PART III: DYNLETl NUMERICAL SOLUTION PROCEDURE 



Model Setup 



41. Svunmarizing from the derivation given in the previous chapter and 

 replacing the velocity v by (l/A, the one -dimensional shallow-water equations 

 for application to tidal inlets are 



(7) 









"-at -^ = 



I2. 



at 



a 

 ay 



^^) = 



Bt 

 -gAS,. — 



gAS^ - 9A^ («) 



42. The procedure for developing a numerical model based on Equations 7 

 and 8 is described in this chapter. The space coordinate y and the time 

 coordinate t are selected as the independent variables; Q and z are selected 

 as the primary dependent variables. Other dependent variables, consisting of 

 A, B, and P, are functions of z, and Sf and S^ are functions of both Q and z. 

 If values of the average velocity v are desired, they are calculated from Q 

 and A. Values of the surface shear stress t^ are functions of t only. 

 Therefore, the numerical model solves Equations 7 and 8 for values of z and Q 

 as functions of y and t. Once z and Q are known, the other dependent vari- 

 ables can be readily calculated. 



43. Application of DYNLETl will be illustrated for a system of 

 five interconnecting channels meeting at two junctions, as shown in Figure 3. 

 The term channel is used in a broad sense to denote any body of water that 

 conveys flow along its length regardless of its width. More complex systems 

 may have more channels and junctions (locations where channels meet) than 

 shown in Figure 3. Each channel must have a beginning node and an end node . 

 An initial flow direction to define the beginning and end of each channel is 

 assumed as indicated by arrows. A channel may have any number of nodes, the 

 nodes being locations at which cross -sectional data are given or are measured 

 in the field. 



44. In Figure 3, Nodes 1, 12, 20, and 26 are external nodes (nodes at 

 which data are introduced to drive the model). Nodes 6, 7, and 13 are 



18 



