Stopping vortex ring - University of Toronto Mississauga

Lecture 8, Bio 325
Jetting locomotion by prolate and oblate medusae
Squid locomotion
Assigned reading:
Dabiri J. O., Colin S.P., Costello J.H., Gharib, M. 2005. Flow patterns generated by
oblate medusan jellyfish: field measurements and laboratory analyses. Journal of
experimental Biology 208: 1257- in which they discover the stopping vortex ring
which contributes to medusa swimming.
JELLYFISH FORM AND FUNCTION Website by John H. Costello & Sean P. Colin, Roger
Williams University. See this website for information about jellyfish swimming:
Gemmell B.J. et al. 2013. Passive energy recapture in jellyfish contributes to
propulsive advantage over other metazoans. PNAS 110: 17904Gosline J.M., & Demont M.E. 1984. Jet-propelled swimming in squids. Scientific
American 252: 96-103.
When I draw a canoe paddle
through still water on a lake, I see
small vortices trail off the paddle
edges downflow. When I stir coffee
or let water down the drain I make
vortices. Smokers blow smoke rings
and cetaceans blow bubble rings.
This picture is of a vortex forming on
the upstream side of a tidal
turbine*. These rings travel through
the fluid. Fluids like water and air
exhibit flow and a vortex is simply
flow that spins.
Toroid: doughnut-shaped object,
e.g., O ring
toroidal vortices produced behind
swimming jellyfish
*the ‘hole’ in the centre is ~15 cm in diameter
Cnidarian morphs: Polyps (e.g., sea anemones) and Medusae (e.g., Jellyfish)
-In contrast to the polypoid
mesoglea (middle layer), which is
more or less thin, the medusoid
mesoglea is extremely thick and
constitutes the bulk of the animal.”
(from Barnes)
What is the function of mesoglea
in a jellyfish? Buoyancy?
Antagonist? Why is the mesoglea
of the locomotory morph so much
more important (based on its
abundance) than the mesoglea of
the sessile morph?
Mesoglea another body material: a
pliant composite material
The mesoglea of jellyfish is
adapted as a viscoelastic
antagonist of the bell’s circular
Medusae can be bullet-shaped (prolate) or flatter (oblate)
Velum has to do with shaping vortices
Oblate medusae have smaller velums than prolate, contract more slowly
when swimming and throw larger amounts of water behind them as they jet.
Jet propulsion and vortices
Barnes: Simplest
seawater beneath
the umbrella is
coronal muscle ,
powerful circular
fibres on the
contracts to jet out
the subumbrellar
oblate medusa
Animal Literature
More complex: Dabiri et al. : jellyfish jetts out seawater making 2 vortex
rings --“doughnuts of water that are continuously rolling into themselves”.
Jetting by Jellyfish
Schematic of a jetting medusa with vortex rings in the wake.
Jetting medusa with vortex rings in wake
Periodic bell contractions decrease volume of
subumbrellar cavity, displacing out the high bulk
modulus (incompressible) water as a jet: jet propulsion.
Swimming cycle: fluid efflux emerges during bell
contraction: a toroidal volume of rotating fluid known as
the power stroke starting vortex ring. This travels
downstream – is shed -- behind the forward progress of
the medusa. There are two things in the wake: this
vortex and a central jet (D).
The cycle continues with a second fluid efflux shed
during bell relaxation and recovery, a recovery stroke
stopping vortex ring as mesoglea returns its elastic force.
of distortion, elastic force)
Dabiri J O et al. J Exp Biol 2005;208:1257-1265
©2005 by The Company of Biologists Ltd
Kinematics of the starting, stopping and co-joined lateral vortex structures.
Dye used to visualize
the behaviour of the
fluid in the wake of the
swimming medusa.
