Unsteady turbulent boundary layers in swimming rainbow trout

Skin friction is a major source of resistance to a swimming fish (Webb, 1975). The possibility that compression of the boundary layer due to undulatory swimming motions induces a large increase in the drag forces originating from skin friction is termed the Bone–Lighthill boundary layer thinning hypothesis (Lighthill, 1971). It has long provided a crucial argument for evaluation of the power requirements of aquatic animals during undulatory swimming. However, there was no conclusive evidence for this hypothesis until Anderson et al. (2001) directly measured the fish boundary layer using the particle tracking velocimetry (PTV) technique. The physical demands on the fish in moving forward in a turbulent flow environment are high as a result of the growing mechanical perturbations for coordinated undulatory motion (Pavlov et al., 2000; Webb, 2004a). Given the metabolic benefits of a lowered cost of locomotion for a given swimming speed, and the complex interaction of boundary layers, drag and thrust production, it seems reasonable to assume that active flow sensing by fish could contribute to improving in the efficiency of locomotion. Indeed, active flow sensing by the lateral line has been shown to be important in allowing rainbow trout Oncorhynchus mykiss (Walbaum 1792) to modify their rhythmic motor pattern profile (Kármán gait; Liao et al., 2003a). This is a hydrodynamic mechanism that enables rainbow trout to reduce their axial muscle activity, which implies an adaptive response to reduce the cost of locomotion (Liao et al., 2003b). The lateral line of fish consists of two varieties of mechano-receptive organs: superficial neuromasts and canal neuromasts. Both contain mechanosensory hair cells embedded within the epithelium and are coupled to the cupula, a gelatinous structure. The cupula transmits hydrodynamic forces from the shear flow near these receptors to deflect the hair bundles and, thereby, generates a nervous response (McHenry et al., 2008). Naturally, these specific characteristics lead to an expectation that superficial neuromasts that lie on the external skin surface of the fish are directly deflected as a result of the wall shear stress acting on the fish surface in rhythmic patterns that are associated with body motion.

The present study's fundamental objective was to characterize the unsteady boundary layer phenomena that are caused by the mechanical interaction with the undulatory surface of steadily swimming rainbow trout. Thus, we examined the oscillatory motion-dependent behaviour of boundary layers at various positions on the surface of the fish. The measurements were conducted with the particle image velocimetry (PIV) technique in a flow condition at Reynolds numbers of the order of Re=4×10⁵, which suggest a transitional flow regime from laminar to turbulence [the critical values typically are Re=3.5–5.0(×10⁵); Schlichting, 1979]. PIV produces non-intrusive velocity measurements for instantaneous velocity vector fields. It measures flow velocities by illuminating only tracer particles in the plane of interest by an appropriate light source (Raffel et al., 1998). The PIV technique, which is based on statistical correlation of small interrogation areas with a high particle density, offers significant advantages for the direct determination of the surface-normal gradient of longitudinal velocity (Eqn 1) and, hence, wall shear stress in a highly heterogeneous flow field that would otherwise require an indirect means of approximation, such as using an equivalent manmade rigid body. Therefore, the PIV algorithm is more sensitive to the velocity fluctuation component, particularly in transient turbulent boundary layers. However, the PTV is inferior in measuring spatial velocity gradients, because the algorithm uses a relatively sparse seeding. Nevertheless, the PTV algorithm provides a reliable predictor for tracking individual particle images when working with image sequences (cf. single image pair) but it also requires a predictor-corrector scheme to match particles between images (Raffel et al., 1998). In turbulent flows, where there is an entire spectrum of eddies with a wide range of dimensions, the eddies may increase the uncertainty of velocity interpolation in the PTV algorithm. This is due to the low signal-to-noise ratio (SNR) that corresponds to the difference between peak and second peak correlations in cross-correlation-based PIV, and overlapping of particle images (Raffel et al., 1998).

Here, we present boundary layer-related parameters and an overall profile of unsteady boundary layers over the surface of steadily swimming rainbow trout. We compare these measurements with data for different species that have been published by Anderson et al. (2001). This comparison will contribute to a greater understanding of the effect of a species-specific manner of swimming on the mechanical interaction between the propulsive surface and surrounding water, which is responsible for the specific flow behaviour observed. Measurement at one speed in a controlled flow environment with known turbulence intensity will provide a starting point for exploration of the real world in which hydrodynamic disturbances are sensed by the fish.

