Is the High Cost of Body/Caudal Fin Undulatory Swimming Due to Increased Friction Drag or Inertial Recoil?

Most studies of undulatory body and caudal fin swimming have focused on strong swimmers from pelagic or stream habitats (e.g. Brett, 1964; Beamish, 1970; Magnuson, 1978; Graham et al. 1990; Webb et al. 1984). Analysis of cruising and prolonged performance of such fishes has shown that mechanical power requirements of ‘steady’ swimming, where variation in speed is small, are 3–5 times greater than for an equivalent rigid reference (see Lighthill, 1975; Webb, 1975; Blake, 1983). The reference is typically a flat plate of equal area at the same Reynolds number, Re, where Re=Lu/v and L is fish total length, u is swimming speed, and vis the kinematic viscosity of water. Q. Bone suggested that the high cost of swimming might be attributed to boundary layer effects increasing friction drag, which was called ‘boundary layer thinning’ (Lighthill, 1971).

Inviscid models that simulate the pressure distribution around a swimming fish also generate power coefficients elevated by a similar factor above those of a rigid reference (Lighthill, 1975; W. W. Schultz, personal communication). In some models, energy losses associated with undulatory self-propulsion can only be lost via inertial effects (W. W. Schultz, personal communication). One source of inertial energy loss is lateral recoil of the anterior of the body as a result of side forces generated by the tail (Lighthill, 1975, 1977).

Deep-bodied fish are considered to have relatively large surface areas of 0.6–0.7L² compared to 0.4–0.5L² for fusiform fish (Bainbridge, 1961; Webb, 1975,1977). However, large body depth also damps recoil. Therefore, if enhanced friction drag is the major cause of high swimming costs in body/caudal fin undulatory propulsion, mechanical power requirements will be relatively higher for deep-bodied fish than for fusiform fish. Alternatively, such fish might have lower power requirements if body recoil were important. These alternatives are explored here using new observations on bluegill sunfish compared with data obtained using similar protocols for rainbow trout and to a lesser extent tiger musky (Webb, 1988a).

Bluegill sunfish (Lepomis macrochirus Rafinesque) were obtained from the Michigan Department of Natural Resources Saline laboratory. They were held in 110-1 tanks with continuous water replacement of 200 % per day. Dissolved oxygen levels were maintained close to air-saturation using air stones. Fish were fed a maintenance ration of worms and chopped fish. Fish used in the experiments averaged 15.6±0.9cm (±2 S.E.; N=10) in total length and weighed 62.26±9.71 g.

Experimental methods have been described in detail by Webb (1988a). Briefly, individual fish were selected at random from stock and swam overnight (18–20 h) at 5–10 cm s⁻¹ in a flume (Vogel and LaBarbara, 1978) with a square observation section, 15 cm wide and 15 cm deep. Next day, locomotor kinematics and behavior were recorded on ciné film (200 frames s⁻¹) and video tape (60 fields s⁻¹) during an increasing velocity test with speed increments of approximately 5cms⁻¹ every 2min (Farlinger and Beamish, 1977). Film and tapes were subsequently analyzed frame-by-frame to record the following data for both the caudal fin trailing edge and the trailing edge of the median fins: frequency, amplitude, span and angle to the plane of lateral motion. The length of the propulsive wave and the amplitude distribution along the body length were measured. Sequences analyzed met the following criteria: there were at least five successive tail-beats, speed did not vary by more than 5 %, and fish were located at the center of the observation chamber.

Wetted surface area was 159±20cm², measured at the end of an experiment as the sum of body and fin circumferences at 1cm intervals along the body length. Myotomal muscle was dissected from the skeleton and skin and weighed, giving an average of 23.13±4.03g.

Total power generation was the sum of that for the caudal fin trailing edge plus that of the non-re-entrant portion of the upstream median fins (Lighthill, 1975; Webb, 1988a).

Bluegill are compared with previously reported data on rainbow trout, Oncorhynchus mykiss, and tiger musky, Esox sp., both swimming in the subcarangiform mode (Webb, 1988a). To evaluate the basis for enhanced resistance during steady swimming, the critical comparisons are with trout, one of the most intensively studied fusiform species, since musky appear to have as yet unidentified mechanisms to reduce recoil energy losses.

During steady caudal fin propulsion, bluegill tail-beat frequencies increased with swimming speed (Fig. 1). Frequencies were intermediate between those of trout and musky, but increased at a greater rate with swimming speed. Tail-beat amplitude increased slightly with swimming speed, but the slope was not significantly different from zero. The average tail-beat amplitude was 1.5±0.2cm (0.1 L). The specific amplitude was lower than the value of 0.2 L commonly reported for fusiform cruising fish (Hunter and Zweifel, 1971; Webb, 1975; Blake, 1983), but was similar to that of 0.1 L for musky (Webb, 1988a).

The span of the caudal fin and the combined span of the dorsal and anal fins did not vary with swimming speed, and averaged 4.2±0.3cm (0.27 L) and 6.1±0.4cm (0.39 L), respectively. Fusiform fish typically have caudal fin spans of about 0.2–0.25 L (Webb, 1988a).

Values of cos0 for the trailing edges of both the caudal fin and of the anterior median fins increased with swimming speed (Fig. 2) and were similar in magnitude to those reported for these fins of musky.

The length of the propulsive wave was independent of swimming speed and averaged 15.8±l.lcm (1.01 L). The specific wavelength was larger than typical values of 0.7–0.8L reported for fusiform subcarangiform fishes (Wardle, 1975; Videler and Wardle, 1978; Videler, 1981).

