TY  - JOUR
A1  - Feudel, Fred
A1  - Seehafer, Norbert
A1  - Tuckerman, Laurette S.
A1  - Gellert, Marcus
T1  - Multistability in rotating spherical shell convection
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - The multiplicity of stable convection patterns in a rotating spherical fluid shell heated from the inner boundary and driven by a central gravity field is presented. These solution branches that arise as rotating waves (RWs) are traced for varying Rayleigh number while their symmetry, stability, and bifurcations are studied. At increased Rayleigh numbers all the RWs undergo transitions to modulated rotating waves (MRWs) which are classified by their spatiotemporal symmetry. The generation of a third frequency for some of the MRWs is accompanied by a further loss of symmetry. Eventually a variety of MRWs, three-frequency solutions, and chaotic saddles and attractors control the dynamics for higher Rayleigh numbers.
Y1  - 2013
U6  - https://doi.org/10.1103/PhysRevE.87.023021
SN  - 1539-3755
VL  - 87
IS  - 2
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Miranda, Rodrigo A.
A1  - Rempel, Erico L.
A1  - Chian, Abraham C.-L.
A1  - Seehafer, Norbert
A1  - Toledo, Benjamin A.
A1  - Munoz, Pablo R.
T1  - Lagrangian coherent structures at the onset of hyperchaos in the two-dimensional Navier-Stokes equations
JF  - Chaos : an interdisciplinary journal of nonlinear science
N2  - We study a transition to hyperchaos in the two-dimensional incompressible Navier-Stokes equations with periodic boundary conditions and an external forcing term. Bifurcation diagrams are constructed by varying the Reynolds number, and a transition to hyperchaos (HC) is identified. Before the onset of HC, there is coexistence of two chaotic attractors and a hyperchaotic saddle. After the transition to HC, the two chaotic attractors merge with the hyperchaotic saddle, generating random switching between chaos and hyperchaos, which is responsible for intermittent bursts in the time series of energy and enstrophy. The chaotic mixing properties of the flow are characterized by detecting Lagrangian coherent structures. After the transition to HC, the flow displays complex Lagrangian patterns and an increase in the level of Lagrangian chaoticity during the bursty periods that can be predicted statistically by the hyperchaotic saddle prior to HC transition.
Y1  - 2013
U6  - https://doi.org/10.1063/1.4811297
SN  - 1054-1500
VL  - 23
IS  - 3
PB  - American Institute of Physics
CY  - Melville
ER  - 
TY  - JOUR
A1  - Feudel, Fred
A1  - Seehafer, Norbert
A1  - Tuckerman, Laurette S.
T1  - Multistability in rotating spherical shell convection
Y1  - 2013
UR  - http://link.aps.org/doi/10.1103/PhysRevE.87.023021 (9.9.2013)
SN  - 1539-3755
ER  - 
TY  - JOUR
A1  - Miranda, Rodrigo A.
A1  - Rempel, Erico L.
A1  - Chian, Abraham C.-L.
A1  - Seehafer, Norbert
A1  - Toledo, Benjamin A.
T1  - Lagrangian coherent structures at the onset of hyperchaos in the two-dimensional Navier-Stokes equations
Y1  - 2013
UR  - http://dx.doi.org/10.1063/1.4811297
ER  -