Turbulence: does vorticity affect the structure and shape of body and fin propulsors?

Over the past century, many ideas have been developed on the relationships between water flow and the structure and shape of the body and fins of fishes, largely during swimming in relatively steady flows. However, both swimming by fishes and the habitats they occupy are associated with vorticity, typically concentrated as eddies characteristic of turbulent flow. Deployment of methods to examine flow in detail suggests that vorticity impacts the lives of fishes. First, vorticity near the body and fins can increase thrust and smooth variations in thrust that are a consequence of using oscillating and undulating propulsors to swim. Second, substantial mechanical energy is dissipated in eddies in the wake and adaptations that minimize these losses would be anticipated. We suggest that such mechanisms may be found in varying the length of the propulsive wave, stiffening propulsive surfaces, and shifting to using median and paired fins when swimming at low speeds. Eddies in the flow encountered by fishes may be beneficial, but when eddy radii are of the order of 0.25 of the fish's total length, negative impacts occur due to greater difficulties in controlling stability. The archetypal streamlined "fish" shape reduces destabilizing forces for fishes swimming into eddies.

Boxfishes (Teleostei: Ostraciidae) as a model system for fishes swimming with many fins: kinematics.

Swimming movements in boxfishes were much more complex and varied than classical descriptions indicated. At low to moderate rectilinear swimming speeds (<5 TL s(-1), where TL is total body length), they were entirely median- and paired-fin swimmers, apparently using their caudal fins for steering. The pectoral and median paired fins generate both the thrust needed for forward motion and the continuously varied, interacting forces required for the maintenance of rectilinearity. It was only at higher swimming speeds (above 5 TL s(-1)), when burst-and-coast swimming was used, that they became primarily body and caudal-fin swimmers. Despite their unwieldy appearance and often asynchronous fin beats, boxfish swam in a stable manner. Swimming boxfish used three gaits. Fin-beat asymmetry and a relatively non-linear swimming trajectory characterized the first gait (0--1 TL s(-1)). The beginning of the second gait (1--3 TL s(-1)) was characterized by varying fin-beat frequencies and amplitudes as well as synchrony in pectoral fin motions. The remainder of the second gait (3--5 TL s(-1)) was characterized by constant fin-beat amplitudes, varying fin-beat frequencies and increasing pectoral fin-beat asynchrony. The third gait (>5 TL s(-1)) was characterized by the use of a caudal burst-and-coast variant. Adduction was always faster than abduction in the pectoral fins. There were no measurable refractory periods between successive phases of the fin movement cycles. Dorsal and anal fin movements were synchronized at speeds greater than 2.5 TL s(-1), but were often out of phase with pectoral fin movements.

Boxfishes as unusually well-controlled autonomous underwater vehicles.

Boxfishes (family Ostraciidae) are tropical reef-dwelling marine bony fishes that have about three-fourths of their body length encased in a rigid bony test. As a result, almost all of their swimming movements derive from complex combinations of movements of their median and paired fins (MPF locomotion). In terms of both body design and swimming performance, they are among the most sophisticated examples known of naturally evolved vertebrate autonomous underwater vehicles. Quantitative studies of swimming performance, biomechanics, and energetics in one model species have shown that (i) they are surprisingly strong, fast swimmers with great endurance; (ii) classical descriptions of how they swim were incomplete: they swim at different speeds using three different gaits; (iii) they are unusually dynamically well controlled and stable during sustained and prolonged rectilinear swimming; and (iv) despite unusually high parasite (fuselage) drag, they show energetic costs of transport indistinguishable from those of much better streamlined fishes using body and caudal fin (BCF) swimming modes at similar water temperatures and over comparable ranges of swimming speeds. We summarize an analysis of these properties based on a dynamic model of swimming in these fishes. This model accounts for their control, stability, and efficiency in moving through the water at moderate speeds in terms of gait changes, of water-flow patterns over body surfaces, and of complex interactions of thrust vectors generated by fin movements.

The effect of size on the mechanical properties of the myotomal-skeletal system of rainbow trout (Salmo gairdneri).

The length and mean cross-sectional area of the myotome of rainbow trout,Salmo gairdneri, scale isometrically with total length (L, cm) and L(2) respectively for fish from 5 to 35 cm in length. The net maximum force, (F, kN·m(-2)) developed by a single twitch of thein situ myotome on one side of the body, and measured normal to the hypural complex increased as; F=1.05×10(-3)·L(2.6), and maximum lateral velocity (W, m·s(-1)) at the hypural plate as; W=0.29 L(-0.47). Maximum power (P, W) increased as; P=7.64×10(-5)·L(3.06). Acceleration rates predicted from these data do not agree well with observations. In addition, except for small fish, predicted maximum speeds differed from those calculated from minimum twitch times of excised muscle blocks and stride length, the popular method for estimating maximum speed. It is suggested that temporal summation of twitches must occur in larger fish. This could provide forces matched to inertial loads which are important in fitness-critical maneuvers.

