Swimming kinematics of rainbow trout behind a 3×5 cylinder array: a computationally driven experimental approach to understanding fish locomotion

Abstract

Fish in the wild often contend with complex flows that are produced by natural and artificial structures. Research into fish interactions with turbulence often investigates metrics such as turbulent kinetic energy (TKE) or fish positional location, with less focus on the specific interactions between vortex organization and body swimming kinematics. Here, we compared the swimming kinematics of rainbow trout (Oncorhynchus mykiss) holding station in flows produced by two different 3×5 cylinder arrays. We systematically utilized computational fluid dynamics to identify one array that produced a Kármán vortex street with high vortex periodicity (KVS array) and another that produced low periodicity, similar to a parallel vortex street (PVS array), both validated with particle image velocimetry. The only difference in swimming kinematics between cylinder arrays was an increased tail beat amplitude in the KVS array. In both cylinder arrays, the tail beat frequency decreased and snout amplitude increased compared with the freestream. The center of mass amplitude was greater in the PVS array than in only the freestream, however, suggesting some buffeting of the body by the fluid. Notably, we did not observe Kármán gaiting in the KVS array as in previous studies. We hypothesize that this is because (1) vorticity was dissipated in the region where fish held station or (2) vortices were in-line rather than staggered. These results are the first to quantify the kinematics and behavior of fishes swimming in the wake of multiple cylinder arrays, which has important implications for biomechanics, fluid dynamics and fisheries management.

Keywords: Computational Fluid Dynamics; Fish; Hydrodynamics; Locomotion; Particle Image Velocimetry.

Fig. 1.

Periodicity optimization study results of computational fluid dynamics (CFD) simulations that lie within the co-shedding regime. (A) The values of the objective function [L-kurtosis of the fast Fourier transform (FFT) spectrum] plotted against the spacing ratio (L_x/D and L_y/D, where L_x and L_y are the ratio of cylinder gap space in the streamwise and in the cross-stream directions, respectively, to cylinder diameter D) identified from an initial sample size of 60 simulations. (B) Optimal [Kármán vortex street (KVS) array] and (C) sub-optimal [parallel vortex street (PVS) array] vorticity contours selected for the experiment. Color gradient scale represents vorticity (s⁻¹). The experimental cylinder array was constructed based on these two arrangements. (x and y axes in L_x/D and L_y/D, respectively.)

Fig. 2.

Experimental set up. (A) Computer aided design (CAD) drawings of parts for an adjustable array of multiple D-shaped cylinders were designed using SolidWorks. (B) Parts were laser cut from clear acrylic and cylinders were purchased separately. Arrays of D-shaped cylinders were manually constructed to replicate both CFD simulations of cylinder arrays within ±1 mm (appears circular because of the use of washers). (C) Five rainbow trout (Oncorhynchus mykiss, length 7.4±0.1 cm) each individually swam downstream from each combination of hydrodynamic treatments (freestream, Kármán vortex street, parallel vortex street) and flow speeds (22, 48 and 74 cm s⁻¹). (D) High-speed video recordings of 16 tail beats of the ventral silhouette were taken for each individual×hydrodynamic treatment×flow speed combination within a pre-determined zone of interest. dsc, D-shaped cylinder; sr, sliding rail; bp, baseplate; zoi, zone of interest.

Fig. 3.

Schematic concept of the computational workflow. Annotations of the snout, tail tip and 6 points along both sides of the fish's body were placed on 260 representative frames in DeepLabCut (ipython). A library was made by training DeepLabCut on those frames for 600,000 iterations. DeepLabCut then estimated the annotated body positions on all video data. These estimations were manually proofread for extreme, obvious miscalculations by DeepLabCut, then sorted into sets of four tail beats (R). The midlines of the fish were constructed, and thence kinematics were calculated (MatLab).

Fig. 4.

Strouhal number comparison between particle image velocimetry (PIV) and CFD results alongside vorticity contours for experimental validation of CFD. (A) Strouhal numbers (St) show good agreement between experimental and simulation results. Instantaneous vorticity contours show (B) an alternating vortex shedding pattern, similar to the KVS array observed via CFD and (C) a symmetric vortex shedding pattern, similar to the PVS array observed via CFD. Vorticity contours show vorticity as a color gradient graphed onto L_x/D versus L_y/D space. Locations of the D-shaped cylinders are represented by rectangles on the L_y/D axis.

Fig. 5.

Mean body wavelength across flow speeds and hydrodynamic treatments. Data are means±s.e.m. (95% error), n=5 fish per treatment combination, where shade indicates hydrodynamic treatment (freestream, Kármán vortex street and parallel vortex street) and L is fish body length. A false discovery rate (FDR)-adjusted two-way ANOVA detected a main effect on wavelength due to hydrodynamic treatment (reported in Results), but no significance (n.s.) was found by a Tukey's post hoc test.

Fig. 6.

Mean tail beat frequency across flow speeds and hydrodynamic treatments. Data are means±s.e.m. (95% error), n=5 fish per treatment combination, where shade indicates hydrodynamic treatment (freestream, Kármán vortex street and parallel vortex street). Tukey's adjusted significance levels according to Tukey's post hoc test following a FDR-adjusted two-way ANOVA are represented by asterisks (****P<0.0001, *P<0.05; n.s., not significant). Also notable, frequency differed significantly (P<0.0001) between each flow speed and either of the other flow speeds within each hydrodynamic treatment, except for between 48 and 74 cm s⁻¹ in the Kármán vortex street.

Fig. 7.

Mean lateral amplitude across flow speeds and hydrodynamic treatments for three different locations along the body. Data are means±s.e.m. (95% error), n=5 fish per treatment combination, where shade indicates hydrodynamic treatment (freestream, Kármán vortex street and parallel vortex street), shape represents body location [square, snout; diamond, center of mass (COM); triangle, tail tip] and L is fish body length. Results of a FDR-adjusted two-way ANOVA with a Tukey's post hoc test are reported in Results.

Fig. 8.

Cases of casting behavior in rainbow trout illustrated by digitized snout position across time. All x–y axis units are 1:1. These instances are at a flow speed of 48 cm s⁻¹ for (A) the parallel vortex street and (B) the Kármán vortex street. Inset graphs show corresponding global position to the multiple cylinder array.

Fig. 9.

A representative, continuous recording of a casting event followed by acceleration through the cylinder array for a single fish in a Kármán vortex street at 74 cm s⁻¹. x–y axis units are 1:1 and time scale is the same as in Fig. 7. Images (A–F) are zoomed-in video frames of the trout swimming at specific time points indicated by the lines that connect the graph to the panels. Scale bar in A: 1 cm (applies to all panels). (A,B) Casting behavior, in which the trout angles its body against the flow and swims left or right in the flume. (C) Following casting, the trout swims quickly and directly to the middle downstream cylinder. The trout lingers and appears to entrain behind the cylinder edge for a moment. (D) The trout accelerates into the cylinder array and (E) continues to swim through the array with the same swimming movement, in this case briefly pausing twice. (F) Once past the cylinder array, the trout shows a similar behavior to that in C, though the position would imply bow waking. The trout resumes a plethora of behaviors shortly after F (observed out of camera view).