents, a 

 great deal of effort has to be spent in tuning the Manning's n in order to 

 achieve good fit between computed and measured results on surface 

 displacements or volume transports. 



39 



