WEIHS: ENERGETIC SIGNIFICANCE IN ENGRAULIS MORDAX 



is, however, not known at the present time), thus 

 changing during the beat-and-glide cycle. No 

 single value may therefore be taken to describe a 

 given beat-and-glide behavior and an average 

 value has to be used. This adds greatly to the 

 inaccuracy as ji is an exponent. Bearing especially 

 the latter factor in mind, no smooth curves of the 

 type appearing in Figures 1-3 can be expected. 



In order to try and make clear how the transi- 

 tion regime influences the energetics of swim- 

 ming, in spite of the difficulties mentioned, curves 

 such as those from Figures 1 and 3 are reproduced 

 in Figure 4. The purpose of this Figure is to show 

 that by using the correct nondimensional descrip- 

 tion, curves for the viscous and nonviscous re- 

 gimes can be compared. Both the dashed and full 

 curves have similar shape, going to infinity for Uc 

 -> and having a minimum at the higher values of 

 Uc, the values increasing again for U ,■ -* Uf. One 

 must recall that the absolute speeds and sizes are 

 very much different for the two cases, this result- 

 ing from the difference in Uo. the maximum sus- 

 tained speed. t/„ is much larger for the full curves. 

 The dashed curves have (i = \ while the full lines 

 are for 13 = 0. Therefore, calculations at any inter- 

 mediate values of /3 are expected to fall between 

 them. 



Some calculated values appear in Figure 4, for 

 two values of average /3. While they show the ex- 

 pected behavior, their actual values are, as men- 



R,S 



05 



Figure 4. — Energy ratio versus nondimensional speed at vari- 

 ous Reynolds numbers. Dashed lines show the low Reynolds 

 number I viscous) regime, full lines are for high Reynolds num- 

 bers (boundary layers) and. ' , + are at mtermediate Reynolds 

 numbers, for U f = 0.7 and Uf = 0.8, respectively. See Figures 1 

 and 3 for other definitions. 



tioned before, unreliable, because they are based 

 on rough estimates of various coefficients which do 

 not have to be made when /3 = or 1 . These compu- 

 tations are to be taken only as an indication that 

 the expected gradual transition actually occurs 

 and are not to be used for actual calculations. 



Keeping these limitations in mind, one can ten- 

 tatively come to the conclusion that the inter- 

 mediate Re regime is one of gradual transition. 

 The advantage of beat-and-glide intermittent 

 swimming becomes more and more significant as 

 the larva grows, after the 4th day after hatching. 



This conclusion can be strengthened, in a 

 roundabout manner, by a different approach. The 

 ratio of swimming to gliding drag for a given ani- 

 mal is 2 in the low Re regime, and up to 4 for high 

 Re. Therefore taking a higher value of a for the 

 viscous domain calculations can indicate, in a dif- 

 ferent manner, the trend of results when increas- 

 ing Re. This appears in Figure 2, where the dashed 

 line stands for a = 3. It can be seen that this curve 

 is intermediate between typical curves for the vis- 

 cous (Figure 1) and inertial regimes (Figure 3). 



CONCLUDING REMARKS 



It was demonstrated in the previous section that 

 the change in swimming style observed when an- 

 chovy larvae reach the age of 4-5 days is correlated 

 with the passage of the animal ft-om the highly 

 viscous regime to the boundary layer regime. My 

 calculations show that this behavioral change is 

 an adaptive energy sparing mechanism. When the 

 larva is <5 mm long, it can only progress by ac- 

 tively swimming as the enhanced effect of viscos- 

 ity will bring it to a rapid halt when coasting. The 

 yolk-sac, which still exists as a spherical protru- 

 sion, increases the drag even further at this stage. 

 The drag coefficient here is inversely proportional 

 to the velocity so that any low-speed motion is very 

 costly in terms of energy. As a result, interspers- 

 ing coasting and accelerating is not an efficient 

 way of progressing. When the larva is larger (>5 

 mm) and moving faster, viscous effects are concen- 

 trated in a thin layer surrounding the fish and the 

 influence of speed and shape on drag changes. At 

 this stage, it is shown that intermittent motion is 

 the more efficient for fish species such as anchovy 

 which swim in the anguilliform mode. Intermit- 

 tent motion is much less efficient for carangiform 

 swimmers at all sizes (Weihs 1974) which may 

 explain why species such as mackerel swim con- 

 tinuously at all phases of life. 



603 



