ar ^ auT ^ dw]_ _^ awT ^ _3_ 

 3t 3x ay 32 ax 



as , aus , avs , aws ^ a 

 at ax ay az ax 



f^=-P9 (2.9) 



(^Ht^)*^«)^A^fl) 



(2.10) 



(»"!!) ^^(»Hg)^^(ove) 



(2.11) 



where u, v, and w are the velocities in x, y, and z directions, f is the 

 Coriolis parameter defined as Ziisim}! where 41 is the latitude, p^ is the 

 reference density, A^, K^, and D^ are the horizontal eddy coefficients, and 

 Ay, Ky, and D^ are the vertical eddy coefficients. The nonlinear inertia 

 terms and the advection terms have been written in conservative forms. 

 Variable eddy coefficients are allowed in the above equations. Source/sink 

 terms may be included in (2.10) and/or (2.11) to account for such effects as 

 radiation, precipitation and evaporation, etc. 



Due to the different scales and intensities associated with the 



horizontal and vertical turbulent eddies in large lakes and oceans, the 



2 6 2 

 lateral eddy coefficients (A^ ^ 10 to 10 cm /sec) are typically several 



2 

 orders of magnitude larger than the vertical eddy coefficients (A - 1 to 10 



2 

 cm /sec). The determination of realistic values and forms of the eddy 



coefficients is a major and difficult task in the modeling of lake and ocean 



currents. 



22 



