Supplemental Materials
1.) Dye visualization of boundary layer
We assume that fluorescein dye is transported at the local water velocity (see error discussion below).
Therefore, the local dye concentration will change according to the flow velocity profile and, in
particular, highlight regions where the flow velocity differs from the free stream. This is the case for the
boundary layers surrounding the jellyfish lappets. Here, the water velocity is similar to the lappet
velocity such that the dye remains for a long time in the vicinity of the lappet whereas the water outside
the boundary layer moves at velocities different from the lappet (i.e. at free stream velocities) allowing
the dye to be advected away. The dye that appears to stick to the lappets therefore outlines the extent
of the fluid layer moving at similar velocities as the lappet, i.e. the boundary layer (Koehl et al. 2001).
The error of the boundary layer visualization can be estimated by the distance the dye will diffuse during
the duration of one pulse and bell relaxation (and thereby blur fluid boundaries between strokes).
Diffusion distance l during time period Δt can be derived by
l  Dc t 
vT
t
Sc
where Dc and Sc are the diffusion constant and Schmidt number, respectively. With Sc=2000 for
fluorescein (Lavertu et al. 2008), we find at T=21°C with ν21=1.05 ·10−6m2s−1 and pulse & relaxation time
Δt=0.7 seconds, that the dye diffuses over a distance of l=4·10−10m. This is 5 orders of magnitude less
than the theoretical boundary layer thickness of ca. 4·10−5m for the dimensions and morphology of the
G13 that we assayed (calculated from equation (4) in the main paper with b=0.5mm, r=1mm and C=0.8).
Similar relations are found for 13°C. Therefore, dye transport is dominated by advection. We conclude
that the visualization error due to diffusion is negligible compared to boundary layer thicknesses as well
as compared to the differences seen in overlap at different temperatures (figure 2a,b in main paper).
2.) Stokes model (additional details)
We simplify the body plan of an ephyrae to a shape made of an inner circle, or “head”, and eight
rectangular lappets (Feitl et al. 2009):
The bell continuity BC, i.e. the percentage of the circular bell that is filled in with tissue is
BC 
Ahead  Alappets
 D2 4
2 D0  D0 

 
D  D
2
(1)
Fluid dynamic constraint: In order for the medusa body to function as a continuous surface, the
boundary layers between the lappets must fill the gaps, i.e.,
Agap 

4
 D  D0 
2
 ABL
The boundary layer area ABL is approximately twice the area of the boundary layer formed on each
lappet edge:
(2)
l
ABL  2 N    r  dr
(3)
0
number of lappets, N
The boundary layer thickness δ(r) is a function of the Reynolds number (Re, ratio of inertial to viscous
forces) and characteristic length scale (i.e. the lappet width b) at each radial position along the lappet:
 r  
Cb
Re  r 
C
b
r
(4)
water viscosity, ν
swimming frequency, ω
proportionality constant, C
Therefore,
ABL  C
And the fluid dynamic constraint
8 N D0  D  D0 

(5)
Agap  ABL becomes
128C 2 N D0    D  D0   0
3
(6)
Equation (6) can be solved to express D0 in terms of D. Hence, D0 can be eliminated from equation (1),
giving a prediction for the minimum BC versus D to fill the gaps with boundary layers.
References
Feitl, KE, Millett, AF, Colin, SP, Dabiri, JO & Costello, JH 2009, “Functional morphology and fluid
interactions during early development of the scyphomedusa Aurelia aurita.” The Biological
Bulletin, vol. 217, no. 3, pp. 283-291.
Koehl, MA, Koseff, JR, Crimaldi, JP, McCay, MG et al. 2001, “Lobster sniffing: antennule design and
hydrodynamic filtering of information in an odor plume.” Science (New York, N.Y.), vol. 294, no.
5548, pp. 1948-1951.
LAVERTU, TM, MYDLARSKI, L & GASKIN, SJ 2008, “Differential Diffusion of High-Schmidt-Number Passive
Scalars in a Turbulent Jet.” Journal of Fluid Mechanics, vol. 612, no. -1, pp. 439-475.