The surface of rainbow trout (body length L=0.305±0.020 m, mean±s.d., N=4) was divided into three regions based on the arc-length (l_x) of the fish surface measured from the rostrum (Table 1). These regions were: the pectoral region (l_x=85±3 mm, N=2), the pelvic region (l_x=131±18 mm, N=3) and the posterior region (l_x=207±14 mm, N=3). The time averages of the maximum tangential flow velocity out of the edge of the boundary layer that are normalized by the free-stream velocity (U_e/U; Fig. 1A) reached a maximum value of 1.24±0.05 (N=3) in the pelvic region when the fish surface was moving towards the free-stream flow (convex-motion phase). This U_e/U value and the 1.19±0.06 U_e/U (N=3) in the same surface region, when the fish surface was retreating from the free-stream flow (concave-motion phase), were significantly greater than the 1.05±0.06 U_e/U (N=4) over a comparable surface region of the rigid body that had been placed in parallel with the free-stream flow (Tukey's HSD test; d.f.=7, versus convex: P<0.01, versus concave: P<0.05). There was no statistically significant position-dependent difference in the U_e/U ratio within the same motion phase or rigid body (ANOVA; d.f.=2, 5; P>0.05).

The time average of the boundary layer thickness (δ) in the pectoral region (6.00±1.31 mm, N=2) in the concave-motion phase significantly exceeded that over the rigid-body surface (1.46±0.37 mm, N=3) in a comparable surface region (Tukey's HSD test; d.f.=4; P<0.05; Fig. 1B). However, there was no statistically significant motion-dependent difference of the δ between comparable surface locations in the other surface regions (ANOVA, d.f.=2, 7; P>0.05). The colour scales for the velocity field over the rigid-body surface (Fig. 2) illustrate clearly the nature of boundary layer behaviour, in which the thickness increases with increasing l_x (and hence the local Reynolds number, Re_x, based on the l_x). Indeed, a thin boundary layer covers the fish from the head part (δ=0.92±0.15 mm, N=2) to the pectoral region, although the boundary layer grew rapidly on the posterior half of the rigid-body surface. The δ reached about 10 mm near the tail. The momentum thickness (θ) is an important measure. It represents the distance from the fish surface through which the same momentum that was removed as a result of the presence of the boundary layer could flow. Using θ as a characteristic length scale and U_e as a characteristic velocity scale, the Reynolds numbers (Re_θ) were calculated to be 198±107 (N=2) in the pectoral region and 671±171 (N=3) in the posterior-most region.

The time averages of the wall shear stress (τ₀) were greater in the concave-motion phase than in the convex-motion phase at comparable positions (Fig. 3A). However, a statistically significant difference was detected only in the posterior region (Tukey's HSD test, d.f.=7; P<0.05). Flow separation that was determined by a negative τ₀ was observed in five sequences of the convex motion in the pectoral region of a particular fish. It is worth noting that the separating flow reattached to the fish surface immediately downstream in all observations. As Fig. 3B shows, the magnitude of the normal component of surface velocity in the convex-motion phase with flow separation [0.048±0.005 m s⁻¹, number of observations (n)=5] and the neighbouring (i.e. previous and following) concave-motion phases (0.059±0.016 m s⁻¹, n=5) was significantly greater than those in the other convex-motion phase (0.024±0.002 m s⁻¹, n=3) and concave-motion phase (0.032±0.011 m s⁻¹, n=3) in the same region without flow separation (ANOVA; within-convex: P<0.01, within-concave: P<0.05). In this case, the normal component of the surface velocity (w) is defined as w=Vcos⁻¹α, where V is the transverse surface velocity, and α is the angle of the fish surface relative to the swimming direction.

