Biomimetic and live medusae reveal the mechanistic advantages of a flexible bell margin

Abstract

Flexible bell margins are characteristic components of rowing medusan morphologies and are expected to contribute towards their high propulsive efficiency. However, the mechanistic basis of thrust augmentation by flexible propulsors remained unresolved, so the impact of bell margin flexibility on medusan swimming has also remained unresolved. We used biomimetic robotic jellyfish vehicles to elucidate that propulsive thrust enhancement by flexible medusan bell margins relies upon fluid dynamic interactions between entrained flows at the inflexion point of the exumbrella and flows expelled from under the bell. Coalescence of flows from these two regions resulted in enhanced fluid circulation and, therefore, thrust augmentation for flexible margins of both medusan vehicles and living medusae. Using particle image velocimetry (PIV) data we estimated pressure fields to demonstrate a mechanistic basis of enhanced flows associated with the flexible bell margin. Performance of vehicles with flexible margins was further enhanced by vortex interactions that occur during bell expansion. Hydrodynamic and performance similarities between robotic vehicles and live animals demonstrated that the propulsive advantages of flexible margins found in nature can be emulated by human-engineered propulsors. Although medusae are simple animal models for description of this process, these results may contribute towards understanding the performance of flexible margins among other animal lineages.

Figure 1. Performance among robots and live medusa.

A. Structural comparison of biological models (top panels) with bio-inspired vehicles (bottom) used for experimental comparisons (both are 16.4 cm diameter). Only flap versions of the robotic vehicles are shown. B. Comparison of the maximum normalized swimming speeds of jellyfish vehicles with representative values for their natural counterparts, Aurelia aurita (14.7 cm diameter) and Cyanea capillata (10 cm diameter). C. Comparison of the normalized swimming speed averaged over the swimming cycle. The Reynolds numbers (Re) shown are averages over 3 swimming cycles. We examined a flap and a no-flap version of both the A. aurita and C. capillata vehicle models (icons illustrate each version). Bars are the mean values over 3 consecutive swimming cycles (± st.dev.). D. Bell kinematics at of no-flap and flap vehicles and live Aurelia during bell contraction. Scale represents 1 cm.

Figure 2. Fluid interactions at the bell margin.

(A) Velocity vector field (from DPIV record) and (B) pressure field of flows around flap and no-flap versions of the Aurelia vehicle. Inset: Area integrated pressure of the pressure field along the bell over time. In the flap version, the greatest fluid velocities and lowest pressure values occurred at the inflexion point of the margin, where the flexible flap joined the more rigid bell. (C) Maximum fluid velocities in the wake were greater for the flap version (red) of the Aurelia vehicle than the no-flap (blue) version although the velocities of the propulsors (bell margins) did not differ. (D) Ratio of the maximum velocities of the fluid entrained (pull) versus expelled (push) by the bell during bell contraction for the flap (red) and no-flap (blue) versions. Velocity and pressure fields of the Aurelia vehicle were representative of the fields for the Cyanea vehicle.

Figure 3. Vehicle performance and wake characteristics.

(A) Swimming bell kinematics measured as changes in bell fineness (bell height/diameter) during contraction and relaxation (indicated by small medusa-shaped icons). (B) Corresponding propulsive performance of flap and no-flap vehicles supplied with identical input power. Although all vehicles accelerated forward during bell contraction, only vehicles with flexible margins – flaps – succeeded in making any net progress during bell relaxation. (C) Swimming speed during the second swimming cycle showing that the no-flap vehicles moved backwards (negative velocities) during bell expansion. (D) Circulation values of the starting vortex. Circulation values were normalized by bell area to account for differences in propulsor surface areas among vehicle versions. The increase in circulation occurs during bell contraction as the starting vortex grows. Circulation of the flap versions peaked at higher levels as a result of generating larger starting vortices.

Figure 4. Comparison of margin tip velocities for flap and no-flap versions of the Aurelia vehicle.

Data represent average (error bars - ±1 standard deviation of mean value) velocities taken during three consecutive pulsation cycles for each vehicle type. Insert depicts the average and maximum tip velocities for either vehicle type. Note that the vehicle possessing a flexible marginal flap did not have either higher maximum or average tip velocities than the vehicle without marginal flaps. The frequency of sampling was increased during the portion of the pulsation cycle characterized by maximum marginal tip velocities.

Figure 5. Flap length versus vortex diameter.

Maximum diameter of the starting vortex versus the distance measured from the bell margin to the inflexion point (location where the flap joined the rigid actuator) for Aurelia vehicle with variable length flaps.

Figure 6. Fluid interactions and performance of vehicles with variable flap lengths.

(A) Maximum fluid velocity and (B) peak circulation of the starting vortex for the Aurelia vehicle with variable length flaps. (C) Maximum swimming speed of the Aurelia vehicle with variable length margins. (D) Velocity vectors and vorticity contours of the starting vortex during bell contraction of the different versions of the vehicle.

Figure 7. Vortex separation for flap and no-flap vehicles.

Average distance between the starting and stopping vortex during bell expansion for the flap (red) and no-flap (blue) version of the vehicles. The error bars represent the range showing the closest and the furthest that the rings were in proximity throughout the recovery.

Figure 8. Proposed mechanism of thrust enhancement.

Schematic of the proposed mechanistic basis of elevated circulation of vehicles with (A) flexible margins relative to those with (B) rigid margins. Kinematics of the flexible margin during bell contraction creates a large low pressure region between the bell margin and the inflexion point. This creates a suction that entrains high velocity flow in the region of the inflexion point. In contrast, higher pressure along the subumbrellar surface ejects fluid from under the bell. The difference in pressure between the two regions generates increased circulation by the extruded fluid that joins flow at the inflexion point to coalesce into a broader vortex at margins of bells with flexible flaps (A) relative to those without flexible flaps (B). (C) The pressure and (D) velocity vector fields around the bell margin of the scyphomedusa Aurelia aurita during bell contraction demonstrate the presence of a low pressure region extending from the bell margin to the inflexion point and maximum fluid velocities in the vicinity of the inflexion point, respectively.

Figure 9. Flow around inflexion points of medusae.

Flow during initial stages of bell contraction and vortex production at the bell margins of six medusan rowing swimmers. (A) Aurelia aurita, (B) Chrysaora quinquecirrha, (C) Mastigias papua, (D) Cyanea capillata, (E) Phyllorhiza punctata, (F) the velarium of a large (13 cm bell diameter) Chironex fleckerii. White scale bars represent a spatial reference of 1.0 cm. Note that, for all species, the highest velocity vectors are directed into the inflexion point at the bell margin as illustrated in Figure 8A.