Module 6

Locomotion: Ice & Water

Pinnipeds split locomotor strategies between otariids (eared seals, forelimb- propelled) and phocids (true seals, hindlimb-propelled). The choice cascades into everything from terrestrial gait to Reynolds-regime swim efficiency. Fish 1996–2008 and Feldkamp 1987 established the quantitative framework.

1. Otariid vs. Phocid Swim Propulsion

Otariids beat their forelimbs as oscillating wings, similar to penguins (M3 in the penguins course). Phocids hold the forelimbs against the body and beat the hindlimbs in a horizontal-plane fluke action. The optimal Strouhal number St = fA/U ≈ 0.2–0.4 is shared across both groups, but the morphology targets different swim-speed regimes.

2. On-Ice / On-Land Locomotion

Otariids rotate their hindlimbs under the body and walk on all fours at ~5–8 km h^-1 on land. Phocids cannot rotate hindlimbs forward and move by caterpillar crawl (“inchworm”) or sliding. Phocid terrestrial speed is much slower, but sliding on ice can reach 25 km h^-1with minimal energy. Kuhn & Frey 2012 measured caterpillar-crawl energetics: ~3× marine COT for the same speed.

Simulation: Swim Regimes & COT

Python

script.py43 lines

import numpy as np, matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

# Swim efficiency: Strouhal number St = f*A / U
# Optimal St ~ 0.2-0.4 (Triantafyllou 1993)
U = np.linspace(0.5, 3.0, 200)   # m/s
# Otariid (forelimb): higher stroke amplitude, lower efficiency at low speed
f_ot = 2.5; A_ot = 0.3
St_ot = f_ot*A_ot / U
# Phocid (hindlimb): more streamlined, efficient at moderate speeds
f_ph = 2.0; A_ph = 0.2
St_ph = f_ph*A_ph / U

# Cost of transport comparison
COT_ot = 6.0 - 1.2 * np.abs(St_ot - 0.3)
COT_ph = 5.5 - 1.4 * np.abs(St_ph - 0.3)

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 5), facecolor='#0a0a1a')
for ax in (ax1, ax2):
    ax.set_facecolor('#111827'); ax.tick_params(colors='#cbd5e1')
    for s in ax.spines.values(): s.set_color('#334155')
    ax.grid(True, color='#334155', alpha=0.3)

ax1.plot(U, St_ot, color='#fbbf24', lw=2.5, label='Otariid (forelimb)')
ax1.plot(U, St_ph, color='#60a5fa', lw=2.5, label='Phocid (hindlimb)')
ax1.axhspan(0.2, 0.4, color='#34d399', alpha=0.15, label='Optimum band')
ax1.set_xlabel('Swim speed (m/s)', color='#cbd5e1')
ax1.set_ylabel('Strouhal number', color='#cbd5e1')
ax1.set_title('Swim propulsion regime', color='#e0f2fe', fontweight='bold')
ax1.legend(facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1')

ax2.plot(U, COT_ot, color='#fbbf24', lw=2.5, label='Otariid COT')
ax2.plot(U, COT_ph, color='#60a5fa', lw=2.5, label='Phocid COT')
ax2.set_xlabel('Swim speed (m/s)', color='#cbd5e1')
ax2.set_ylabel('COT (J/kg/m)', color='#cbd5e1')
ax2.set_title('Cost of transport in water', color='#e0f2fe', fontweight='bold')
ax2.legend(facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1')

plt.tight_layout()
plt.savefig('output.png', dpi=120, bbox_inches='tight', facecolor='#0a0a1a')
print('Otariids swim with forelimbs (oscillating wings); phocids with hindlimbs (fluke-like)')
print('Phocids are more efficient but less manoeuvrable on land')

Click Run to execute the Python code

Code will be executed with Python 3 on the server

3. Reynolds-Regime Considerations

Re = ρUL/μ for a 300 kg seal at 2 m s^-1 is ~6×10⁶— fully turbulent regime where skin-friction and pressure drag dominate. Streamlined body shape, counter-current shaped fluke, and potential drag- reducing boundary-layer management (blubber compliance, surface microstructure) have been proposed but remain incompletely quantified.

Key References

• Fish, F. E. (1996). “Transitions from drag-based to lift-based propulsion in mammalian swimming.” Am. Zool., 36, 628–641.

• Feldkamp, S. D. (1987). “Swimming in the California sea lion.” J. Exp. Biol., 131, 117–135.

• Kuhn, C. E. & Frey, S. (2012). “Pinniped locomotion: hind-limb vs fore-limb propulsion.” In Marine Mammal Ecology and Conservation, Oxford UP.

• Triantafyllou, M. S., Triantafyllou, G. S. & Yue, D. K. P. (2000). “Hydrodynamics of fishlike swimming.” Annu. Rev. Fluid Mech., 32, 33–53.

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