Starting vortex ring
involves fluid originating
from ‘regions inside the
subumbrellar volume’, but
also from outside the bell
via ‘entrainment of
ambient fluid’ [flow
induced by vortex
rotation]; motion of this
ring is oriented at an angle
away from the bell margin
toward the central axis of
the bell and downstream
(broken arrows).
direction of
Dabiri J O et al. J Exp Biol 2005;208:1257-1265
©2005 by The Company of Biologists Ltd
Kinematics of the starting, stopping and co-joined lateral vortex structures.
Stopping vortex ring: bell
coronal muscle fibres relax
and bell opens (mesoglea
returns energy for this that
originated with the coronal
muscle) . This bell recoil
makes a stopping vortex
initially within the
subumbrellar cavity. But
fluid originating from
outside the bell is also
entrained: it is drawn
toward the subumbrellar
My first attempt to make
these ‘kinematics’
to make the information my
own. Drawings, scribbles are
important to me in this
process. I recommend
something like this for both
learning and for testing.
L1/L2, adjacent lateral
vortex superstructures
created between the
two toroids.
Stopping vortex lateral
structure contributes
to advance of swimmer
during recovery cycle.
Gemmell B.J. et al. 2013. Passive energy recapture in jellyfish contributes to propulsive
advantage over other metazoans. PNAS 110: 17904-
“Gelatinous zooplankton” (jellyfish) blooms are problems in ‘perturbed ecosystems’.
How are jellyfish able to do so much better than the fish? Jellyfish are such
apparently poor swimmers, so ‘primitive’ and inefficient in comparison to fish; how
can they so thoroughly outcompete fish in these degraded habitats?
Note that both medusae and fish have to pursue their food in the water column, i.e.,
swim after what they eat rather than filter it out of currents bringing food to them: we
are comparing animal predators that pursue their food and must “rely on direct
contact with prey to feed”.
Jellyfish are “one of the most energetically efficient propulsors on the planet”.
The ‘passive energy recapture’ involved in the vortices is credited with this
greater locomotion efficiency: [from abstract of Gemmell] “...jellyfish exhibit a
unique mechanism of passive energy recapture, which is exploited to allow
them to travel 30% further each swimming cycle, thereby reducing metabolic
energy demand by swimming muscles.”
Nature News, October 2013, Ed Yong: “The sockeye salmon is a sleek torpedo
that uses its strong muscles to leap up waterfalls. The moon jellyfish (Aurelia
aurita) is a flimsy blob that drifts along like a gently pulsating bell. The salmon is
obviously the more powerful swimmer, but a study has revealed that the jellyfish
outclasses it in efficiency. For its mass the jellyfish spends less energy to travel a
given distance than any other swimming animal.”
“When moon jellyfish contract their umbrella-shaped bells, they create two
vortex rings – doughnuts of water that are continuously rolling into
themselves. The creature sheds the first ring in its wake, propelling itself
forward. As the bell relaxes, the second vortex ring rolls under it and starts
to spin faster. This sucks in water which pushes up against the centre of the
jellyfish and gives it a secondary boost...”
Maybe explanation of role of stopping vortices in
jellyfish locomotion is easier to understand in
Gemmel (and Yong)?
Land snail
Shell is a skeleton that doesn’t function in locomotion. Snail body, visceral mass and
foot, seems amorphous; these animals are ‘shape-shifters’ (octopus reknowned for
escaping cages through cracks): versatility in body shape change marks the
importance of its hydraulic skeleton: its use of fluid force translocation in moving
about: changing body shape by the interaction of fluid and muscle and collagen
A mollusc ancestral to squids, to see how foot shell & mantle
cavity changed during evolution
dorsal view
Shell is an internal
remnant sunk within the
mantle tissue; it is called
the pen
Funnel (not visible in
this photo) developed
from posterior of
primitive foot.
Primitive ventral surface
of ancestor became
functional anterior end.
primitive dorsum
Chromatophores are
pigment cells in skin,
circlet of smooth
muscle cells, disperse
Fins set up waves; posterior lateral
fins act as stabilizers and rudders; squids
achieve greatest swimming speeds of any
aquatic invertebrate, up to 40 kmph.
