Simulations of He3He4 mixtures with negative separation ratios in two-dimensional containers with realistic boundary conditions and moderately large aspect ratio Γ are described. The system exhibits a large variety of states with complex time dependence including intermittent wave localization and chaotic “repeated transients.” Steady but localized states are also found. Particular attention is paid to the transitions that occur for (RRc)RcΓ2, where R is the Rayleigh number and Rc its critical value for the primary instability, in order to clarify the gradual transition from a small number of active degrees of freedom [(RRc)RcΓ2] to many active degrees of freedom [(RRc)RcΓ2].

1.
T. S.
Sullivan
and
G.
Ahlers
, “
Nonperiodic time dependence at the onset of convection in a binary liquid mixture
,”
Phys. Rev. A
38
,
3143
(
1988
).
2.
P.
Kolodner
,
C. M.
Surko
, and
H.
Williams
, “
Dynamics of traveling waves near the onset of convection in binary fluid mixtures
,”
Physica D
37
,
319
(
1989
).
3.
V.
Steinberg
,
J.
Fineberg
,
E.
Moses
, and
I.
Rehberg
, “
Pattern selection and transition to turbulence in propagating waves
,”
Physica D
37
,
359
(
1989
).
4.
P.
Kolodner
, “
Repeated transients of weakly nonlinear traveling-wave convection
,”
Phys. Rev. E
47
,
1038
(
1993
).
5.
G.
Dangelmayr
and
E.
Knobloch
, “
Hopf bifurcation with broken circular symmetry
,”
Nonlinearity
4
,
399
(
1991
).
6.
A. S.
Landsberg
and
E.
Knobloch
, “
Oscillatory bifurcation with broken translation symmetry
,”
Phys. Rev. E
53
,
3579
(
1996
).
7.
O.
Batiste
,
I.
Mercader
,
M.
Net
, and
E.
Knobloch
, “
Onset of oscillatory binary fluid convection in finite containers
,”
Phys. Rev. E
59
,
6730
(
1999
).
8.
O.
Batiste
,
E.
Knobloch
,
I.
Mercader
, and
M.
Net
, “
Simulations of oscillatory binary fluid convection in large aspect ratio containers
,”
Phys. Rev. E
65
,
016303
(
2001
).
9.
D. R.
Caldwell
, “
Experimental studies on the onset of thermohaline convection
,”
J. Fluid Mech.
64
,
347
(
1974
).
10.
G.
Ahlers
and
I.
Rehberg
, “
Convection in a binary mixture heated from below
,”
Phys. Rev. Lett.
56
,
1373
(
1986
).
11.
T. S.
Sullivan
and
G.
Ahlers
, “
Hopf bifurcation to convection near the codimension-two point in a He3He4 mixture
,”
Phys. Rev. Lett.
61
,
78
(
1988
).
12.
T. J.
Bloodworth
,
M. R.
Ardron
,
J. K.
Bhattacharjee
,
P. G. J.
Lucas
, and
N. D.
Stein
, “
Convection in He3He4 mixtures with large negative separation ratios
,”
Nonlinearity
3
,
981
(
1990
).
13.
A. L.
Woodcraft
,
P. G. J.
Lucas
,
R. G.
Matley
, and
W. Y. T.
Wong
, “
Visualisation of convective flow patterns in liquid helium
,”
J. Low Temp. Phys.
114
,
109
(
1999
).
14.
O.
Batiste
and
E.
Knobloch
, in
Perspectives and Problems in Nonlinear Science
, edited by
E.
Kaplan
,
J.
Marsden
, and
K.
Sreenivasan
(
Springer
, Berlin,
2003
), pp.
91
144
.
15.
E.
Knobloch
,
M. R. E.
Proctor
, and
N. O.
Weiss
, in
Turbulence in Fluid Flows: A Dynamical Systems Approach
,
IMA Volumes in Mathematics and its Applications
Vol.
55
, edited by
G. R.
Sell
,
C.
Foias
, and
R.
Temam
(
Springer
, New York,
1993
), pp.
59
72
.
16.
T.
Clune
and
E.
Knobloch
, “
Mean flow suppression by endwalls in oscillatory binary fluid convection
,”
Physica D
61
,
106
(
1992
).
17.
S.
Hugues
and
A.
Randriamampianina
, “
An improved projection scheme applied to pseudospectral methods for the incompressible Navier-Stokes equations
,”
Int. J. Numer. Methods Fluids
28
,
501
(
1998
).
18.
S.
Zhao
and
M. J.
Yedlin
, “
A new iterative Chebyshev spectral method for solving the elliptic equation (σu)=f
,”
J. Comput. Phys.
113
,
215
(
1994
).
19.
G.
Dangelmayr
and
E.
