P'l.lFRI. AXinVRORI.FWSKI: WARM CORK (H'I.K STKKAM RINCS 



Finally, we make recommendations for further 

 investigations of the influence of warm core rings on 

 the northeast coast marine ecosystem. 



Our very simplified modelling approach to the 

 problem of resolving biological distributions in a 

 variable oceanic tlow regime could, with proper 

 reparameterizations, be applied to estimating the im- 

 pact of rings on chemical distributions as well -an 

 example would be determining the distribution of 

 pollutants dumped in deepwater dumpsite 106. For 

 variables which do not behave as passive particles in 

 the flow, the model has limitations. Vertical migra- 

 tion behavior by fish larvae may play an important 

 role in their distribution which is not resolved by our 

 preliminary modelling. Other potentially important 

 details, such as the mechanism for mixing on the 

 shelf, have also not been included in this first, 

 simplified calculation. Nevertheless, we feel that the 

 results are extremely suggestive, indicating ways to 

 examine existing data sets and hypotheses to be 

 tested in future field studies. 



THE MODEL 



There are many possible approaches to modelling 

 the effects of rings upon fish larvae, ranging from 

 simple order-of-magnitude estimates to complex 

 physical models which predict the mean and varying 

 currents from winds, heating, topography, and coast- 

 lines. The water motions could then be coupled with 

 complex biological models of spawning, predation, 

 growth, and mortality. However, we are not yet at 

 the stage where such a full-scale calculation is really 

 justifiable; we do not understand enough about the 

 physics of the shelf-slope region and the rings or 



enough about larval fish biology to ensure that only 

 important processes are included and that these are 

 being properly represented in our numerical model. 

 In addition, the questions we wish to address are 

 fairly simple ones: How large could the impact of 

 rings upon larval fish populations be and how do 

 these impacts depend upon the flow structure and 

 translational speed of the rings? We, therefore, shall 

 take the simplest approach to the problem of esti- 

 mating our primary variable, the larval fish density 

 (or abundance). The various processes which affect 

 the population distribution will be represented in the 

 model in an almost schematic form. The actual popu- 

 lations vary in all three dimensions and in time, but 

 we shall include only the downstream and time vari- 

 ations in the model. Likewise, the actual current pat- 

 terns are quite complicated and we choose only to 

 represent the impact of the ring-induced currents by 

 a specification of the flow at the outer edge of the 

 shelf, with onshore flow ahead of the ring and off- 

 shore flow behind the eddy. The mean downshelf 

 drift currents will also be included. The biological 

 processes of predation, physiological mortality, and 

 metamorphosis out of the planktonic larval stage will 

 be represented simply as a loss rate f^ which will be 

 assumed to be independent of space or time. With 

 these simplifications, the general equation governing 

 the density n{x,y,z,t) of the planktonic larvae can be 

 reduced to a manageable form 



d d d d 



— n + — un + — im + — wn = - [xn. 



dt dx dy dz 



(1) 



We shall use the geometry shown in Figure 2 with x 

 the downshelf coordinate, y the offshore coordinate. 



/SOURCE 

 OF 5 

 X .  . M-ARVAE J 



Figure 2. -Schematic diagram of the geometry 

 assumed in the mathematical model. Y is the shelf 

 width, h is the average depth, and U is the average 

 longshore velocity of the shelf w^ater. 



315 



