SUMMARY Boxfishes (Teleostei: Ostraciidae) are marine fishes having rigid carapaces that vary significantly among taxa in their shapes and structural ornamentation. We showed previously that the keels of the carapace of one species of tropical boxfish, the smooth trunkfish, produce leading edge vortices (LEVs) capable of generating self-correcting trimming forces during swimming. In this paper we show that other tropical boxfishes with different carapace shapes have similar capabilities. We conducted a quantitative study of flows around the carapaces of three morphologically distinct boxfishes(spotted boxfish, scrawled cowfish and buffalo trunkfish) using stereolithographic models and three separate but interrelated analytical approaches: digital particle image velocimetry (DPIV), pressure distribution measurements, and force balance measurements. The ventral keels of all three forms produced LEVs that grew in circulation along the bodies, resembling the LEVs produced around delta-winged aircraft. These spiral vortices formed above the keels and increased in circulation as pitch angle became more positive,and formed below the keels and increased in circulation as pitch angle became more negative. Vortices also formed along the eye ridges of all boxfishes. In the spotted boxfish, which is largely trapezoidal in cross section, consistent dorsal vortex growth posterior to the eye ridge was also present. When all three boxfishes were positioned at various yaw angles, regions of strongest concentrated vorticity formed in far-field locations of the carapace compared with near-field areas, and vortex circulation was greatest posterior to the center of mass. In general, regions of localized low pressure correlated well with regions of attached, concentrated vorticity, especially around the ventral keels. Although other features of the carapace also affect flow patterns and pressure distributions in different ways, the integrated effects of the flows were consistent for all forms: they produce trimming self-correcting forces, which we measured directly using the force balance. These data together with previous work on smooth trunkfish indicate that body-induced vortical flows are a common mechanism that is probably significant for trim control in all species of tropical boxfishes.

SUMMARY Flow in aquatic systems is characterized by unsteadiness that creates destabilizing perturbations. Appropriate correction responses depend on response latency. The time between a disturbance induced by either removal of a flow refuge or striking various parts of the body with a narrow water jet was measured for three species, chosen as examples of modes in teleostean body/fin organization that are expected to affect stability. Creek chub Semotilus atromaculatus is representative of fusiform-bodied soft-rayed teleosts, smallmouth bass Micropterus dolomieu of fusiform-bodied spiny-rayed forms and bluegill Lepomis macrochirus of deep-bodied spiny-rayed forms. Observations were made at 23°C. Loss of refuge resulted in a surge that fish corrected by starting to swim within 129±29 ms (mean ± 2 s . e . m .) for chub, which was significantly shorter than minimal times of approximately 200 ms for bluegill and bass. Slips and heaves induced by water jets initially resulted in extension of the median and paired fins that would damp growth of the disturbance, but otherwise these disturbances were ignored. Yaws and pitches were more likely to cause fish to swim away from the stimulus, making corrections as they did so. There were no differences in latencies for slip,heave, yaw and pitch disturbances within each species, but latencies varied among species. For these disturbances, responses averaged 123±19 ms for chub, again significantly smaller than those of 201±24 ms for bass and 208±52 ms for bluegill. Values for the two centrarchids were not significantly different ( P >0.08). The response latency for rolling disturbances did not differ among species but was significantly smaller than that for other disturbances, with an overall latency of 70±15 ms. The greater responsiveness to hydrostatic rolling instability is attributed to functions requiring an upright posture and differences among species in habitat preferences.