Fig. 4 shows the time averages of the local friction coefficient (C_fx), which is defined as C_fx=τ₀/(0.5ρU_e²), where ρ is the density of the water, in each of the three surface regions of the swimming fish and rigid body. They are compared with theoretical estimates for a flat plate in the cases of laminar and turbulent boundary layers. The time average of C_fx in the posterior region during the concave-motion sequence was significantly greater than that in the same region during the convex-motion sequence (Tukey's HSD test, d.f.=7; P<0.05). The C_fx values in the pectoral (0.0041±0.0030, N=3) anterior region (0.0071±0.0028, N=2) at l_x=38±9 mm on the rigid-body surface are very similar to the flat-plate estimates for the laminar boundary layer.

The distribution wave of the U_e/U ratio, δ, τ₀ and C_fx in each of the three surface regions behaved in a manner similar to the out-of-phase wave with body motion. Fig. 5 shows phase (φ) of the surface movement in which the maximum and minimum peaks of these parameters were recorded. This phase is indicated by the azimuth projected on the complex plane (Re^φi, where R is the vector length). The maximum τ₀ occurred after the fish surface passed the mid-point (φ=π) of the time sequence in the concave-motion phase [pectoral region: 3.66±0.26 rad (210±15 deg), N=2; pelvic region: 3.40±0.16 rad (195±9 deg), N=3; posterior region: 3.76±0.31 rad (216±18 deg), N=3]. The minimum τ₀ occurred around the mid-point (φ=0) of the convex-motion sequence [pectoral region: 6.17±0.04 rad (354±3 deg), N=2; pelvic region: 6.03±0.83 rad (346±48 deg), N=3; posterior region: 0.30±0.26 rad (17±15 deg), N=3]. The peak U_e/U ratio was roughly π out of phase with the other parameters. C_fx and δ were roughly in phase with τ₀. However, it is important to note that there was a case (fish 2 in the posterior region; Table 1) where the φ for the maximum and minimum δ did not show significant one-sidedness [maximum δ: φ=0.32e^{(3.27±1.39)i}, z=1.13<z_crit(α=0.05)=2.92; minimum δ: φ=0.30e^{(6.09±1.52)i}, z=0.89<z_crit(α=0.05)=2.93; number of observations (n)=11; the Rayleigh test; Batschelet, 1981].

Fig. 6 compares the temporal variation in the average τ₀ in the pectoral region during one complete cycle of transverse surface movement of the fish with and without flow separation. The data plots for the fish with flow separation correspond to the plots denoted by red and blue circles in Fig. 3B. As Fig. 6 shows, the τ₀ recorded negative values during flow separation, but then returned to a positive range, suggesting a separation-and-reattachment phenomenon. Fig. 7 shows the sequential images of the velocity vector field that were selected from the five convex-motion sequences with flow separation. Fig. 7A shows the image of the velocity vector field when the flow separation was first identified by negative τ₀ in the oscillatory cycle. The separation point, which may lie slightly upstream of l_x=81 mm, was not determined because it was outside of the imaged area. The tangential velocity (u) and normal velocity (v) profiles in Fig. 7A show that a small recirculation region with clockwise vortex (counter-clockwise in the velocity vector field image) reached l_x=91 mm, where τ₀ was nearly zero. Consequently, this was assumed to be the reattachment point. A negative value for v at the edge of the detached shear layer (distance from surface to 99% free-stream velocity) reveals that there was a net normal flow of fluid from the free stream into the boundary layer. The size of the recirculation region was minimized nine frames after the flow separation was first identified (Fig. 7B). The recirculation region eventually vanished (Fig. 7C). The positive value of v near the fish surface (Fig. 7C) reveals a wall injection characteristic that was found consistently in the intermediate to later phase of the convex-motion sequence without separation across the surface regions.

The displacement thickness (δ*), as one may recall, represents a virtual distance by which the fish surface must be displaced outwards to yield the same flow rate of an inviscid flow at free-stream velocity. The ratio of δ* to the momentum thickness (θ), which is known as the shape factor (H), is used to evaluate unknown boundary layers for their proximity to a laminar or turbulent boundary layer profile. H was independent of l_x (regression analysis, P>0.05) in both the convex-motion (1.62±0.07, N=8) and concave-motion sequences (1.56±0.09, N=8). The momentum thickness Reynolds number (Re_θ) was independent of l_x (regression analysis, P>0.05) in both the convex-motion (760±360, N=8) and concave-motion phases (789±294, N=8).

