FISHRRY BULLETIN: VOL. 74, NO. 3 



toring the flow. The solution of such problems lie in 

 the realm of classical hydrodynamics. See Lind- 

 gren (1967) for a brief, but explicit statement of 

 the hydrodynamics involved. Fishes leave no wake 

 in the usual sense of the word, but do leave a series 

 of dying vortices, alternately on either side of the 

 swimming axis of their producer. The rotational 

 direction of the flow within the vortices on one side 

 is always the same and is opposite to the rotation 

 of those on the other side. The flow within the 

 vortices is such that, on the side nearest the axis of 

 the fish producing them, the flow is opposite to the 

 direction of travel of that fish, while on the side 

 away from the axis the flow is in the same direc- 

 tion of travel as the fish. These rotational direc- 

 tions are opposite to those of vortices formed in a 

 typical Karman trail produced by a rigid solid. A 

 following fish thus has the choice of swimming 

 through the side that would help it on its way or 

 the other that would retard it. Swimming through 

 a vortex center would push the head of the fish to 

 one side before the center was reached and to the 

 other side after the center had been passed. The 

 fish that follows is normally found in the water 

 flow that is in its direction of swimming, see Rosen 

 (19r)9), Hreder (1%.")), and Weihs (1973a). This 

 arrangement evidently helps the locomotor efforts 

 of all but the lead fishes. As the energy in the 

 vortices dissipates rapidly it is doubtful if more 

 than the immediately following fishes benefit 

 significantly. As each fish produces a similar 

 short-lived set of vortices there is no appreciable 

 additive effect of successive rows of fish ahead. 

 Thus all the fishes after the first transverse row 

 receive approximately the same energy input 

 from the vortices, so long as they remain in the 

 specified positions. The value of this has not been 

 measured as yet or even estimated. 



These friction reducing effects evidently in- 

 fluence small fishes to sometimes closely associate 

 with much larger, usually solitary, fishes of other 

 affinities. The small attendant fishes evidently 

 gain locomotor advantages that are otherwise only 

 obtained by schooling with their own kind. Many 

 authors, including Breder (1959, 1965, 1967) and 

 Aleev (1968), have noted a variety of such fishes. 

 These fishes station themselves close to and in 

 definite positions relative to the larger fish, often a 

 shark. The behavior is habitual, as in Seriola, but 

 may be occasional, as in Caranx. Shuleikin (1958) 

 discussed the hydrodynamics of Naucratcs ductor 

 (Linnaeus) in its persistent association with large 

 sharks. 



Weihs (1973a) indicated additional energy sav- 

 ing advantages consequent on fish swimming his 

 diamond pattern; the channeling effect of rows of 

 similar fishes, the effects of the phase of the 

 tail-wagging of one fish with respect to the tail 

 phases of its near neighbors, and the extent of 

 length variations in the participating fishes. He 

 calculated this variation as up to 50%. Actually 

 over 60% variation has been found in unquestion- 

 able schools (Breder 1954), although it is impossi- 

 ble from this data to determine the permanency of 

 such groups or the efficiency loss at this greater 

 range of variation. 



Active fishes, especially schooling types, lack the 

 protuberances and hollows often present on the 

 bodies of sluggish fishes. Aleev (1963) enumerated 

 many instances of the latter. He indicated that 

 this lack of streamline integrity leads to the 

 production of minor vortices and that these dis- 

 turbances, depending on their size and point of 

 origin, could lower the locomotor efficiency of a 

 fish. The utility of the larger terminal vortices, 

 here under discussion, could be reduced or de- 

 stroyed, thus eliminating one of the advantages of 

 .school formation. 



Turbulent Friction Reduction 



Until recently, students of fish locomotion were 

 not in agreement concerning what function in 

 relation to swimming, if any, was served by the 

 presence of the mucus that covers the bodies of 

 living fishes. Aleev (1963), in a well-documented 

 review, indicated that he agreed with Richardson 

 (1936) and Gero (1952) that whatever part it may 

 play, the effect must be very small. That this could 

 not be so was mentioned by Rosen (1959) and 

 Walters and Liu (1967). Recent advances in hy- 

 drodynamics now indicate clearly that it has a very 

 considerable role. 



Polysaccharides are known to be released by a 

 variety of aquatic organisms, both plant and 

 animal. One of the effects of the presence of those 

 forming long-chain molecules is friction reduction 

 in turbulent water flow. Some of the history of the 

 development of this information was recorded by 

 Newton (1960), Barnaby and Dorey (1965), and 

 Hoyt (1966, 1968, 1972, 1975). These papers dis- 

 cussed naturally occurring polysaccharides from 

 algae as well as synthetic high polymers, some of 

 the latter being used for very practical purposes as 

 very efficient reducers of turbulent friction. The 

 application of extremely small amounts of such 

 materials can reduce drag by over 60%. 



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