SUMMARY The hydrodynamic bases for the stability of locomotory motions in fishes are poorly understood, even for those fishes, such as the rigid-bodied smooth trunkfish Lactophrys triqueter , that exhibit unusually small amplitude recoil movements during rectilinear swimming. We have studied the role played by the bony carapace of the smooth trunkfish in generating trimming forces that self-correct for instabilities. The flow patterns, forces and moments on and around anatomically exact, smooth trunkfish models positioned at both pitching and yawing angles of attack were investigated using three methods: digital particle image velocimetry (DPIV), pressure distribution measurements, and force balance measurements. Models positioned at various pitching angles of attack within a flow tunnel produced well-developed counter-rotating vortices along the ventro-lateral keels. The vortices developed first at the anterior edges of the ventro-lateral keels,grew posteriorly along the carapace, and reached maximum circulation at the posterior edge of the carapace. The vortical flow increased in strength as pitching angles of attack deviated from 0°, and was located above the keels at positive angles of attack and below them at negative angles of attack. Variation of yawing angles of attack resulted in prominent dorsal and ventral vortices developing at far-field locations of the carapace; far-field vortices intensified posteriorly and as angles of attack deviated from 0°. Pressure distribution results were consistent with the DPIV findings, with areas of low pressure correlating well with regions of attached, concentrated vorticity. Lift coefficients of boxfish models were similar to lift coefficients of delta wings, devices that also generate lift through vortex generation. Furthermore, nose-down and nose-up pitching moments about the center of mass were detected at positive and negative pitching angles of attack, respectively. The three complementary experimental approaches all indicate that the carapace of the smooth trunkfish effectively generates self-correcting forces for pitching and yawing motions — a characteristic that is advantageous for the highly variable velocity fields experienced by trunkfish in their complex aquatic environment. All important morphological features of the carapace contribute to producing the hydrodynamic stability of swimming trajectories in this species.

SUMMARY The kinematics of plaice ( Pleuronectes platessa, L =22.1 cm) and cod ( Gadus morhua, L =25.0 cm, where L is total fish length)swimming at various speeds at the bottom and lifted to heights, h , of 10, 50 and 100 mm by a thin-wire grid were measured. For cod, tailbeat frequency, amplitude, body and fin span and propulsive wavelength were unaffected by h and varied with speed as described for fusiform pelagic species. In contrast, the kinematics of plaice was affected by h . Body and fin spans and propulsive wavelength were independent of swimming speed and h . Tailbeat amplitude was independent of swimming speed, but averaged 1.5 cm at h =0 and 2.5 cm at h ≥10 mm. Plaice tailbeat frequency increased with swimming speed for fish at the bottom but was independent of swimming speed at h =10, 50 and 100 mm,averaging 4.6, 6.0 and 5.8 Hz respectively. Total mechanical power, P , produced by propulsive movements calculated from the bulk-momentum form of elongated slender-body theory was similar for cod and plaice swimming at the bottom but, at h ≥10 mm, P for plaice was larger than that for cod. Plaice support their weight in water by swimming at a small tilt angle. The small changes in swimming kinematics with swimming speed are attributed to decreasing induced power costs to support the weight as speed increases. The contribution of the tail to power output increased monotonically with the tail gap/span ratio, z/B , for z/B =0.23 ( h =0 mm) to z/B =1.1 ( h =50 mm). The smaller tailbeat amplitude of the tail decreased both z/B and the power output for plaice swimming at the bottom. For the maximum body and fin span of plaice, the contribution to power output increased for local z/B values of 0.044 ( h -0 mm) to 0.1 ( h =10 mm) and declined somewhat at larger values of z/B . The smaller effect of the bottom on power output of the largespan anterior body sections may result from the resorption of much of the upstream wake at the re-entrant downstream tail.

Deep-bodied fish, such as the bluegill sunfish { Lepomis macrochirus ), are considered to have relatively larger wetted surface areas for their size than fusiform fish. On the basis of the boundary layer thinning hypothesis attributing high power requirements of undulatory swimming to enhanced friction drag, power (=drag) coefficients should be higher for such fish. Areas are typically normalized with total length, L , as L 2 for comparison among species. Bluegill had a wetted surface area of 0.65 L 2 , compared with areas of about 0.41 L 2 for trout of similar mass. However, absolute areas and volume 2/3 of bluegill and trout were similar. Power requirements and power coefficients calculated from kinematics during steady swimming were lower for bluegill sunfish than for cruisers, such as trout, and power coefficients were also lower than those of accelerators, such as tiger musky. Large body depth also damps inertial recoil arising from the side force generated largely by the tail. Inertial energy losses appear to be more important contributors than friction to mechanical power requirements.

