Jellyfish Bell Contraction: Vortex-Ring Thrust

Pulsation Controls

Contraction frequency 1.00 Hz

Duty cycle (contraction share) 25%

Bell diameter 20 cm

Drag coefficient C_d 0.50

Live State

Stroke phase relaxing

Bell diameter

20.0 cm

Swim speed

0.0 cm/s

Jet thrust

0.0 mN

Jet velocity

0.0 cm/s

How it works

A medusa jellyfish swims by rhythmically contracting its bell, expelling water from the subumbrellar cavity through the sub-umbrella orifice as a pulsed jet — then slowly relaxing to refill before the next stroke. Real medusae contract fast (a short power stroke) and relax slowly (a long recovery stroke); that asymmetric duty cycle is exactly what the duty-cycle slider controls.

Bell volume:     V(t) = (2/3)·π·r(t)³
Ejected flow:    Q(t) = max(0, -dV/dt)
Orifice area:    A_o  = π·(0.5·r)²
Jet velocity:    u_jet = Q / A_o
Jet thrust:      F = ρ_water · Q · u_jet
Swim dynamics:   m_eff·(dv/dt) = F − ½ρ_water·C_d·A_frontal·v·|v|

Frequency — how many contraction/relaxation cycles per second; higher frequency means more, weaker pulses of thrust.
Duty cycle — the fraction of each cycle spent contracting. Real jellyfish keep this low (a fast power stroke, a slow recovery), which is why the slider caps near 50%.
Bell diameter — sets the animal's size, which scales both the volume of water displaced per stroke and the effective (added) mass being accelerated.
Drag coefficient — how strongly the surrounding water resists the bell's forward motion between pulses; a lower value coasts further after each stroke.

Each contraction sheds a doughnut-shaped vortex ring of rotating fluid from the bell margin — the same wake structure documented in jellyfish and squid propulsion research (Dabiri, Colin & Costello). The ring you see expanding below the bell each pulse is that shed vortex; some oblate jellyfish even recapture a little extra thrust from it during the recovery stroke, a refinement this model simplifies away in favor of the primary jet-thrust balance above.

Bell (contracting) Shed vortex ring

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