Control of vortex rings for manoeuvrability

Abstract

Manoeuvrability is critical to the success of many species. Selective forces acting over millions of years have resulted in a range of capabilities currently unmatched by machines. Thus, understanding animal control of fluids for manoeuvring has both biological and engineering applications. Within inertial fluid regimes, propulsion involves the formation and interaction of vortices to generate thrust. We use both volumetric and planar imaging techniques to quantify how jellyfish (Aurelia aurita) modulate vortex rings during turning behaviour. Our results show that these animals distort individual vortex rings during turns to alter the force balance across the animal, primarily through kinematic modulation of the bell margin. We find that only a portion of the vortex ring separates from the body during turns, which may increase torque. Using a fluorescent actin staining method, we demonstrate the presence of radial muscle fibres lining the bell along the margin. The presence of radial muscles provides a mechanistic explanation for the ability of scyphomedusae to alter their bell kinematics to generate non-symmetric thrust for manoeuvring. These results illustrate the advantage of combining imaging methods and provide new insights into the modulation and control of vorticity for low-speed animal manoeuvring.

Keywords: jellyfish; manoeuvrability; position control; swimming; vortex ring.

Figure1.

Two-dimensional comparison of straight swimming and turning behaviour in A. aurita. (a) A representative straight swimming case at the completion of a contraction (maximum bell fineness ratio) showing a perpendicular trajectory relative to the vortex ring (87°). Arrows indicate the location of a jet formed between the body and vortex ring. Scale bar represents 1 cm, vorticity scale is in s⁻¹ and the vector scale arrow represents 60 mm s⁻¹. (b) A representative turning case at an identical point in the swimming cycle to (a) but with a different position relative to the vortex ring (72°). Arrows indicate the location of a jet formed between the body and vortex ring. (c) Straight swimming. Arrow shows the location of the bell margin; scale bar, 1 cm. (d) Inside region of turn (pivot location) showing reduced bending. (e) Outside region of turn showing enhanced bending. Panels (c–e) were all captured at 120 ms after initiation of localized bell contraction. (Online version in colour.)

Figure 2.

Visualized wakes of swimming A. aurita performing straight swimming and turning. Stopping (STP) and starting (STR) vortices are indicated. Panels (a) and (d) show the instantaneously captured three-dimensional vorticity produced in the wake of a straight swimming jellyfish. Grey hemisphere shows approximate location of the jellyfish. Panels (b) and (e) represent horizontal slices from sequences shown in (a) and (d), respectively. Panels (c) and (f) show results from planar PIV sequences of straight and turning behaviour to illustrate the relationship between body position, kinematics and vorticity.

Figure 3.

Vorticity magnitude of the vortex ring during straight swimming and turning. (a) Diagram of straight swimming case showing the location of the jellyfish (white hemisphere), the vortex ring (blue) and the location of the two-dimensional slice. (b) Vorticity magnitude (s⁻¹) of the vortex ring created during straight swimming with the slice number corresponding to the location in panel (a). (c) Diagram of the turning case showing the location of the jellyfish (white hemisphere), the vortex ring (blue) and the location of the two-dimensional slice. (d) Vorticity magnitude (s⁻¹) of the vortex ring created during turning with the slice number corresponding to the location in panel (c).

Figure 4.

Manoeuvring in the jellyfish A. aurita (3.4 cm diameter). (a) Planar PIV showing vorticity generation relative to body position, with the starting vortex circled in yellow. Note that the starting vortex on the inside of the turn (red) remains in close proximity to the body. (b) High-magnification view showing the loose array of radial muscle fibres in the bell margin. (c) Actin staining of Aurelia muscle showing both the bell (with circular muscle) and bell margin.

Figure 5.

Conceptual visualization based on two- and three-dimensional data of the vortex ring position relative to body position during jellyfish swimming. (a) Straight swimming case showing the three-dimensional starting vortex structure from two bell contractions where I represents the first contraction and II represents the vortex from the second contraction. (b) Conceptual visualization of vortex orientation relative to the jellyfish (grey hemisphere) vortices during consecutive straight swimming pulses. (c) Turning case showing three-dimensional starting vortex structure from two bell contractions. (d) Conceptual visualization of vortex orientation relative to the jellyfish (grey hemisphere) vortices during a turning manoeuvre. (Online version in colour.)