TY - JOUR
T1 - Stability of oscillating hexagons in rotating convection
AU - Echebarria, Blas
AU - Riecke, Hermann
N1 - Funding Information:
H. Riecke wishes to express his appreciation for the many discussions he had over the years with John David Crawford, whose clarity of thought and insight impressed him deeply. We gratefully acknowledge interesting discussions with F. Sain and M. Silber. The numerical simulations were performed with a modification of a code by G.D. Granzow. We also thank one of the referees for pointing to the special symmetry properties of the solutions at the band-center ( q =0). This work was supported by D.O.E. Grant DE-FG02-G2ER14303 and NASA Grant NAG3-2113.
PY - 2000/9/1
Y1 - 2000/9/1
N2 - Breaking the chiral symmetry, rotation induces a secondary Hopf bifurcation in weakly nonlinear hexagon patterns which gives rise to oscillating hexagons. We study the stability of the oscillating hexagons using three coupled Ginzburg-Landau equations. Close to the bifurcation point, we derive reduced equations for the amplitude of the oscillation, coupled to the phase of the underlying hexagons. Within these equations, we identify two types of long-wave instabilities and study the ensuing dynamics using numerical simulations of the three coupled Ginzburg-Landau equations.
AB - Breaking the chiral symmetry, rotation induces a secondary Hopf bifurcation in weakly nonlinear hexagon patterns which gives rise to oscillating hexagons. We study the stability of the oscillating hexagons using three coupled Ginzburg-Landau equations. Close to the bifurcation point, we derive reduced equations for the amplitude of the oscillation, coupled to the phase of the underlying hexagons. Within these equations, we identify two types of long-wave instabilities and study the ensuing dynamics using numerical simulations of the three coupled Ginzburg-Landau equations.
KW - Ginzburg-Landau equation
KW - Hexagon patterns
KW - Phase equation
KW - Rotating convection
KW - Side-band instabilities
KW - Spatio-temporal chaos
KW - Traveling waves
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U2 - 10.1016/S0167-2789(00)00101-9
DO - 10.1016/S0167-2789(00)00101-9
M3 - Article
AN - SCOPUS:0040778386
VL - 143
SP - 187
EP - 204
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
SN - 0167-2789
IS - 1-4
ER -