Flying snakes use a unique method of aerial locomotion: they jump from tree branches, flatten their bodies, and undulate through the air to produce a glide. The shape of their body cross-section during the glide plays an important role in generating lift. This paper presents a computational investigation of the aerodynamics of the cross-sectional shape. Two-dimensional simulations of incompressible flow past the anatomically correct cross-section of the species Chrysopelea paradisi show that a significant enhancement in lift appears at a 35° angle of attack, above Reynolds numbers 2000. Previous experiments on physical models also obtained an increased lift, at the same angle of attack. The flow is inherently three-dimensional in physical experiments, due to fluid instabilities, and it is thus intriguing that the enhanced lift also appears in the two-dimensional simulations. The simulations point to the lift enhancement arising from the early separation of the boundary layer on the dorsal surface of the snake profile, without stall. The separated shear layer rolls up and interacts with secondary vorticity in the near-wake, inducing the primary vortex to remain closer to the body and thus cause enhanced suction, resulting in higher lift.

1.
R.
Dudley
,
G.
Byrnes
,
S. P.
Yanoviak
,
B.
Borrell
,
R. M.
Brown
, and
J. A.
McGuire
, “
Gliding and the functional origins of flight: Biomechanical novelty or necessity?
,”
Annu. Rev. Ecol. Evol. Syst.
38
,
179
201
(
2007
).
2.
U. M.
Norberg
,
Vertebrate Flight
(
Springer-Verlag
,
1990
).
3.
J. J.
Socha
, “
Gliding flight in Chrysopelea: Turning a snake into a wing
,”
Integr. Comp. Biol.
51
(
6
),
969
982
(
2011
).
4.
J. J.
Socha
, “
Kinematics: Gliding flight in the paradise tree snake
,”
Nature (London)
418
(
6898
),
603
604
(
2002
).
5.
J. J.
Socha
,
K.
Miklasz
,
F.
Jafari
, and
P. P.
Vlachos
, “
Non-equilibrium trajectory dynamics and the kinematics of gliding in a flying snake
,”
Bioinspir. Biomim.
5
(
4
),
045002
(
2010
).
6.
J. J.
Socha
,
T.
O'Dempsey
, and
M.
LaBarbera
, “
A 3-D kinematic analysis of gliding in a flying snake, Chrysopelea paradisi
,”
J. Exp. Biol.
208
(
10
),
1817
1833
(
2005
).
7.
D.
Holden
,
J. J.
Socha
,
N. D.
Cardwell
, and
P. P.
Vlachos
, “
Aerodynamics of the flying snake Chrysopelea paradisi: How a bluff body cross-sectional shape contributes to gliding performance
,”
J. Exp. Biol.
217
(
3
),
382
94
(
2014
).
8.
K.
Miklasz
,
M.
LaBarbera
,
X.
Chen
, and
J.
Socha
, “
Effects of body cross-sectional shape on flying snake aerodynamics
,”
Exp. Mech.
50
(
9
),
1335
1348
(
2010
).
9.
W.
Shyy
,
Aerodynamics of Low Reynolds Number Flyers
(
Cambridge University Press
,
2008
).
10.
C. H. K.
Williamson
, “
Vortex dynamics in the cylinder wake
,”
Annu. Rev. Fluid Mech.
28
,
477
539
(
1996
).
11.
P.
Kunz
and
I.
Kroo
, “
Analysis and design of airfoils for use at ultra-low Reynolds numbers
,” in
Fixed and Flapping Wing Aerodynamics for Micro Air Vehicle Applications
,
Progress in Astronautics and Aeronautics
Vol.
195
, edited by
T. J.
Mueller
35
60
(
American Institute of Aeronautics and Astronautics
,
2001
).
12.
S.
Sunada
,
K.
Yasuda
, and
K.
Kawachi
, “
Comparison of wing characteristics at an ultralow Reynolds number
,”
J. Aircraft
39
(
2
),
331
338
(
2002
).
13.
Md. M.
Alam
,
Y.
Zhou
,
H. X.
Yang
,
H.
Guo
, and
J.
Mi
, “
The ultra-low Reynolds number airfoil wake
,”
Exp. Fluids
48
(
1
),
81
103
(
2010
).
14.
A.
Vargas
,
R.
Mittal
, and
H.
Dong
, “
A computational study of the aerodynamic performance of a dragonfly wing section in gliding flight
,”
Bioinspir. Biomim.
3
(
2
),
026004
(
2008
).
