VLYMEN: SWIMMING ENERGETICS OF THE LARVAL ANCHOVY 



• (vi + vj ) ''» 



• cos^tan"^ 7J7 — tan'^ -r^ ) dsdt 

 where {vl +(4^)^)'^^ = 



P g{s) ds = dm. 



dx 



When the above terms are expanded we get, tak- 

 ing account of f/s, 



/ dv d y \ 



dW^ = P As) (Vx Vx +— — f) 

 ^11 ^ ^ dt dt^ 



(i.(gr)-'=dxA. 



4 A 



Integrating dW^.^ + dW^^^iYOva to tg in t and /// 

 to / in X we get the accelerative body work, 



pendent analogue of the function chosen in Hol- 

 will and Miles (1971). 



The motion pictures used were obtained from 

 John Hunter of the Southwest Fisheries Center, 

 National Marine Fisheries Service, NOAA, and 

 the techniques used in obtaining them are de- 

 scribed fully (Hunter, 1972). The particular se- 

 quences used were of fish larvae varying in 

 length from 1.2 to 1.7 cm standard length. All 

 sequences were analyzed starting with the larvae 

 at rest through the sine-wave execution and sub- 

 sequent forward movement to rest again. The 

 X-axis was considered to be parallel to the direc- 

 tion of forward motion as monitored by a point 

 midway between the eyes of the fish. This point 

 was also used to monitor forward progression. 



The sequences were projected with a 16-mm 

 Kodak^ analyst projector on an elevated stand, 

 through a right-angle mirror onto a table en- 

 closed with a darkened viewing hood. At the be- 

 ginning of an excursion the contour of the body 

 was outlined with a fine-point pen on heavy-duty, 

 low-absorbance paper. Once the outline was 

 traced, the next frame was advanced (each frame 

 representing Vi28 of a second) until the larva 



dsdt 



(8) 



+ ^f f Trh^is) 



\fv'x-V'.'\\vxV'x^^^] 

 Ldx ^ J L dt dt -■ 



[-i^(0)T 



— dxdt. 



The total work estimated per excursion is then 



given by the sum of W'g, W^ , and W 



H- 



METHODS 



Motion picture photographs (16 mm, 128 fps) of 

 swimming and feeding anchovy larvae were used 

 to ascertain the various parameters in the pro- 

 posed body displacement function y{x, t) = A {t) 



sm 



277 



{X + 



dx u- 



,^ , t) where A (t) is the wave amp 



K{t) dt 



litude of the propagated wave, A (0 



the 



wavelength andx^. (0 the wave position as func- 

 tions of time. Because of the intermittent charac- 

 ter of the motion, variance with x was not consi- 

 dered as important an independent variable as t 

 in the various functions comprising 3' (x, t). The 

 above displacement function is a general time de- 



came to rest again. The mean excursion time of 

 the larvae examined was 12.9 frames. The contour 

 sequences thus obtained were taken to be repre- 

 sentative of the feeding-searching behavior and 

 were used in elucidating the wave-form param- 

 eters. In addition to the wave-contour param- 

 eters, the midpoint between the eyes was moni- 

 tored for use in determining Vx and Vx. 



When the above contours and position points 

 were obtained along with the proper 

 magnification factors derived from knowledge of 

 the lengths of the fish in a particular film, rele- 

 vant parameter values from the tracings were 



^Reference to trade names does not imply endorsement by 

 the National Marine Fisheries Service, NOAA. 



889 



