Using a stereoscopic vision method, we have experimentally investigated the time evolution of a free thin disk motion with six degrees of freedom for the first time. It is found that, as the dimensionless moment of inertia I decreases, the trajectory of the disk transits from planar to nonplanar. New types of free falling motions were identified for small I values, including the spiral state and the transitional state. An extended ReI phase diagram corresponding to different flow regimes was given. The underlying physics associated with the transition is found to be connected to the interactions between the moving object and induced vortices.

1.
R.
List
and
R. S.
Schemenauer
, “
Free-fall behavior of planar snow crystals, conical graupel and small hail
,”
J. Atmos. Sci.
28
,
110
(
1971
).
2.
R. E.
Stewart
and
R.
List
, “
Gyrational motion of disks during free-fall
,”
Phys. Fluids
26
,
920
(
1983
).
3.
G. E.
Stringham
,
D. B.
Simons
, and
H. P.
Guy
, “
The behavior of large particles falling in quiescent liquids
,”
U.S. Geol. Surv. Prof. Pap.
562-c
,
1
(
1969
).
4.
Z. H.
Xia
,
K. W.
Connington
,
S.
Rapaka
,
P. T.
Yue
,
J. J.
Feng
, and
S. Y.
Chen
, “
Flow patterns in the sedimentation of an elliptical particle
,”
J. Fluid Mech.
625
,
249
(
2009
).
5.
C. W.
McCutchen
, “
The spinning rotation of ash and tulip tree samaras
,”
Science
197
,
691
(
1977
).
6.
D. G.
Karamanev
,
C.
Chavarie
, and
R. C.
Mayer
, “
Dynamics of the free rise of a light solid sphere in liquid
,”
AIChE J.
42
,
1789
(
1996
).
7.
Z. J.
Wang
, “
Dissecting insect flight
,”
Annu. Rev. Fluid Mech.
37
,
183
(
2005
).
8.
P. G.
Saffman
, “
On the rise of small air bubbles in water
,”
J. Fluid Mech.
1
,
249
(
1956
).
9.
S.
Field
,
M.
Klaus
,
M.
Moore
, and
F.
Nori
, “
Chaotic dynamics of falling disks
,”
Nature (London)
388
,
252
(
1997
).
10.
Y.
Tanabe
and
K.
Kaneko
, “
Behavior of a falling paper
,”
Phys. Rev. Lett.
73
,
1372
(
1994
).
11.
A.
Belmonte
,
H.
Eisenberg
, and
E.
Moses
, “
From flutter to tumble: Inertial drag and Froude similarity in falling paper
,”
Phys. Rev. Lett.
81
,
345
(
1998
).
12.
L.
Mahadevan
,
W. S.
Ryu
, and
A. D. T.
Samuel
, “
Tumbling cards
,”
Phys. Fluids
11
,
1
(
1999
).
13.
U.
Pesavento
and
Z. J.
Wang
, “
Falling paper: Navier-Stokes solutions, model of fluid forces, and center of mass elevation
,”
Phys. Rev. Lett.
93
,
144501
(
2004
).
14.
A.
Andersen
,
U.
Pesavento
, and
Z. J.
Wang
, “
Unsteady aerodynamics of fluttering and tumbling plates
,”
J. Fluid Mech.
541
,
65
(
2005
).
15.
W. W.
Willmarth
,
N. E.
Hawk
, and
R. L.
Harvey
, “
Steady and unsteady motions and wakes
,”
Phys. Fluids
7
,
197
(
1964
).
16.
P. C.
Fernandes
,
F.
Risso
,
P.
Ern
, and
J.
Magnaudet
, “
Oscillatory motion and wake instability of freely rising axisymmetry bodies
,”
J. Fluid Mech.
573
,
479
(
2007
).
17.
Z. Y.
Zhang
, “
A flexible new technique for camera calibration
,”
IEEE Trans. Pattern Anal. Mach. Intell.
22
,
1330
(
2000
).
18.
H. J.
Zhong
, “
Free falling disks in fluids
,” Ph.D. thesis,
Peking University
,
2010
.
19.
A.
Azuma
and
K.
Yasuda
, “
Flight performance of rotary seeds
,”
J. Theor. Biol.
138
,
23
(
1989
).
20.
H. J.
Lugt
, “
Autorotation
,”
Annu. Rev. Fluid Mech.
15
,
123
(
1983
).
21.
H. J.
Zhong
and
C. B.
Lee
, “
Paths of freely falling disks
,”
Mod. Phys. Lett. B
23
,
373
(
2009
).
22.
M.
Howe
, “
On the force and moment on a body in an incompressible fluid, with application to rigid bodies and bubbles at high and low Reynolds numbers
,”
Q. J. Mech. Appl. Math.
48
,
401
(
1995
).
23.
P.
Ern
,
F.
Risso
,
P. C.
Fernandes
, and
J.
Magnaudet
, “
Dynamical model for the buoyancy-driven zigzag motion of oblate bodies
,”
Phys. Rev. Lett.
102
,
134505
(
2009
).
24.
K.
Ellingsen
and
F.
Risso
, “
On the rise of an ellipsoidal bubble in water: Oscillatory paths and liquid-induced velocity
,”
J. Fluid Mech.
440
,
235
(
2001
).
25.
N.
Vandenberghe
,
J.
Zhang
, and
S.
Childress
, “
Symmetry breaking leads to forward flapping flight
,”
J. Fluid Mech.
506
,
147
(
2004
).
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