where κ and B are universal constants for which κ=0.40 and B=5.5 are the values that are used in this paper. Meanwhile, in a series of 18 subsequent image pairs (100 Hz) of the fish surface moving towards the opposite peak of oscillation, the mean u⁺ profile (Fig. 8A) at distances further than y⁺=5 still followed the linear law y⁺=u⁺ until y⁺ reached approximately 12 (y≈1.1 mm). Of particular interest is that this mean u⁺ profile for y⁺>12 shows characteristics that are similar to the polymeric sublayer, which is known as Virk's asymptote: u⁺=11.7ln y⁺−17 (Virk, 1975). Virk's asymptote describes an empirically observed limit to drag reduction caused by adding high molecular weight polymers to wall-bounded turbulent flows. Virk's asymptote pushes the log-law away from the surface, as illustrated by the line u⁺=0.41⁻¹ln y⁺+5.0+Δu⁺ [Δu⁺=10.5±4.5, number of image pairs (n)=18; Fig. 8A]. The average τ₀ during this period was 0.130±0.006 Pa (n=18), and U_τ approached zero (0.0114±0.0012, n=18). Hence, u⁺ became very large relative to the increase in y⁺. It is worth noting that a wake-like structure extended into the internal boundary layer (y⁺<δ=74±19, n=18).

Anderson et al. (2001) previously measured the unsteady boundary layer of two species, the scup (Stenotomus chrysops) and the dogfish (Mustelus canis), with different swimming methods, namely carrangiform and anguilliform modes. The streamwise trends of boundary layer-related variables, such as U_e/U, δ, τ₀ and C_fx, and local oscillations with the same variables and the overall profile of these species are comparable to those of rainbow trout. The streamwise trend of the U_e/U ratio reflects the effect of mean streamwise acceleration of the near-field flow, which was superimposed by the local oscillatory acceleration associated with the transverse surface motion, on the behaviour of these variables (Anderson et al., 2001). The U_e/U ratio in the pectoral to pelvic regions of swimming rainbow trout was more pronounced than that of scup at a comparable position (x=0.5L). However, the U_e/U ratio of dogfish at x=0.7L was much greater than that of rainbow trout in a comparable position. We attribute these differences to the species-specific difference in swimming methods of rainbow trout and the two species tested by Anderson et al. (2001) as they explain the difference between scup and dogfish. Based on the classification of the body area that is utilized for significant propulsion while swimming, sub-carrangiform swimming for rainbow trout falls into the spectrum of body and caudal fin (BCF) propulsors between carrangiform and anguilliform swimming. Anguilliform swimming is at one extreme where the anterior body area contributes more to providing rearward transfer of momentum to the water (Webb, 1984). Thus, this difference appears to be directly reflected in the difference among the U_e/U ratios of the three species.

Anderson et al. (2001) explained that the skin friction increase in the posterior body part of the dogfish with decreasing δ was a realization of the boundary layer thinning hypothesis (Lighthill, 1971). As shown in Fig. 5, the δ of rainbow trout was instantaneously minimized as would be expected in a boundary layer under an accelerating exterior flow, where the U_e/U ratios tended to be maximized. However, the distribution wave of the C_fx in rainbow trout oscillated at roughly π out of phase with that of the dogfish (see fig. 11 in Anderson et al., 2001). This phase discrepancy is attributed partly to the flow separation that did not occur in Anderson et al. (2001), but occurred exclusively in the pectoral region of rainbow trout and the polymeric flow-like profile (Fig. 8A) that was revealed in entire surface regions during the convex-motion sequence. At the mid-point of this time sequence, the wall shear stress (τ₀) approached zero. Hence, the time-averaged C_fx became smaller. In contrast to that of the scup and the dogfish, the time-averaged C_fx of rainbow trout in the concave-motion phase (the trough-motion phase in Anderson et al., 2001) exceeded that in the convex-motion phase (the crest-motion phase in Anderson et al., 2001). It is interesting to note that this trend agrees qualitatively with time-dependent simulations of skin friction at comparable positions over the surface of a moving flat plate, emulating aquatic animal locomotion, by Ehrenstein and Eloy (2013; see fig. 16 in their paper). The body-motion phase (φ) at the maximum peak C_fx in rainbow trout was fixed in the third quadrant in Fig. 5 throughout the entire surface regions that were measured. This was immediately after the fish surface passed the mid-point (φ=π) of the time sequence in the concave-motion phase, whereas a clockwise phase procession of the maximum C_fx was observed in the dogfish. The present study limited the capability to measure the travelling body wave. However, this inter-species difference depends on the relationship between wavelengths of the undulatory body wave and distribution wave of the C_fx that can travel in a single cycle of surface movement. This means that the distribution wave of the C_fx in rainbow trout, which can be represented as a travelling wave moving in the same direction as the undulatory body wave, is similar in frequency (f), wave-length (λ) and thus wave velocity (c) to the travelling body wave, as c=fλ.

