Boundary Conditions for Mean Variables 



Boundary conditions at the free-surface are: (a) the wind stress is 

 specified, 



Po \ (fl' ll) = (^sx. ^sy) = PaCda("& ' ^2)1/2 (u„. vj (2.12) 



where t and t are the wind stresses in the x and y directions 

 respectively, p^ is the air density, C^j., is the drag coefficient, u^ and v^ 

 are wind velocities at a certain height (6 m or 10 m) above the surface; 

 (b) the kinematic condition is satisfied, 



w = If + u ^ + V ^ (2.13) 



3t 3x 3y 



where c is the displacement of the free surface; (c) the dynamic condition is 

 satisfied, 



P = Pa (2.14) 



where p, is the atmospheric pressure, and (d) the heat flux is specified, 



PoKvi7= Is = "s (T-Tg) (2.15) 



where H^ is the surface heat exchange coefficient, and Tg is an equilibrium 

 air temperature at which the surface and heat flux q^ is zero. 



Utilizing the dynamic boundary condition (2.13), the vertical momentum 

 equation can be integrated vertically to yield: 



■Jf 



p = -/ pg dz + p^ (2.16) 



The pressure gradient terms in Eqs. (2.7) and (2.8) can thus be replaced by. 



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