3. Formulation . 



A navigation channel serving as access to an enclosed harbor is assumed to 

 be sustained, and possibly created, by currents resulting from the rise and 

 fall of the tide and by upland river discharge. Wave scour is not considered. 

 It is further assumed that a relation of cross-sectional channel area to water 

 discharge through a harbor channel, during ebbtide, will fall on a curve of the 

 relationship of ebb discharge through natural channels cut in the same material 

 at nearby locations. Ebbtide is used because at that time river and tidal dis- 

 charges are additive, and tidal-flat flow is downslope into the channels. 



The total water volume moved through a harbor channel or a natural channel 

 during ebbtide, Q, produces the best relationship with the channel cross- 

 sectional area where 



Q = / [qe(t) + qr(t)]dt 



(3) 



where 



q = ebbtide discharge of water through the channel cross section result- 

 ing from the previous flood discharge up the channel or on a tidal 

 flat, or from the rise in channel stage caused by the backwater 

 effect of river discharge; 



q = normal river discharge, if any, that would occur if the tide was 

 not present; 



t^ = time of high vjater; 



ti = time of low water. 



Values q and q^. in channels may be determined using existing tide gage 

 and river stage data and natural channel dimensions. The harbor basin discharge 

 is equal to the water volume difference in the harbor between high and low tides. 

 It is calculated using the proposed harbor dimensions and the tidal range at the 

 harbor site. 



In intertidal regions, it is assumed water moves into the channels from the 

 adjacent planar parts of the tidal flat only during ebbtide and only when the 

 vertical distance between the water surface and the tidal flat is small. It is 

 further assumed that tidal-flat flow is downslope only, and thus conforms to the 

 topography (usually a combination of seaward and channel-directed slopes) . Flow 

 on the tidal flats thereby adds to the channel discharge. Because of the vari- 

 able topography of tidal flats and tidal-flat channels, the discharge must be 

 obtained from cross sections and contour maps of the tidal flats. The volume 

 discharged through a channel at any elevation on the tidal flat is, therefore, 

 assumed equal to the volume under a horizontal plane at an elevation of the 

 boundaries of the tidal-flat drainage at the channel location, bounded by down- 

 slope flow streamlines which intersect the channel above the cross section being 

 studied. This is illustrated in the example provided in the next section. 