Knobloch
, in
The Physics of Structure Formation: Theory and Simulation
, edited by
W.
Güttinger
and
G.
Dangelmayr
(
Springer
, Berlin,
1987
), pp.
387
393
.
20.
G.
Dangelmayr
,
E.
Knobloch
, and
M.
Wegelin
, “
Travelling wave convection in finite containers
,”
Europhys. Lett.
16
,
723
(
1991
).
21.
E.
Kaplan
,
E.
Kuznetsov
, and
V.
Steinberg
, “
Burst and collapse in traveling-wave convection of a binary fluid
,”
Phys. Rev. E
50
,
3712
(
1994
).
22.
P.
Kolodner
, “
Neutrally stable fronts of slow convective traveling waves
,”
Phys. Rev. A
42
,
2475
(
1990
).
23.
J. J.
Niemela
,
G.
Ahlers
, and
D. S.
Cannell
, “
Localized traveling-wave states in binary-fluid convection
,”
Phys. Rev. Lett.
64
,
1365
(
1990
).
24.
A. E.
Deane
,
E.
Knobloch
, and
J.
Toomre
, “
Travelling waves in large-aspect-ratio thermosolutal convection
,”
Phys. Rev. A
37
,
1817
(
1988
).
25.
C.
Martel
and
J. M.
Vega
, “
Dynamics of a hyperbolic system that applies at the onset of the oscillatory instability
,”
Nonlinearity
11
,
105
(
1998
).
26.
R.
Heinrichs
,
G.
Ahlers
, and
D. S.
Cannell
, “
Traveling waves and spatial variation in the convection of a binary mixture
,”
Phys. Rev. A
35
,
2761
(
1987
).
27.
E.
Moses
,
J.
Fineberg
, and
V.
Steinberg
, “
Multistability and confined traveling-wave patterns in a convecting binary mixture
,”
Phys. Rev. A
35
,
2757
(
1987
).
28.
P.
Kolodner
, “
Stable and unstable pulses of traveling-wave convection
,”
Phys. Rev. A
43
,
2827
(
1991
).
29.
H.
Yahata
, “
Travelling convection rolls in a binary fluid mixture
,”
Prog. Theor. Phys.
85
,
933
(
1991
).
30.
L.
Ning
,
Y.
Harada
, and
H.
Yahata
, “
Modulated traveling waves in binary fluid convection in an intermediate-aspect-ratio rectangular cell
,”
Prog. Theor. Phys.
97
,
831
(
1997
).
31.
M. C.
Cross
, “
Traveling and standing waves in binary-fluid convection in finite geometries
,”
Phys. Rev. Lett.
57
,
2935
(
1986
).
32.
M. C.
Cross
, “
Structure of nonlinear traveling-wave states in finite geometries
,”
Phys. Rev. A
38
,
3593
(
1988
).
33.
S.
Tobias
,
M. R. E.
Proctor
, and
E.
Knobloch
, “
Convective and absolute instabilities of fluid flows in finite geometry
,”
Physica D
113
,
43
(
1998
).
34.
H.
Riecke
, “
Self-trapping of traveling-wave pulses in binary mixture convection
,”
Phys. Rev. Lett.
68
,
301
(
1992
).
35.
H.
Riecke
and
W.-J.
Rappel
, “
Coexisting pulses in a model for binary-mixture convection
,”
Phys. Rev. Lett.
75
,
4035
(
1995
).
36.
S.
Blanchflower
, “
Magnetohydrodynamic convectons
,”
Phys. Lett. A
261
,
74
(
1999
).
37.
P.
Kolodner
, “
Coexisting traveling waves and steady rolls in binary-fluid convection
,”
Phys. Rev. E
48
,
R665
(
1993
).
38.
J.
Guckenheimer
, in
Dynamical Systems and Turbulence
,
Lecture Notes in Mathematics
Vol.
898
, edited by
D. A.
Rand
and
L. S.
Young
(
Springer
, New York,
1981
), pp.
99
142
.
39.
E.
Knobloch
and
D. R.
Moore
, “
A minimal model of binary fluid convection
,”
Phys. Rev. A
42
,
4693
(
1990
).
40.
V.
Croquette
and
H.
Williams
, “
Nonlinear competition between waves on convection rolls
,”
Phys. Rev. A
39
,
2765
(
1989
).
41.
W.
Barten
,
M.
Lücke
,
M.
Kamps
, and
R.
Schmitz
, “
Convection in binary fluid mixtures. II. Localized traveling waves
,”
Phys. Rev. E
51
,
5662
(
1995
).
42.
D.
Jung
and
M.
Lücke
, “
Localized waves without the existence of extended waves: oscillatory convection of binary mixtures with strong Soret effect
,”
Phys. Rev. Lett.
89
,
054502
(
2002
).
You do not currently have access to this content.