The empirical C_fx in the pectoral region in both the convex- and concave-motion phases deviates from theoretical estimates for laminar and turbulent boundary layers on a flat plate (Fig. 4). This makes it difficult to predict an unknown C_fx on the anterior surface of swimming rainbow trout by extrapolating empirical data in the downstream regions. Indeed, the C_fx of swimming rainbow trout in the concave-motion phase significantly exceeded that in the convex-motion phase only in the posterior region. However, as Fig. 4 shows, the difference may be cancelled entirely in one cycle of the surface movements by the skin friction reduction that occurred at the same time on the contralateral side of the fish surface in the convex-motion phase. Therefore, an undulatory surface motion between the pectoral and posterior regions contributed nothing to the total increase in skin friction in these regions relative to the rigid-body case. Even though the unknown C_fx upstream of the pectoral region can increase to a theoretical estimate for a stationary flat plate in the case of a turbulent boundary layer, regardless of flow separation, it is possible that the skin friction increase due to undulatory motion will be less than the estimate (20%) based on the time-dependent simulations for a moving flat plate emulating aquatic animal locomotion by Ehrenstein and Eloy (2013). The above findings and the lack of streamwise acceleration in the posterior region, in contrast to the dogfish case, suggest that a 1.9-fold (in the dogfish case) or even 3- to 5-fold skin friction increase (based on the Bone–Lighthill boundary layer thinning hypothesis) relative to the rigid-body case is extremely unlikely under the conditions that are present in this study.

The mean u⁺ profile during the intermediate to later phase in the convex-motion sequence (black crosses in Fig. 8A) showed a structure similar to that achieved in experimental demonstrations and computer-based simulations for drag reduction by adding high molecular weight polymers to wall-bounded turbulent flows in engineering research (Virk, 1975; L'vov et al., 2004; Benzi et al., 2006). It is believed that the mean u⁺ profile in the early phase of the concave-motion sequence (blue crosses in Fig. 8B) retained some memory of the previous history of the lower mean flow velocity in the later phase of the convex-motion sequence. During these periods, the boundary layer profile realized a particularly small degree of wall shear stress (τ₀), which represents a state of near separation (i.e. incipient separation). As Anderson et al. (2001) suggested, how rainbow trout can capitalize on this benefit, but with less pressure drag than if the flow separated from the surface, is considered to be a key strategy for drag reduction.

As illustrated in Fig. 8, the wake-shape velocity fluctuation extending in the internal turbulent boundary layer represents a strong interaction between the free-stream turbulence and boundary layers. Furthermore, it is possible that turbulence transition would occur at a lower Re_x than the critical range [Re_x=3.5–5.0(×10⁵)] in a flow environment that has a turbulence intensity greater than 0.001 (Schlichting, 1979). Preston (1958) proposed a momentum thickness Reynolds number (Re_θ) of 320, above which the flow is likely to be fully turbulent. The Re_θ in swimming rainbow trout exceeded this critical value across the entire surface regions that were measured. Regardless of the position and direction of the surface movement, the shape factor (H) of the boundary layer profiles showed convergence around 1.62±0.07 (N=8) and 1.56±0.09 (N=8) in the convex-motion and concave-motion sequences, respectively. These H values are closer to the value of 1.3 based on the 1/7th power law turbulent velocity distribution than to the value of 2.59 based on the so-called Blasius profile for a laminar boundary layer (Schlichting, 1979). If taken together, these observations explain why, unlike what was observed in Anderson et al. (2001), the boundary layer profile of rainbow trout did not permit good approximation by the known laminar boundary layer profile.

