60 REDFIELD, KETCHUM AND RICHARDS [CHAP. 2 



Similarly, the difference in the quantity of A T in the respective layers changes along the 

 axis of flow according to 



dQL-dQu 



-*GH-(*-'-S) 



dx 



while the rate of change in the difference in mean concentration is 

 dN L -dN v 1 /V v hu \ (dQ R . dN\ 



dx 



-Tkiiti£+ l Y&-*& 



These expressions indicate that the gradients developed in the horizontal and vertical 

 depend on the ratio of the velocity in the two layers, and vary inversely with the absolute 

 velocities as indicated by the term l/Vy. Sluggish currents are more effective than rapid 

 ones in producing differential distribution, other things being equal. It may be noted also 

 that the effects on the gradients in quantity depend on the velocities in the two layers, but 

 that the effects on concentration vary with the product of the respective velocities and 

 depths, that is with the flux in the respective layers, provided the vertical exchange 

 remains the same. 



The term (dQujdt — A-dN jdz) indicates that the gradients will develop in proportion to 

 the balance between the biological effect and that of vertical diffusion. As the vertical 

 separation develops along the axis of flow, in accordance with equation (7c), dN/dz will 

 increase in value. Consequently the gradients will not develop linearly with distance along 

 the #-axis but will tend to approach a limit at which the biological effect is balanced by 

 the effect of diffusion. The coefficient of eddy diffusion, A, varies greatly under natural 

 conditions, and in general in inverse proportion to the stability. Under stable conditions 

 vertical diffusion may be small and have little effect on the gradients developed. If A is 

 large, as in the case of shallow estuaries subject to strong tidal currents, the diffusion 

 term may be so large that gradients in the distribution of nonconservative elements do not 

 develop. 



The foregoing discussion is intended to clarify the factors which lead to a differential 

 distribution of nonconservative elements in sea-water in situations where water moves 

 with different velocities at various depths. It will provide a basis for discussion of the 

 natural systems in the following pages. 



a. The estuarine circulation 



In estuaries fresh water derived from the land by runoff and seepage mixes 

 with sea-water and is carried seaward in the upper layer of the embayment. A 

 countercurrent of sea-water moves in from the outer sea to replace that en- 

 trained in the surface outflow. The estuarine circulation is a special case of 

 differential advection in which V l is negative. Consequently, the redistribution 

 of nonconservative elements by the sinking of organized matter will tend to 

 cause the concentration of N to increase upstream relative to the motion of 

 the surface layer. The estuarine circulation creates a trap in which nutrients 

 tend to accumulate. 



The Gulf of Venezuela is an example of an embayment in which the estuarine 

 circulation is accompanied by an accumulation of phosphorus (see Fig. 11). 

 The upper layers of the Gulf are diluted by fresh water escaping from the 

 Maracaibo basin. The salt water entrained in the surface layer as it moves sea- 

 ward is replaced by water from the Caribbean. In the deeper water at the head 

 of the Gulf the concentration of phosphate phosphorus is 1 mg atom/m 3 , which 



