Volumetric imaging of shark tail hydrodynamics reveals a three-dimensional dual-ring vortex wake structure

Abstract

Understanding how moving organisms generate locomotor forces is fundamental to the analysis of aerodynamic and hydrodynamic flow patterns that are generated during body and appendage oscillation. In the past, this has been accomplished using two-dimensional planar techniques that require reconstruction of three-dimensional flow patterns. We have applied a new, fully three-dimensional, volumetric imaging technique that allows instantaneous capture of wake flow patterns, to a classic problem in functional vertebrate biology: the function of the asymmetrical (heterocercal) tail of swimming sharks to capture the vorticity field within the volume swept by the tail. These data were used to test a previous three-dimensional reconstruction of the shark vortex wake estimated from two-dimensional flow analyses, and show that the volumetric approach reveals a different vortex wake not previously reconstructed from two-dimensional slices. The hydrodynamic wake consists of one set of dual-linked vortex rings produced per half tail beat. In addition, we use a simple passive shark-tail model under robotic control to show that the three-dimensional wake flows of the robotic tail differ from the active tail motion of a live shark, suggesting that active control of kinematics and tail stiffness plays a substantial role in the production of wake vortical patterns.

Figure 1.

Three-dimensional wakes from the robotic heterocercal plastic foil (left) and spiny dogfish (right). (a) Robotic heterocercal plastic foil swimming (self-propelled) in laser volume. (b) Tail fin of the spiny dogfish. Lateral (c,d) and dorsal (e, f) views of the wake structure isosurfaced by absolute vorticity and then colour-coded by Y vorticity (±5.0 s⁻¹) of the wake produced by the robotic foil (c,e; actuated at 2.0 Hz) and spiny dogfish (d,f; swimming at 0.5 l s⁻¹, or 0.63 Hz), respectively. Lateral isosurface views include a vertical slice (XY plane) with velocity vectors; dorsal isosurface views include a horizontal slice (XZ plane) with velocity vectors. Every third velocity vector is shown for clarity.

Figure 2.

Instantaneously captured three-dimensional vorticity patterns in the wake produced by a robotic heterocercal plastic foil swimming (self-propelled) actuated at the leading edge at a frequency of 2.0 Hz. (a) Lateral view of vorticity magnitude isosurface (6.5 s⁻¹) of linked vortex rings produced by a steadily swimming robotic foil. (b) Top, (c) middle and (d) bottom horizontal (XZ plane) slices from sequence shown in (a) coloured by Y vorticity (±5.0 s⁻¹) to demonstrate the separated and connected portions of the rings (e.g. blue areas of vorticity). The strongest jets are produced in the dorsal portion of the ring, as illustrated by the vectors in (b). (e) Dorsal view of (a) in which the laterally displaced linkage of the rings is apparent. (f) Same structures as (a) at a vorticity magnitude isosurface of 4.0 s⁻¹. The small ring in the dorsal region is of lower vorticity less than or equal to 4.5 s⁻¹.

Figure 3.

Sequential time series of vortices being shed from the tail of a swimming shark (0.5 l s⁻¹, or 0.63 Hz) in lateral (XY plane, (a)) and ventral (XZ plane, (b)) views. Isosurfaces and slices are contoured by Y vorticity. White asterisks denote the downstream edge of the forming vortex through the time series. The grey-dashed line at t = 0.133 s in (a) represents the location of the slices shown in panel (b). In (b), high-speed video of the same shark that produced the vortex in this figure, swimming at approximately the same frequency, was matched to each time frame by comparison with the silhouette of the tail visible in the upstream edge of the three-dimensional isosurface reconstruction to show tail position.

Figure 4.

Shark tail-shaped plastic robotic flapping foil (left) and lateral view of Y vorticity isosurface (3.5 s⁻¹; right) of vortex produced when swimming at 2.0 Hz, recorded with volumetric imaging. Velocity vectors are shown for two horizontal (XZ plane) slices, one through each the dorsal and ventral rings. The isosurface is shown as a mirror-image to the original recording, to have same upstream orientation as other figures. These results demonstrate that the inclined trailing edge of a passive foil actuated only in heave at the leading edge can generate a ring-within-a-ring vortex structure. Only every third velocity vector is shown for clarity.

Figure 5.

(a) Two-dimensional (XY plane) PIV reanalysis of swimming dogfish data from Wilga & Lauder [13,28] with high-vorticity regions used to produce hypothetical vortex ring structure circled in white. The Wilga & Lauder [13,28] data were from planar PIV only, and were used to infer the vortex structure described in that paper. The volumetric data presented here show the same vorticity patterns when sliced appropriately in the vertical plane, but further demonstrate that the previously reconstructed vortex wake is inaccurate. (b) Vorticity magnitude isosurface (grey) of three-dimensional vortex ring structure produced by swimming dogfish recorded with volumetric imaging, along with corresponding XY plane showing similar vorticity patterns to (a). Dorsal (c) and posterior (d) views of the volumetric isosurface and XY plane in (b) with vortex rings coloured by vorticity. Only every third velocity vector is shown for clarity.

Figure 6.

(a) Wake vortices created by steady swimming chain dogfish (Scyliorhinus retifer) in the lateral, (b) dorso-lateral, (c) posterior or downstream and (d) ventral views, produced with volumetric imaging. The major vortex loop is shown as a vorticity isosurface which is then coloured by Y vorticity. Also shown is a vertical (XY) planar vector field through the centre of the vortex ring. Note the strong side jet flows in panel (c) and the downwash through the centre of the ring in (b). Only every third velocity vector is shown for clarity.