In summary, we characterized the boundary layer over the surface of swimming rainbow trout as streamwise trends and local oscillations in the boundary layer-related parameters that behaved like an out-of-phase wave with transverse surface movement. The boundary layer profile showed unsteadiness, oscillating above and beneath the log-law: u⁺=0.41⁻¹ln y⁺+5.0 in the classical law of the wall for a turbulent boundary layer. There was no definitive evidence to support the Bone–Lighthill boundary layer thinning hypothesis (Lighthill, 1971) that attributes high power requirements of undulatory swimming to drag enhancement. The wall shear stress tended to approach zero on the convex surface around the mid-point of the time sequence, while the fish surface was moving towards the free-stream flow. Thus, the time-averaged skin friction was locally dampened on the convex surface. However, the skin friction was amplified on the concave surface during the retreat of the fish surface. These findings contradicted previous findings in different species measured by Anderson et al. (2001), but offer insight into drag reduction strategies employed by rainbow trout in a turbulent flow environment. Demonstrating the effect of mucus on the skin friction reduction has proved elusive in the present study. The reason for this is that the physical properties of the mucus concentration in the viscous sublayer, which consists partly of high molecular weight polymers that are soluble in water (Daniel, 1981), are uncertain. Therefore, further work is necessary to clarify the speculation about the effect of fish skin mucus on drag reduction. This approach definitely should be explored in the future.

Flow separation was the most notable event that differentiated swimming rainbow trout from the two species tested by Anderson et al. (2001). A small recirculation region near the fish surface (Fig. 7A) that was created by flow separation resembles a laminar separation bubble (Gaster, 1967). Laminar separation bubbles occur when the previously attached laminar boundary layer encounters an adverse pressure gradient of sufficient magnitude to cause the flow to separate (O'Meara and Mueller, 1987). The disturbance level of the near-field flow upstream of the pectoral region would not have been high without local oscillatory acceleration associated with the transverse surface motion because the momentum thickness Reynolds numbers (Re_θ) upstream of the pectoral region of the rigid body surface were far smaller than the value for the onset of the laminar-to-turbulent transition (Re_θ=320). Not surprisingly, the transverse surface velocity became greater with increasing arc-length (l_x) from the rostrum because the propulsive surface near the tail travels a greater distance in the same period of oscillatory motion than does the anterior body surface (Triantafyllou et al., 2002). However, the significantly increased magnitude of the normal component (w) of surface velocity during both the convex-motion sequence with flow separation and the neighbouring concave-motion sequences (Fig. 3B) suggests that self-generated hydrodynamic perturbation caused the flow separation. Hydrodynamic perturbations from flow over the fish body in a horizontal plane can cause translational disturbance, side slip for lateral displacement or rotational disturbance, and yaw for rotation to the left/right about a vertical axis (Webb, 2004b). Because the entire cycle of the surface movement occurred within a fixed view field as small as 20×20 mm², one cannot reasonably assume that the fish experienced a side-slip disturbance. Therefore, one can interpret the incidence that occurred in our rainbow trout as follows. As a result of the self-generated rotational disturbance (yaw), incident vortices of sufficient magnitude that had been shed backwards from the leading edge would interact with the boundary layer flow or fish surface that was moving towards the free-stream flow at a faster w when they were encountered. This interaction should cause considerable unsteadiness of the structure of the boundary layer that previously attached to the fish surface, thereby leading to flow separation. Normal mass flux from free-streaming into the detached shear layer (i.e. negative velocity v at the outer edge, Fig. 7A) could enhance the momentum transfer in the detached shear layer and, consequently, increase the thickness of the detached turbulent shear layer. Shortly thereafter, with phase transition of transverse surface movement from a convex- to concave-sequence posteriorly, the pressure downstream of the separation point was progressively directed downstream (favourable pressure gradient). This is supported by a negative value of the equilibrium pressure gradient parameter β=(δ*τ₀⁻¹)(dp/dx) in the early phase of concave-motion sequence. One can assume that, along with increased thickness of the detached shear layer, a progressive change in the pressure gradient near the fish surface from adverse to favourable would facilitate reattachment of the detached shear layer to the fish surface immediately downstream from the separation point by eliminating the reversed flow direction in the separation bubble (O'Meara and Mueller, 1987).

