WEIHS ENERGETIC SIGNIFICANCE IN ENGRAULIS MORDAX 



velocity Uf, varying the initial velocity {/, to ob- 

 tain different average speeds. 



The main result of this Figure is that S is always 

 >1, i.e., for the speeds and sizes at which viscous 

 effects dominate continuous swimming is always 

 more efficient. This calculation is based on the 

 relation Cq « Re"' and is therefore valid for Re up 

 to 10. Larval anchovy tend to swim at speeds of 

 about 0.8 body length/s (Hunter 1972) when 

 swimming intermittently. Thus the Re typical of 

 3-day-old larvae whose length (Zweifel and 

 Hunter^) is about 4 mm at 18° C is also about 10. At 

 age 3 days, larvae spent <20% of the time swim- 

 ming intermittently, but 2 days later (Hunter 

 1972, fig. 1) about 90*7^ of the time is spent in 

 beat-and-glide motion. This level of intermittent 

 swimming is retained thereafter. This sharp 

 change coincides with the time the animal "grows 

 out" of the viscous regime (the Re is essentially 

 proportional to fish length squared ), e.g., when the 

 larvae is 5 mm long, the Re is 20. 



Recalling that at high Re, beat-and-glide 

 swimming is the more efficient motion (Weihs 

 1974), the energy saving obtained is probably one 

 of the reasons for the observed change in swim- 

 ming behavior. 



The fact that the average continuous speeds are 

 much higher also results in savings of energy. For 

 a 3-4 mm long larva, swimming at over 1 cm/s 

 brings it again to Re of over 20, so that the drag 

 coefficient is smaller, and some coasting at the end 

 of the bout of continuous swimming is possible. At 

 lower Re, in the purely viscous regime, no coasting 

 is possible as the inertial effects are negligible and 

 motion ceases immediately when oscillations stop. 

 It is therefore advantageous for the fish, for hydro- 

 dynamic reasons, to swim continuously during the 

 first few days of the larval phase, changing to 

 beat-and-glide swimming later on. It should be 

 noted here that the present calculations and data 

 are for a water temperature of 17°-18° C. Both 

 viscosity of water and the growth rate of larvae 

 (see footnote 2) depend on the temperature, so that 

 data collected under different ambient conditions 

 might lead to a later (or earlier, if the temperature 

 is higher) change of swimming mode. 



Further examination of Figure 1 shows that for 

 each terminal velocity in the beating stage there is 



a value of U^ for which the ratio S attains a 

 minimum (marked by the dashed line). The value 

 of this minimum approaches unity and the curves 

 become more shallow as Uf increases. Thus, if an 

 anchovy larva swims intermittently at low Re, it 

 should do so at high average speeds, so that the 

 energy penalties incurred due to swimming in the 

 beat-and-glide mode are minimal. 



Figure 1 also shows that the lowest penalties for 

 using intermittent swimming are obtained when 

 Uf approaches unity, for the whole^range of aver- 

 age speeds. Therefore, the value Uf = 0.995 was 

 chosen for calculations of the effect of varying a. 

 (the ratio of swimming to coasting drag). These 

 appear in Figure 2, where the dependence of S on 

 U^ is shown. The range of values of a to be expected 

 in nature is described by the shaded area, showing 

 as expected that the smaller the a the more advan- 

 tageous is continuous swimming. When a>2, 

 which can only happen at higher Re, a range of 

 values of [7;. and Uf exists where S is smaller than 

 unity, i.e., intermittent swimming is more 

 efficient. This is shown by the dashed curve on 

 Figure 2 where for Of = 0.995 and 0.79<[/,<l, 

 S<1. This curve will be discussed later, in refer- 

 ence to the transition region between the low and 

 high Re domains. 



The results discussed above all dealt with the 

 low Re range. For comparison, we now show the 

 equivalent energy ratio for high Re, i.e., the do- 

 main relevant to larger larvae as well as adult 

 anchovy (>15 mm long). The results presented 



a = 3\ 



^Zweifel, J. R., and J. R Hunter 1978. Temperature 

 specific equations for growth and development of anchovy {En- 

 graulis mordax) during embryonic and larval stages. Unpubl. 

 manuscr., 13 p. Southwest FisheriesCenter.NMFS.NOAA, P.O. 

 Box 271, La Jolla, CA 92038. 



05 



Figure 2. — influence of changes m ratio of swimming drag to 

 gliding drag a on the energy ratio S, versus nondimensional 

 average speed Uc Shaded area is the range of possible a at low 

 Reynolds numbers, tjf = 0.995 (See Figure 1 for definitions). 



601 



