The accumulation of river water between Cape Cod and C hesapeake Bay 353 



effect over the entire shelf is delayed, as would be expected considering the length of 

 time required for transport of river water through the area. 



Table III 



Flushing times of the continental shelf between Cape Cod and Chesapeake Bay for an 



average river flow of 14-5 x 10» ff'lday (167,764 ft^jsec.) 



Depth 

 Range 

 Fathoms 



FLUSHING TIME, DA YS 

 April-June July-Sept. Oct.-March 



THE FLUX OF FRESH AND SALT WATER 



The total transport through any complete cross-section must result in the move- 

 ment seaward of a quantity of river water equivalent to the quantity contributed by 

 the rivers in unit time if the distribution is to remain in steady-state. The cross- 

 sections must completely surround the source of fresh water. Those we have used 

 extend from shore at the eastern boundary of area A, to a depth contour, along the 

 contour line to the southern boundary of area F, and back to the shore. 



For any given part of the cross-section this transport is a complicated sum of 

 the effects of horizontal and vertical advection and eddy diffusion. However, our 

 method of averaging gives the depth mean salinity and obscures the vertical effects. 

 Thus, it seems possible to treat the system as Stommel (1953) has treated estuarine 

 circulation, as a two dimensional one in which the advection produced by river 

 water entering the system is balanced by horizontal eddy diflusion normal to the 

 coast. 



The flux of material in the direction normal to the coast (Fx) is given by Stommel 

 (1953): 



F^= Qc- SA f- 

 dx 



in which c is the fraction of fresh (or salt) water, Q is the rate of river flow. 5 the 

 cross-sectional area, A the horizontal mixing coefficient, and v is the distance normal 

 to the coast. Under steady-state conditions the flux of river water through any 

 cross-section equals the rate of river flow (F = 0, and the flux of salt through any 

 cross-section is zero. 



The eddy diff"usion parallel to the coast has been neglected in the above equation. 

 If the coefficient of horizontal diff"usion is the same in the two directions, the transport 

 by diffusion parallel to the coast must be proportionately very small. The gradients 

 in this direction range from one tenth to one thirtieth the value o\' the gradients 

 normal to the coast; and the cross-sectional areas at the ends are also small com- 

 pared to the area along the contour line. For example, the product 5,J^//. >.vis 



N 



