Kl.IKKl. AMI WKOUl.KWSKI: WAKMCORE GULF STKKAM KINGS 



which would be present without any cross-shelf cur- 

 rents (A^^, y,i = 0). This figure shows clearly the in- 

 creasing impact with stronger transports onto or off 

 of the shelf edge. There are slight differences in this 

 ratio if the biological decay is ignored and if the 

 cross-shelf flows occur over large distances, since the 

 longshore flow slows down significantly. We should 

 note that the decrease in larval fish density com- 

 pared with the no-ring case depends on two nondi- 

 mensional parameters Pq = ALIUqY and Pj = 

 \jiLIU(t. Thus for values of ^, L^o. or Y other than 10""^ 

 s"\ 5 cm/s, and 200 km, the graph can be read with 

 suitable values of A and L to give the desired values 

 for these two nondimensional numbers: 



^graph = -Pi X 500 km = "— X 500 km 



region influenced by the ring's cross-shelf flows while 

 the longshore current speed is maintained. P^igure 6 

 shows clearly that such an increase in L will cause a 

 greater reduction in larval density downstream of 

 the eddy. As the eddy translation rate becomes 

 closer and closer to the flow rate on the shelf (effec- 

 tively increasing L in Figure 6), the effect upon the 

 population becomes larger and larger, until even- 

 tually the eddy is drawing all of the larvae off the 

 shelf as it passes. This occurs when the ring's speed is 

 great enough so that the longshore transport of 

 water relative to the ring is smaller than the offshore 

 transport induced by the currents at the shelf edge: 



C/n 



C< 



Uo 



s: 



Y 



dx 



(18) 



P A 



A , = — X 2 cm/s = — X 2 cm/s. 



^gjaph 



Pi \^y 



MOVING EDDIES 



In the previous examples, we have considered the 

 changes in fish larvae distributions which occur when 

 the shelf water flows by a stationary eddy. But rings 

 frequently translate to the southwest, following a 

 track between the continental slope and the Gulf 

 Stream. The translational speeds vary considerably, 

 ranging from a few cm/s to perhaps 10 cm/s. This 

 along-shelf ring movement has a profound influence 

 on the ring's contribution to decreasing the concen- 

 tration of larvae- in some cases, they may be swept 

 offshore in the entrainment flow of a slowly trans- 

 lating ring; in other cases the ring may catch up to, 

 dilute, and pass the organisms. Finally, if the ring 

 and shelf water are moving at the same rate, the lar- 

 vae may never experience the impact of the ring, or 

 alternatively may be in a region under constant 

 influence. 



The physical effects of a moving ring upon the lar- 

 val fish population can be estimated readily from the 

 previous results; it is only necessarj' to remember 

 that the important quantity is the rate at which the 

 shelf water moves relative to the eddy. If the ring is 

 propagating westward more slowly than the west- 

 ward drift of the shelf water, the organisms are in 

 contact with the ring for longer periods of time, cor- 

 responding to a decreased value for the effective cur- 

 rent [/q- But decreasing the effective downstream 

 flow rate while keeping the eddy size constant is 

 equivalent to increasing the length scale of the shelf 



where c is the speed of translation of the ring. 



If the ring is moving faster than the shelf currents, 

 the situation is somewhat different; now the eddy 

 catches up to the larvae and they are first influenced 

 by a region of onshore flows and then by offshore 

 currents. We can calculate the impact upon the 

 population using the same methods as were 

 employed in deriving Equation (10). For simplicity, 

 we consider a domain which is infinite in x and com- 

 pare the population density in regions which have 

 not felt the ring with that in regions which have pass- 

 ed through the ring. For a ring moving at speed c, 

 the equations describing the effects of the currents 

 upon the population are 



10 



o 



o 

 o 



-i 

 u 



> 



u 



X 



(/) 



I 



w 

 o 

 cc 

 o 



50 



40- 



30 



20 



O 



0.75 



10 20 30 40 50 



L 



LENGTH SCALE IMPACT (KM) 



Figure 6. -The ratio of the number of larvae present far down- 

 stream of the eddy N^ to the number present if there were no eddy, 

 N^( Vq = 0). Contours of the ratio are plotted for different values of 

 eddy size (L) and cross-shelf velocity A. 



321 



