Sep 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987rspsa.413...71w&link_type=abstract
(Royal Society, Discussion on Dynamical Chaos, London, England, Feb. 4, 5, 1987) Royal Society (London), Proceedings, Series A -
Other
5
Chaos, Free Convection, Partial Differential Equations, Spatial Distribution, Transition Flow, Branching (Mathematics), Isothermal Flow, Two Dimensional Flow
Scientific paper
Numerical experiments with idealized symmetry and boundary conditions make it possible to explore nonlinear behavior of thermal convection in a fluid layer and to relate bifurcation structures to those found in appropriate low-order systems. Two examples are used to illustrate transitions to chaos. In two-dimensional thermosolutal convection, where the spatial structure is essentially trivial, chaos is caused by a heteroclinic bifurcation involving a symmetric pair of saddle foci. When convection is driven by internal heating, several competing spatial structures are involved and the transition to chaos is more complicated in both two- and three-dimensional configurations. Although the first few bifurcations can be isolated, a statistical treatment is needed for behavior at high Rayleigh numbers.
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