Class Cephalopoda includes
squid, octopus, cuttlefish, Nautilus
Assigned reading: Gosline J.M., & Demont M.E. 1984. Jet-propelled swimming in
squids. Scientific American 252: 96-103.
A swimming squid takes up and expels water by contracting radial
and circular muscles in its boneless mantle wall. Elastic collagen
“springs” in the muscle increase the power of the jet.
Beware potential confusion: squids jet-propel themselves and of course
there is a fluid-filled cavity involved – the mantle cavity. The seawater
in this cavity functions in locomotion by virtue of its high bulk modulus;
if the seawater were not incompressible the jetting wouldn’t work. But
this cavity is NOT functioning as a hydrostatic skeleton antagonizing
mantle muscles. Rather the mantle wall itself is a muscular hydrostat.
The seawater within the mantle cavity of the squid is not
functioning as a hydrostatic skeleton. But it is the
basis of the animal's jet propulsion, which in turn depends
upon the incompressibility of seawater. When the radial
muscles of the mantle contract, the volume of the mantle
cavity is increased and seawater is drawn in. When the
circular muscles of the mantle contract, the volume of the
mantle cavity is decreased and seawater is squirted
out. The action-force of the jetted seawater creates a
reaction force that pushes the squid in the opposite
direction: opposite to whatever direction the funnel is
One-way valves* control
intake of water into mantle
cavity at sides.
Pressure build up in
seawater inside mantle
cavity (circulars contract)
forces the inner flaps of the
funnel against the mantle
water jets out funnel
[*recall starfish canals]
In the mantle structures interact: 1) collagen fibres make a tunic that prevents
longitudinal dimension change 2) radial muscles contract to thin the mantle wall and
3) circular muscles of the mantle contract to thicken the wall.
Circulars and radials are antagonists.
The mantle (the actual wall) is a muscular hydrostat and its volume must stay constant
(just as if it were a fluid-filled cavity).
But (per Kier) the fibres are very critical: because of the collagen ‘tunic’ the mantle
cannot get longer in the A to B dimension: it can change in girth.
[Imagine as it isn’t: no tunic: would lengthen in response to circulars.]
Escape Jet
Cycle of
Radial muscles contract to cause:
hyperinflation: seawater intake into
mantle cavity: outside diameter of mantle
increases by approximately 10% over
resting diameter (girth increase); cavity
volume increases 22% re relaxed volume,
wall thins.
Circular muscles contract to bring mantle
to about 75% of its relaxed diameter,
radials restored to precontracted length
(girth decrease): volume drops &
pressure rises sharply , forcing the inlet
valvesl against the mantle wall and
leaving only the funnel as exit.
The mantle wall functions as a muscular hydrostat -- a fluid-based skeleton
[muscles mostly water] without a distinct fluid chamber -- it makes antagonists of
the radial and circular muscles: contraction of one kind of muscle restores the
other to its relaxed state via this type of fluid skeleton. The radial and circular
muscles become coupled as antagonists by virtue of their own tissue being
significantly water and so incompressible – and because the mantle cannot
lengthen. Because the mantle is incompressible it must retain an overall constant
volume; and it cannot get longer as mantle muscles contract because of the
collagen fibre tunic that prevents any movement in that direction. Thus, it can only
increase or decrease in thickness – at the same time changing its overall diameter
and the capacity of the mantle cavity. When the radials contract the mantle walls
must get thinner and the walls move apart -- to maintain hydrostat volume.
Conversely when the circulars contract the mantle wall must get thicker as the
overall outside diameter of the mantle decreases. If there were no inextensible
fibres, if the animal’s mantle was not in a jacket of fibres preventing it from
lengthening, then the radials and the circulars could not have an antagonistic
effect on each other.

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