Mechanical properties of the myotomal musculo-skeletal system of rainbow trout, Salmo gairdneri.

Net forces and velocities resulting from in situ contractions of the myotomal musculature on one side of the body were measured at the hypural bones. Forces, velocities and power were determined with the body bent into a range of postures typical of those observed during fast-start swimming. For trout averaging 0.178 m in length and 0.0605 kg in body mass, the muscle system exerts a maximum normal force of 2.2N at the base of the caudal fin. This force is equivalent to 11.8 kN m-2 based on the mean cross-sectional area of the myotomal muscle. The maximum velocity was 1.11 m s-1, and the maximum mechanical power output, 0.64 W, or 42.4 W kg-1 muscle. Based on estimates of swimming resistance, these results would suggest acceleration rates of 7.5 to 16.5 m s-2, similar to averages observed during fast-starts. Maximum sprint speeds would range from 6.5 to 17.8 body lengths s-1, spanning the range of maximum speeds reported in the literature. It is suggested that maximum speed is limited by interactions between muscle contraction frequency and endurance. Losses in the mechanical linkages between muscle fibres and propulsive surfaces were estimated at about 50% for power with possibly greater losses in force transmission. Maximum force and power did not vary over the range of postures tested, supporting Alexander's (1969) suggestions that white muscle should contract over a small portion of the resting length of the fibres.

Measurement of sublethal metabolic stress in rainbow trout (Salmo gairdneri) using automated respirometry.

Sublethal effects of rotenone on the metabolic rates of rainbow trout (Salmo gairdneri Richardson) were determined. Metabolic measurements were made by the method of increasing velocity steps, using a miniature version of the Blazka respirometer with automatic dissolved oxygen measurement. Regressions of log metabolic rate versus swimming speed (expressed as relative performance) were compared for the toxicant levels tested. Results were interpreted in terms of Fry's classification of environmental factors using metabolic response categories ("Fry's paradigm"). At high rotenone dosages (96 hr. LC 50), reduction in the critical swimming speed and the active metabolic rate (limiting effect) were observed. At lower toxicant levels (0.20 x 96 hr. LC 50) the standard metabolic rate was elevated (masking effect) and the limiting effect disappeared. The elevation in metabolic rate decreased in competition with locomotor energy costs as they increased with swimming speed (modulated masking effect).

The effect of size on the fast-start performance of rainbow trout Salmo cairdneri, and a consideration of piscivorous predator-prey interactions.

The fast-start (acceleration) performance of seven groups of rainbow trout from 9-6 to 38-7 cm total length was measured in response to d.c. electric shock stimuli. Two fast-start kinematic patterns, L- and S-start were observed. In L-starts the body was bent into an L or U shape and a recoil turn normally accompanied acceleration. Free manoeuvre was not possible in L-starts without loss of speed. In S-starts the body was bent into an S-shape and fish accelerated without a recoil turn. The frequency of S-starts increased with size from 0 for the smallest fish to 60-65% for the largest fish. Acceleration turns were common. The radius of smallest turn for both fast-start patterns was proportional to length (L) with an overall radius of 0-17 L. The duration of the primary acceleration stages increased with size from 0-07 s for the group of smallest fish to 0-10 s for the group of largest fish. Acceleration rates were independent of size. The overall mean maximum rate was 3438 cm/s2 and the average value to the end of the primary acceleration movements was 1562 cm/s2. The distance covered and velocity attained after a given time for fish accelerating from rest were independent of size. The results are discussed in the context of interactions between a predator and prey fish following initial approach by the predator. It is concluded that the outcome of an interaction is likely to depend on reaction times of interacting fish responding to manoeuvres initiated by the predator or prey. The prey reaction time results in the performance of the predator exceeding that of the prey at any instant. The predator reaction time and predator error in responses to unpredictable prey manoeuvre are required for prey escape. It is predicted that a predator should strike the prey within 0-1 s if the fish are initially 5-15 cm apart as reported in the literature for predator-prey interactions. These distances would be increased for non-optimal prey escape behaviour and when the prey body was more compressed or depressed than the predator.