2.6 Grid Alignment 



In the present model, a staggered grid is used in both the horizontal and 

 vertical directions of the computational domain (Figure 2.3). Along the 

 shoreline, the normal velocities are zero or specified by river inflow or 

 outflow. In the vertical direction, the free surface and the bottom both fall 

 on the full grid points where the vertical velocities and turbulent fluxes are 

 computed or specified. The horizontal velocities are computed at the half 

 grid points in the vertical direction. Many models, however, use a vertical 

 grid which computes the horizontal velocities at the full grid points 

 including the free surface and bottom. Special finite-difference treatment 

 was thus required for the boundary points. 



2.7 Dimensionless Equations and Boundary Conditions in the 

 Transformed Coordinates 



Dimensionless Variables 



It is convenient to write the above system of equations and boundary 

 conditions in non-dimensional form and in the transformed coordinates (a, y. o) 

 by defining the following non-dimensional quantities: 



(u*, V*, w*) = (u, V, wL/D)/Ur 



(x*, y*. z*) = (x. y, zL/D)/L 



(t*, t^*) = (tx'', Ty'^)/Pr(Av)rUr 



t* = tf . q* = q/Pr(Kj^Tr (2.23) 



P* = (f^Pr)/Pr , T* = (T-Tr)/T^ . C* = g?/fU^L 



aJ = AH/(AH)r . < = Kh/(Kh)p . dJ = DH/(DH)r 



A* = \/{\)r . K* = Ky/(Ky)^ , D* = 0^/(0^)^ 



31 



