Codimension Two Bifurcation with Double-Zero Eigenvalue for Two-Dimensional Double Diffusive Convection in a Square Container

The limitations of existing one-dimensional experiments on double-diffusive convection are discussed, and a variety of new two-dimensional phenomena are described. We have used the sugar-salt system and shadowgraph photography to make exploratory studies of motions which can arise in a fluid with two smooth, opposing, vertical concentration gradients, with and without horizontal gradients. Many different effects have been observed, the most important of which are the following, (a) In the ‘finger’ case, local disturbances can propagate rapidly as wave motions, which cause a simultaneous breakdown to convection over large horizontal distances. (b) Layers formed in the’ diffusive’ sense overturn locally to produce fingers, but propagate more slowly, as convective rather than wave motions, (c) A series of layers, separated by diffusive interfaces, can become unstable, in the sense that successive layers merge in time as their densities become equal, (d) The presence of horizontally separated sources of water of similar density but differentT,Scharacteristics can lead to the development of strong vertical gradients and extensive quasi-horizontal layering.Most of our results are qualitative, but it is hoped that they will stimulate further quantitive work on each of the new processes described. It is already clear that much more needs to be done before the mechanism of formation of layers observed in the ocean can be regarded as properly understood.

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Oscillations in double-diffusive convection

Journal of Fluid Mechanics ◽

10.1017/s0022112081000918 ◽

1981 ◽

Vol 109 ◽

pp. 25-43 ◽

Cited By ~ 104

Author(s):

L. N. Da Costa ◽

E. Knobloch ◽

N. O. Weiss

Keyword(s):

Rayleigh Number ◽

Period Doubling ◽

Thermosolutal Convection ◽

Two Dimensional ◽

Double Diffusive Convection ◽

Dimensional Problem ◽

Diffusive Convection ◽

Steady Solutions ◽

Steady Convection ◽

Double Diffusive

We have studied the transition between oscillatory and steady convection in a simplified model of two-dimensional thermosolutal convection. This model is exact to second order in the amplitude of the motion and is qualitatively accurate for larger amplitudes. If the ratio of the solutal diffusivity to the thermal diffusivity is sufficiently small and the solutal Rayleigh number, RS, sufficiently large, convection sets in as overstable oscillations, and these oscillations grow in amplitude as the thermal Rayleigh number, RT, is increased. In addition to this oscillatory branch, there is a branch of steady solutions that bifurcates from the static equilibrium towards lower values of RT; this subcritical branch is initially unstable but acquires stability as it turns round towards increasing values of RT. For moderate values of RS the oscillatory branch ends on the unstable (subcritical) portion of the steady branch, where the period of the oscillations becomes infinite. For larger values of RS a birfurcation from symmetrical to asymmetrical oscillations is followed by a succession of bifurcations, at each of which the period doubles, until the motion becomes aperiodic at some finite value of RT. The chaotic solutions persist as RT is further increased but eventually they lose stability and there is a transition to the stable steady branch. These results are consistent with the behaviour of solutions of the full two-dimensional problem and suggest that period-doubling, followed by the appearance of a strange attractor, is a characteristic feature of double-diffusive convection.

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Some properties of two-dimensional stochastic regimes of double-diffusive convection in plane layer

Chaos An Interdisciplinary Journal of Nonlinear Science ◽

10.1063/1.1615911 ◽

2003 ◽

Vol 13 (4) ◽

pp. 1231-1241 ◽

Cited By ~ 2

Author(s):

I. N. Sibgatullin ◽

S. Ja. Gertsenstein ◽

N. R. Sibgatullin

Keyword(s):

Plane Layer ◽

Two Dimensional ◽

Double Diffusive Convection ◽

Diffusive Convection ◽

Stochastic Regimes ◽

Double Diffusive

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Reduction Method for Search of Chaotic Attractors in Generic Autonomous Quadratic Dynamical Systems

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127417500365 ◽

2017 ◽

Vol 27 (03) ◽

pp. 1750036 ◽

Cited By ~ 2

Author(s):

Vasiliy Ye. Belozyorov

Keyword(s):

Dynamical System ◽

Reduction Method ◽

Fluid Layer ◽

Search Method ◽

Chaotic Attractors ◽

Search Problem ◽

Two Dimensional ◽

Double Diffusive Convection ◽

Diffusive Convection ◽

Double Diffusive

The search method of chaotic attractors for arbitrary [Formula: see text]-dimensional autonomous quadratic dynamical system, which contains at least two nonlinear equations, is presented. This method allows to reduce the search problem to that of chaotic attractors for some two-dimensional nonautonomous quadratic dynamical system with periodic coefficients. Examples of new chaotic attractors in 4D hyperchaotic Rabinovich system and 5D chaotic system arising from double-diffusive convection in a fluid layer, which were found by the Reduction Method, are given.

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