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A numerical study is made on the fully developed bifurcation structure and stability of the forced convection in a curved duct of square cross-section (Dean problem). In addition to the extension of three known solution branches to the high Dean number region, three new asymmetric solution branches are found from three symmetry-breaking bifurcation points on the isolated symmetric branch. The flows on these new branches are either an asymmetric two-cell state or an asymmetric seven-cell structure. The linear stability of multiple solutions are conclusively determined by solving the eigenvalue system for all eigenvalues. Only two-cell flows on the primary symmetric branch and on the part of isolated symmetric branch are linearly stable. The symmetric six-cell flow is also linearly unstable to asymmetric disturbances although it was ascertained to be stable to symmetric disturbances in the literature. The linear stability is observed to change along some solution branch even without passing any bifurcation or limit points. Furthermore, dynamic responses of the multiple solutions to finite random disturbances are also examined by the direct transient computation. It is found that possible physically realizable fully developed flows evolve, as the Dean number increases, from a stable steady two-cell state at lower Dean number to a temporal periodic oscillation state, another stable steady two-cell state, a temporal intermittent oscillation, and a chaotic temporal oscillation. Among them, three temporal oscillation states have not been reported in the literature. A temporal periodic oscillation between symmetric/asymmetric two-cell flows and symmetric/asymmetric four-cell flows are found in the range where there are no stable steady fully developed solutions. The symmetry-breaking point on the primary solution branch is determined to be a sub-critical Hopf point by the transient computation. [Copyright &y& Elsevier]

A numerical study is made on fully developed bifurcation structure and stability of combined free and forced convection in a rotating curved duct of square cross-section. The solution structure is determined as the variation of a parameter indicating the magnitude of buoyancy force. Steady solution structure is very complicated. Flow and temperature fields on various solution branches are identified to be symmetric/asymmetric multi-cell patterns. Dynamic responses of multiple solutions to finite random disturbances are examined by direct transient computation. Five types of physically realizable solutions are identified numerically. They are stable steady 2-cell solution, stable steady multi-cell solution, periodic oscillation, chaotic oscillation and symmetry-breaking oscillation led by sub-harmonic bifurcation (period doubling). Among them, three kinds of stable steady solutions are found to co-exist within a range of parameters. In addition, temporal periodic and chaotic oscillations can also co-exist in another range of parameters. Furthermore, sub-harmonic bifurcation is identified to be another route to chaos. Spectral analysis is used to demonstrate the presence of additional frequencies for the case of sub-harmonic bifurcations. Results show that symmetry-breaking oscillation driven by sub-harmonic bifurcations appear to be identical with the mode observed in Lipps [J. Fluid Mech. 75 (1976) 113], McLaughlin and Orszag [J. Fluid Mech. 122 (1982) 123], and Gollub and Benson [J. Fluid Mech. 100 (1980) 449] for problem of free convection between flat horizontal plates. [Copyright &y& Elsevier]