Provided that lateral-line afferents that innervate the hair cells in a single superficial neuromast are flow sensitive, the reversed flow that was observed immediately upstream of the reattachment point (Fig. 7A) could cause a time-shifted irregular pattern of neuronal signals from a superficial neuromast in the reverse-flow region unlike those in upstream and downstream regions. Of course, there is the possibility that the observed recovery from flow separation was due to self-correction without sensory input. Whatever the reason, the immediate recovery must have influenced swimming performance more favourably than if the reattachment was delayed until further downstream to the trailing edge. In the latter case, the wake-induced unsteadiness, pressure fluctuations, structure vibrations and noise would have been further increased within the separated shear layer and the reattachment region (Troutt et al., 1984). It is uncertain how the temporal patterns of lateral-line afferent discharge respond to the physical act of shear flow that behaves in an out-of-phase waveform with surface movement and how they are perturbed by flow separation. To answer these questions, we require an inter-disciplinary approach that incorporates a neurophysiological technique into the present capabilities of hydrodynamic studies. This is a key objective of future studies.

Rainbow trout were obtained from a fish farm (Pohtiolampi Osprey Centre, Kangasala, Finland). The fish were held indoors in a 300 l aquarium at the Flow Research Laboratory of Tampere University of Technology, Finland. The water in the holding tank was sufficiently oxygenized and maintained in an appropriate condition while being recirculated through a filtration system.

Unidirectional flow was induced in a 1.5 m open channel of the recirculating flow system (Fig. 9) by drawing the water from a settling tank (2 m²) that was located downstream of the open channel using a centrifugal pump (AHLSTAR, Sulzer, Kotka, Finland). Fine mesh screens and a stainless steel honeycomb that were located in a contraction directly upstream of the open channel provided strong damping of the flow disturbance over the cross-sectional area of the test section. Assuming that the turbulence in the free-stream flow was isotropic, the turbulence intensity (T) is defined as T=u_rms/U, where u_rms is the root mean square of the fluctuating velocity component in the free-stream direction (Schlichting, 1979). T in the free-stream flow (U=0.311±0.027 m s⁻¹) that was measured using the PIV technique at 16 positions of different depths (0.04−0.08 m from the bottom) in a 0.21×0.24×0.50 m (width×height×length) test section (without fish) was 4.7±0.7%. The volumetric flow rate did not change during the experimental trials. Consequently, the depth of water in the test section was maintained at 0.12 m. The water temperature was maintained at 20°C.

To facilitate the station-holding behaviour of the swimming fish (1.02±0.09 L s⁻¹, N=4), a transparent Plexiglas wall of the test section was marked with black stripes that were spaced at 5.0 cm intervals as a visual reference. The solid blocking effect is known as a phenomenon in which the presence of the fish in an enclosed flow channel increases the flow velocity around the fish (Bell and Terhune, 1970). However, the cross-sectional area of the fish was less than 10% of the cross-sectional flow area of the open channel. Therefore, no correction of the flow velocity was necessary (Brett, 1964).

