ENERGETIC SIGNIFICANCE OF CHANGES IN SWIMMING MODES 

 DURING GROWTH OF LARVAL ANCHOVY, ENGRAULIS MORDAX 



Daniel Weihs' 



ABSTRACT 



The swimming behavior of larval northern anchovy, Engrauhs mordax, in the first few days after 

 hatchmg is different from the intermittent beat-and-glide mode used by older larvae and later stage 

 fish. It is shown mathematically that the bursts of continuous swimming typical of these yolk-sac 

 larvae is the more efficient form of locomotion at this stage, because of their small size. This advantage 

 changes as the larva grows out of the size range in which water viscosity is the dominant factor (small 

 Reynolds numberl. When the larva reaches a length of 5 mm, typical Reynolds numbers are such that 

 intermittent swimming gradually becomes the more economical mode, and this mode is dominant 

 when the larvae reach 15 mm. These analytical results compare well with observed behavioral 

 changes. 



Swimming behavior of the northern anchovy, En- 

 graulis mordax, changes dramatically during 

 growth in the larval stage (Hunter 1972). At 

 hatching, the motion of yolk-sac larvae consists of 

 bouts of continuous, very energetic swimming. 

 This behavior persists for the first 3-4 days of 

 growth, changing to beat-and-glide swimming at 

 the close of the yolk-sac period. The beat-and-glide 

 mode is then retained during the rest of the fish's 

 life. 



Intermittent swimming, or beat and glide, is an 

 efficient mode of locomotion for adult fish, enabl- 

 ing increases by a factor of two or more in the 

 range achieved for a given energy expenditure 

 (Weihs 1974). The problem addressed in the pres- 

 ent paper is whether the changes in swimming 

 behavior mentioned above also have an energy- 

 saving function. The energetic advantage of in- 

 termittent swimming may not exist during the 

 early life stages of fishes because of the importance 

 of viscous effects on small organisms. This study 

 includes setting up a theoretical framework for 

 the analysis of energetics of swimming during the 

 various stages of the fish's life history. The forces 

 and energy required for swimming in the continu- 

 ous and intermittent modes are then calculated 

 and compared at different stages of larval de- 

 velopment. These stages are hydrodynamically 

 distinguished by the nondimensional Reynolds 

 number. Re, which is a function of both length and 



'Southwest Fisheries Center La Jolla Laboratory. National 

 Marine Fisheries Service, NOAA, La Jolla. Calif; present ad- 

 dress; Department of Aeronautical Engineering, Technion, 

 Haifa, Israel. 



speed. The value of the Re defines the relative 

 importance of viscous and inertial effects on the 

 hydrodynamic resistance to motion. 



THEORETICAL MODEL 



Consider a fish swimming in a straight line at 

 constant depth. We shall assume the fish to be 

 neutrally buoyant so that the only forces acting 

 are in the horizontal plane. Fish of negative 

 buoyancy can be included in the following analysis 

 by equating the excess weight of the fish in water 

 ( which is usually not more than 6% of its weight in 

 air) and lift forces produced on the body and fins. 

 However, this is not directly relevant to the pres- 

 ent discussion as these forces are perpendicular to 

 the plane of motion, and shall therefore be left out 

 for simplicity. 



Returning to the horizontal plane, the forces 

 acting are the thrust applied by the fish, T',and the 

 drag on the fish, D, acting in the opposite direc- 

 tion. The drag is a combination of viscous drag due 

 to friction and form drag, which also is an indirect 

 result of the friction caused by areas over which 

 the flow is separated from the fish body. The drag 

 force can be written (Hoerner 1965) as 



D -^pACoU^ 



(1) 



Manuscript accepted Marc)i 1979 

 FISHERY BULLETIN: VOL. 77, NO, 3. 19 



where p is the water density; A the frontal area 

 (seen in frontal projection); Cjj a nondimensional 

 drag coefficient dependent on shape, roughness, 

 and other factors to be discussed below; and ;/ the 

 relative velocity between the fish and the water 



597 