The amplitudes of lateral movement were smallest at a point located at 0.2 L, measured from the nose (Fig. 3), and increased anteriorly and posteriorly from this point (Bainbridge, 1963). However, amplitude did not increase continuously towards the tail, but increased slowly to a plateau in the region of the median fins before increasing rapidly over the caudal fin and tail to the maximum at the caudal fin trailing edge. This pattern is similar to that found in trout, but relative amplitudes of bluegill (normalized by the caudal fin trailing edge amplitude) were slightly lower (Fig. 3). Since trailing-edge amplitudes of bluegill were about half those of trout, absolute lateral movements along the entire body length were substantially lower than those of trout.

The rate of working (power) of the body/caudal fin propulsive system increased with swimming speed (Fig. 4). Rates of working were lower than those for trout and higher than those for musky (Webb, 1988a). Power coefficients (Fig. 5) were substantially lower for bluegill than for trout and musky at the same Re.

This requires revision of the original hypothesis. Originally, higher power requirements were expected for the fish with the relatively larger surface area estimated from the traditional method of normalizing area with L². Since S_v is similar for trout and bluegill, both would now be expected to have the same rates of working and the same C_P at the same Re.

Comparisons between bluegill and trout might also be affected by the difference in lengths of the fish used in the experiments. Although both had similar areas, the area of trout extends over a longer downstream length than that of bluegill. The thickness of the boundary layer grows approximately with the square of distance from the nose (Schlichting, 1968). As a result, local drag coefficients tend to decrease with distance from the nose, and the average drag coefficient is lower for a longer body with the same wetted surface area as a shorter body. On this basis, trout might be expected to have lower power coefficients than bluegill.

Differences in length might also affect mean power coefficients if transition to turbulence occurred relatively closer to the nose of the longer fish. In practice, flumes used for studying fish swimming, including that used here, introduce microturbulent flow to provide rectilinear flow profiles. The intensity of turbulence exceeds critical values for transition (Webb, 1975). In addition, swimming movements probably induce turbulent boundary layer flow (Webb, 1975). Therefore, it is unlikely that the differences in length of the fish used in these experiments would have a significant effect on power coefficients and thus affect the conclusions.

In practice, C_P was lower for bluegill than for trout, and rates of working for bluegill were 1.5 times lower on average than for trout. Thus, these results do not support the boundary layer thinning hypothesis, irrespective of how relative area is defined.

Lighthill showed that energy wastage in recoil is large when ζ is large, but lateral recoil is effectively damped by the anterior virtual mass of the body when ζ is small.

It is important to recognize that the models used in this analysis are imprecise. Although the correlation between predictions of power requirements from slender-body theory and from biological expectations is remarkably good, calculated forces and power are probably only reliable to within an order of magnitude (Weihs, 1973; Yates, 1983; Webb, 1988b). Nevertheless, the various theories used in studying fish swimming appear to be reliable in ranking mechanical performance (Webb, 1988b). Similarly, Lighthill’s analysis of recoil correctly applies only to carangiform fishes with a good separation of mass centers associated with thrust and inertial damping of recoil. Again, the model accurately illustrates the principal factors of body/caudal fin morphology and function that are critical in determining recoil in other swimming modes where thrust generation is concentrated at the tail, as with bluegill and trout (Webb, 1988a). Therefore, in spite of considerable uncertainty about the actual values of thrust and resistance, this analysis strongly suggests that bluegill swimming power requirements are lower than those of trout. Furthermore, this is probably attributable to reduced recoil energy losses, this being a property of the deep-bodied shape.

The conclusion that enhanced friction drag is less important than is usually assumed is at variance with several interpretations of other experimental and comparative observations. For example, reduction in area by forked tails, culminating in the lunate tail of thunniform animals, has been considered to be a mechanism for minimizing friction drag in that region of the body where drag enhancement by boundary layer thinning would be greatest (Lighthill, 1975; Webb, 1982, 1984). However, as Lighthill has regularly pointed out (Lighthill, 1975), this will also reduce energy losses by reducing the side force and, hence, recoil. Similarly, Hunter and Zweifel (1971) found that tail-beat frequencies increased at different rates among fish species and this correlates with tail area. Thus, species with larger tail areas work harder at a given speed, which is consistent with a hypothesis of enhanced drag (Webb, 1982). Following Lighthill (1977), this trend could be explained by differences in energy wastage in recoil. Finally, prolonged swimming performance is virtually unaffected by caudal fin amputation in spite of the fact that this must reduce thrust (Webb, 1973). Since fin amputation reduces fin area, I originally suggested that the small effect of amputations on performance occurred because friction drag, enhanced by boundary layer thinning, was reduced by a similar amount to the reduction in thrust (Webb, 1973). These data are consistent with an alternative explanation, that energy losses following tail amputation occur through reduction of the side force and hence reduction of energy loss in recoil.

With the wisdom of hindsight, observations previously used to support the boundary layer thinning hypothesis fail to discriminate between hypotheses for resistance enhancement via drag and others, such as resistance enhancement by inertial energy losses. In contrast, the observations on deep-bodied bluegill suggest that the latter sources for the high costs of undulatory body/caudal fin propulsion should be given greater weighting in analyzing the functional morphology of aquatic vertebrates.

This work was supported by the National Science Foundation grants PCM-8401650 and DCB-8701923.