Fast-start performance of rainbow trout (mass 0.187±0.022kg; mean±2S.E., N = 10) was measured in water of various depths. Relative water depth was defined as z/B , where z is the water depth measured from the air/water surface to the longitudinal midline of the body and B is the span of the caudal fin, 0.062±0.004m. Relative water depths (at absolute depths) tested were; 0.31 (at 0.05m), 1.11 (at 0.1m), 1.92 (at 0.15m), 2.73 (at 0.2m) and 7.56 (at 0.5m). Performance was defined in terms of the motion of the centre of mass as measured by the turning radius and the cumulative distance travelled in a given elapsed time. Turning radius was not affected by water depth and averaged 0.018±0.003m. Distance travelled was a positive function of water depth, although paired t -tests showed no significant effect of depth at 0.15 and 0.2 m after about 70 ms. Energy dispersion due to the formation of surface waves increased with decreasing relative water depth. The largest energy dispersion in wave formation at a relative water depth of 0.31 averaged about 70% of the useful mechanical work performed in deep water. Energy dispersion in wave generation was negligible for relative water depths larger than approximately 3. Energy dispersion is similar to that for rigid streamlined bodies moving at constant speed

Station-holding performance was determined on a smooth substratum and on a grid substratum for three species of benthic fishes differing in body shape, surface texture, density, friction coefficient and behavioural repertoire. The grid was made of wires parallel to the flow, which raised fish into the free stream. Limited observations were also made on the benthopelagic cod. Station-holding performance was evaluated at two speeds. The first was defined as the slip speed, above which activities such as swimming, fin-beating, body arching, body clamping and gripping the substratum were required to hold position on the substratum. The second was defined as the swim speed, when fish began swimming out of ground contact. Cod and lasher started swimming when they began slipping, so that slip and swim speeds were the same, averaging 6cms −1 for cod and 32cms −1 for lasher on the smooth surface. Body postures and fin-beating delayed swimming from a slip speed of about 20cms −1 to swim speeds of 47–58cms −1 for plaice and rays. The grid had relatively little effect on slip and swim speeds of plaice and rays. Lasher grasped the grid with their pectoral fins, increasing swim speeds to 55cms −1 . Amputation of the posterior portion of the median fins of plaice reduced swim speeds on the smooth surface to 36cms −1 . Amputation of the pectoral fins of lasher reduced the swim speed on the grid to 38cms −1 . Estimates of drag coefficients for fish were made using published data for blisters. These were used to determine lift coefficients and the effects of grasping the substratum on the friction coefficient. Comparison of lift coefficients of rays on the smooth substratum with those on the grid showed that flow beneath the body reduced lift. Amputation of the posterior of the median fins of plaice and the rarity of body posturing by plaice and rays on the grid showed that the major role of this station-holding behaviour was reduction of lift through induction of flow beneath the body. Lashers were able to hold station at speeds comparable to plaice and rays when they could utilize the small amount of surface structure of the grid to increase friction. Benthic fishes tend to have either ‘flattened’ plaice- or ray-like forms with low drag coefficients but high lift coefficients, or more fusiform lasher-like forms with high drag coefficients and low lift coefficients. High-lift forms use behaviour to reduce lift coefficients, whereas high-drag forms use behaviour to increase friction.

Locomotor kinematics of tiger musky ( Esox sp.) and rainbow trout ( Salmo gairdneri ) were measured at ‘steady’ swimming speeds of up to 85 cm s −1 . Tail beat frequencies of musky were approximately 2 Hz higher than those of trout at any swimming speed, but tail beat amplitudes were 0.04L (where L is total body length) smaller. The product of these two variables was similar for the two species at any speed. The length of the propulsive wave was independent of speed, and was 0.8L for musky, somewhat smaller than the value for trout, 0.9L. The depth of the caudal fin trailing edge of trout was greater than that of musky, but the greater depth of the posteriorly located median fins of musky also contributed to thrust production. The cosine of the angle of the trailing edge to its beat plane showed the same phase relationship with lateral displacement in both musky and trout. It increased with speed for both species, and values for musky were slightly smaller. Thrust power requirements of musky and trout were similar. Thrust (= drag) coefficients of musky were 1.55 times larger than those for trout: this is roughly as expected on the basis of the larger proportion of the total area of musky located caudally and the higher drag coefficients in this region of the body. Lateral recoil movements of musky were unexpectedly smaller than for trout and were associated with smaller energy wastage from undamped recoil movements. The large recoil expected for the body form of musky was damped to some extent by higher tail beat frequencies, although this entailed some loss in Froude efficiency. Otherwise, no hydrodynamic explanation for the small recoil movements of musky was apparent. It is suggested that the myotomal muscles could be involved in minimizing recoil. The esociform morphology incurs costs in steady swimming, in comparison with generalist cruises, because of reduced sprint speeds for fish of a given length or increased power requirements for fish of a given mass.