15.
A.
Krishnan
,
J. J.
Socha
,
P. P.
Vlachos
, and
L. A.
Barba
, “
Body cross-section of the flying snake Chrysopelea paradisi
,” Data set and figure on figshare under CC-BY license, May
2013
.
16.
C. E.
Willert
and
M.
Gharib
, “
Digital particle image velocimetry
,”
Exp. Fluids
10
(
4
),
181
193
(
1991
).
17.
J. W.
Bahlman
,
S. M.
Swartz
,
D. K.
Riskin
, and
K. S.
Breuer
, “
Glide performance and aerodynamics of non-equilibrium glides in northern flying squirrels (Glaucomys sabrinus)
,”
J. R. Soc. Interface
10
(
80
),
20120794
(
2013
).
18.
K. L.
Bishop
, “
Aerodynamic force generation, performance and control of body orientation during gliding in sugar gliders (Petaurus breviceps)
,”
J. Exp. Biol.
210
(
15
),
2593
2606
(
2007
).
19.
K.
Taira
and
T.
Colonius
, “
The immersed boundary method: A projection approach
,”
J. Comput. Phys.
225
(
2
),
2118
2137
(
2007
).
20.
Y.
Morinishi
,
T. S.
Lund
,
O. V.
Vasilyev
, and
P.
Moin
, “
Fully conservative higher order finite difference schemes for incompressible flow
,”
J. Comput. Phys.
143
(
1
),
90
124
(
1998
).
21.
A.
Krishnan
and
L. A.
Barba
, “
Validation of the cuIBM code for Navier-Stokes equations with immersed boundary methods
,” Technical Report on figshare, CC-BY license, 6 July 2012.
22.
M. S.
Chong
,
A. E.
Perry
, and
B. J.
Cantwell
, “
A general classification of three-dimensional flow fields
,”
Phys. Fluids
2
,
765
(
1990
).
23.
J. C. R.
Hunt
,
A. A.
Wray
, and
P.
Moin
, “
Eddies, stream, and convergence zones in turbulent flows
,” Center for Turbulence Research Report No. CTR-S88 (Center for Turbulence Research,
Stanford University
,
1988
), pp.
193
208
.
24.
J.
Jeong
and
F.
Hussain
, “
On the identification of a vortex
,”
J. Fluid Mech.
285
,
69
94
(
1995
).
25.
J.
Zhou
,
R. J.
Adrian
,
S.
Balachandar
, and
T. M.
Kendall
, “
Mechanisms for generating coherent packets of hairpin vortices in channel flow
,”
J. Fluid Mech.
387
(
1
),
353
396
(
1999
).
26.
See https://bitbucket.org/anushk/cuibm for information on how to download and install the cuIBM source code.
27.
A.
Krishnan
,
J. J.
Socha
,
P. P.
Vlachos
, and
L. A.
Barba
, “
Lift and drag coefficient versus angle of attack for a flying snake cross-section
,” Data set and figure on figshare under CC-BY license, May
2013
.
28.
A.
Krishnan
and
L. A.
Barba
, “
Flying snake wake visualizations with cuIBM
,” Video on figshare, CC-BY license, February
2013
.
29.
A.
Krishnan
,
J. J.
Socha
,
P. P.
Vlachos
, and
L. A.
Barba
, “
Time-averaged surface pressure on a flying-snake cross-section
,” Data set and figure on figshare under CC-BY license, May
2013
.
30.
P.
Koumoutsakos
and
A.
Leonard
, “
High-resolution simulations of the flow around an impulsively started cylinder using vortex methods
,”
J. Fluid Mech.
296
,
1
38
(
1995
).
31.
A.
Prasad
and
C. H. K.
Williamson
, “
The instability of the shear layer separating from a bluff body
,”
J. Fluid Mech.
333
(
1
),
375
402
(
1997
).
32.
R.
Mittal
and
S.
Balachandar
, “
Effect of three-dimensionality on the lift and drag of nominally two-dimensional cylinders
,”
Phys. Fluids
7
(
8
),
1841
1865
(
1995
).
33.
C. P.
Ellington
,
C.
van den Berg
,
A. P.
Willmott
, and
A. L. R.
Thomas
, “
Leading-edge vortices in insect flight
,”
Nature (London)
384
,
626
630
(
1996
).
34.
P.
Freymuth
, “
Propulsive vortical signature of plunging and pitching airfoils
,”
AIAA J.
26
(
7
),
881
883
(
1988
).
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