|?=-gy^|^dz.p,g!^.i^ (2.17) 



3x I ax ^ 3x 3x 



i£=-g r If dz-.p,g?f .^ (2.18) 



3y f 3y =* 3y 3y 



where pg is the density at the free surface. 



The transfer of momentum and heat at the air-sea interface is extremely 

 complicated. A proper treatment requires understanding of the planetary 

 boundary layer, the mixed layer of oceans, and their interactions. Most 

 models of lake or ocean currents resort to empirical formulae as shown above. 

 Based on the wind speed at 6 m above the surface, Wilson (1960) used a value 

 of 0.00237 for C^jg during strong winds and 0.00166 for light winds. 

 Hicks (1972) considered wind speed at 10 m above the surface and arrived at 

 Cjjg of 0.001 for low wind and 0.0015 for high wind. Additional complications 

 surrounding the specification of surface shear stress include the 

 determination of the time-dependent wind field, the relationship between the 

 over-land wind and the over-water wind, and the effect of atmospheric 

 stability on the simple quadratic stress law (2.12). Hg and Tg in (2.15) 

 depend on the wind speed, air temperature, humidity, and solar and terrestial 

 radiation. Empirical methods to evaluate Hg and T^. can be found in Edinger 

 and Geyer (1967). An alternative approach by TVA (1972) treats the sensible 

 heat transfer and the evaporative heat loss separately. 



At the bottom, the boundary conditions are: (a) a quadratic stress law 

 is used. 



' 'v (fl' tf) = (^bx. ^by) = P Cd (uj - v^)'^' (Uj. v^) (2.19) 



where C^ is the drag coefficient, and u. and v. are horizontal velocities at a 

 point z above the bottom; (b) the heat flux or temperature is specified. 



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