A rainbow trout was constrained to swim in the test section. After an hour of acclimation of the fish to the experimental environment, PIV images were acquired from the bottom of the test section by use of a mirror that was angled at 45 deg and two high-speed cameras (ImagerProHS, LaVision, Göttingen, Germany). A number of singly exposed particle image pairs with a resolution of 1040×1024 pixels were recorded simultaneously by the cameras at 200 frames s⁻¹. The flow field that was seeded with neutrally buoyant tracer particles was illuminated by a horizontal laser sheet with a pulse delay of 300 µs (Nd:YLF pulsed laser, ESI New Wave Division, Cambridge, UK). We chose seeding particles with diameters as small as 10 and 20 μm (glass spheres, LaVision) to ensure an adequate tracer response of the particles in turbulent flow (Hadad and Gurka, 2013). The laser and the camera with a 20×20 mm² view field (approximately) that was used to image the boundary layer, which is described as the boundary layer camera, and the other camera, which has a 50×50 mm² view field (approximately) and is described as the near-field camera, were synchronized according to the pulse generated by a software-programmable timing unit (PTU-9, LaVision) under the control of DaVis software (v. 7.2, LaVision). The boundary layer camera completed PIV flow imaging with the use of a 105 mm macro lens (Sigma 105mm f2.8D EX DG, Sigma, Tokyo, Japan) without image distortion. To acquire particle image pairs of a wider flow field from the near-field camera, a 50 mm macro lens (MicroNikkor 50mm f1.2D, Nikon, Tokyo, Japan) was used in combination with a tilt/shift lens adaptor and a teleconverter extension ring (N-AFD 1.5× TLLEPLUS SHQ, Kenko, Tokyo, Japan). The positions of the boundary layer camera and the near-field camera that were mounted on a custom-built motor-driven slider were finely adjustable using the joysticks of a controller (Motionline, Lenord, Bauer & Co., Oberhausen, Germany). To describe the oscillatory motion of the fish surface, we use the term ‘convex’ and ‘concave’, depending on the direction of transverse surface movement in an approximately 20×20 mm² field of view of the boundary layer camera. Convex motion describes the situation when the section of the fish surface in the view field of the boundary layer camera was directed in the negative y₀ direction in Fig. 10, while the fish surface was moving towards the free-stream flow. Concave motion describes the situation when the section of the fish surface was directed in the positive y₀ direction in Fig. 10, while the fish surface was retreating from its extreme position after the convex-motion sequence was completed. To locate the position of the laser sheet on the fish, the lateral view of the test section was recorded using a high-speed camera (EX-F1, Casio, Tokyo, Japan). Immediately after PIV flow imaging of the swimming fish, the fish was killed by administration of anaesthetic (emulsified solution of oil of cloves, 5 drops of 100% pure oil of cloves per 4 l of water). PIV measurement was also conducted for the rigid body set in the flow from head to tail at each 0.05 m downstream position.

Post-PIV analysis of boundary layer-related parameters over the fish surface during 1−3 cycles of tail oscillation and the rigid body was conducted on 200−500 quality sequential image pairs that were acquired from each camera per single PIV image-acquisition trial using software custom-written in Matlab (R2012b v.8.0.0.783, MathWorks, Natick, MA, USA). After the targeted PIV image was optimized using the Gaussian filter or average filter to eliminate the noise of the image, the fish surface was separated from the background by the Sobel edge-detection operator in Matlab and approximated by a fourth-degree polynomial function. Every pair of PIV images was analysed using the PIV flow imaging software DaVis (v. 7.2, LaVision), based on a multi-pass interrogation algorithm, where the search window for peak correlation was reduced by three steps from an initial interrogation window size of 32×32 pixels to a final window size of 8×8 pixels, while keeping a 50% overlap. The magnification factors were 18−20 pixels mm⁻¹ for the near-field camera and 55−60 pixels mm⁻¹ for the boundary layer camera. Therefore, velocity vectors were analysed at 260×256 node points (66,560 vectors) with an equal space of approximately 0.07 mm (4 pixels) in the particle images from the boundary layer camera.

The wall shear stress (τ₀) was estimated from the linear slope of the velocity profiles in the immediate neighbourhood of the surface (Eqn 1 at y=0; Kähler et al., 2006). It was considered to be statistically reliable if this analysis was performed at 100 Hz. However, to identify the temporal position of the flow separation as precisely as possible, where τ₀ passed from positive to negative, further analysis was undertaken at 200 Hz. To eliminate the influence of boundary layers that developed in proximity to the side walls and floor of the flow channel on the accuracy of the estimates for boundary layer-related parameters, sequential image pairs that were acquired between 0.04 and 0.08 m above the bottom of the test section and more than 0.04 m from the side walls of the test section were used for analysis. Computation of the normal distance (d) from a particular data sampling point to the fish surface was handled as a problem of finding the shortest path between the point and curve. Tangential flow velocity (u) was defined as a velocity component that was parallel to the tangent line at the point on the fish surface where d was determined. Normal velocity (v) was defined as a component of the velocity normal to the tangent line.

We gratefully acknowledge the assistance of the personnel of the Pohtiolampi Osprey Centre (Kangasala, Finland) in providing rainbow trout. We also thank two anonymous reviewers for their constructive suggestions.