KLIKKL AND V\ KOBLliW SKI: WARM ('(IKK ( ;r 1 ,K STKKAM KINGS 



100 



o 



OL 



2 T 



2 (days) 



cr 



t- 



<n 



z 



$ 



g 501- 



o 



H 

 UJ 



2 



5 



EC 



»- 



a 



Vo • 20CM/S 



Vo -q,^ 



Vq .-20CM/S 



LONGSHORE DISTANCE X (K M ) 



500 



Figure 4. -a) The travel time t necessar\' for lanae to 

 reach the point x down the shelf from the spawning site at x 

 = 0. The values of t are computed in the absence of an eddy 

 (Vq = 0) and when an eddy induces onshore ( Vq = - 20 

 cnVs) and offshore (Vq = 20 cm/s) flows, b) The rate of 

 change in numbers of larvae N with distance down the shelf 

 X, plotted against longshore position for the three values of 



LONGSHORE DISTANCE (KM) 



500 



When the flow is onshore (y,, < 0) we can also solve 

 Equations (8) and (9) and find 



N{x,t) = N,it - t) 



U{x) 



(14) 



In this case, the timelike variable t increases less 

 rapidly with x than in the base case. This alone would 

 lead to a slower spatial decay; however, the dilution 

 effect (the UJU factor) counters this. In most cases, 

 the dilution will be stronger than the effects of 

 decreased transit time. 



Perhaps the simplest way to see this is to consider 

 the downstream decay rates when the source of lar- 

 vae is constant in time and the onshore or offshore 

 flows are spatially uniform. The spatial decay rates 

 - ( dN/dx)/N for the three flow cases are 



(15) 



U U dx 



We have plotted these as functions of x in Figure 4b 

 using /^ = 10""^ s""', U^) = 5 cm/s, Vq = ±20 cm/s, and 

 Y = 200 km. With this value for fu, two-thirds of the 

 larvae disappear from the population because of the 

 various biological causes within 4 mo from hatching. 

 Most values of ^x in the literature (e.g., Sissenwine et 

 al. 1983) tend to be higher (see, however, Peterson 



319 



