×

zbMATH — the first resource for mathematics

Bifurcation phenomena in confined thermosolutal convection with lateral heating: Commencement of the double-diffusive region. (English) Zbl 1039.76506
Summary: As has recently been reported by Tsitverblit and Kit [ibid. 5, 1062 ff (1993)], a vertical rectangular enclosure containing stably stratified brine and differentially heated from its side walls is characterized by complex steady bifurcation phenomena. In the present work, the structure of steady solutions in the enclosure has been studied in detail for several values of the salinity Rayleigh number, \(\text{Ra}_S\), fixed near the commencement of the double-diffusive region. It was found that when the thermal Rayleigh number, \(\text{Ra}_T\), is either very small or sufficiently large, the steady solution is unique while in an intermediate region of this parameter, there exists a great variety of the multiple steady flows, being the result of nondegenerate hysteresis points and isolas of asymmetric solutions forming as \(\text{Ra}_S\) is increased. In particular, at the maximal value of \(\text{Ra}_S\) considered there have been observed symmetric and asymmetric one-, two-, three-, four-, and five-cell flows. Despite the multiplicity of the flow patterns, a critical interval of the buoyancy ratio has been distinguished, above and below which the generic characteristics of the steady solutions were found to resemble the respective features of the “successive” and “simultaneous” regimes of layer formation whose existence was established in previous studies. Although the set of the steady solutions has been found to contain no linearly stable multicell flows, the perturbation was so long retained in the close proximity of the unstable steady solutions that such flows could be easily observable in the experiment. In spite of the appreciably different range of the Rayleigh numbers, the physically meaningful parameters suggested in previous studies were found to be represented in the present results.

MSC:
76E06 Convection in hydrodynamic stability
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1017/S0022112069000231 · doi:10.1017/S0022112069000231
[2] DOI: 10.1017/S0022112071002052 · doi:10.1017/S0022112071002052
[3] DOI: 10.1017/S0022112073001412 · doi:10.1017/S0022112073001412
[4] DOI: 10.1017/S0022112079000252 · doi:10.1017/S0022112079000252
[5] DOI: 10.1017/S0022112081000335 · Zbl 0476.76044 · doi:10.1017/S0022112081000335
[6] DOI: 10.1016/0017-9310(75)90240-9 · doi:10.1016/0017-9310(75)90240-9
[7] DOI: 10.1016/0017-9310(71)90140-2 · doi:10.1016/0017-9310(71)90140-2
[8] DOI: 10.1080/03091927208236083 · doi:10.1080/03091927208236083
[9] DOI: 10.1016/0017-9310(91)90065-M · doi:10.1016/0017-9310(91)90065-M
[10] DOI: 10.1063/1.858345 · doi:10.1063/1.858345
[11] DOI: 10.1002/nme.1620200305 · Zbl 0535.76096 · doi:10.1002/nme.1620200305
[12] DOI: 10.1017/S0022112088002642 · doi:10.1017/S0022112088002642
[13] DOI: 10.1063/1.857431 · doi:10.1063/1.857431
[14] DOI: 10.1017/S0022112089002600 · Zbl 0685.76020 · doi:10.1017/S0022112089002600
[15] DOI: 10.1017/S0022112090000830 · Zbl 0706.76090 · doi:10.1017/S0022112090000830
[16] DOI: 10.1017/S0022112091001222 · doi:10.1017/S0022112091001222
[17] DOI: 10.1017/S002211209200137X · doi:10.1017/S002211209200137X
[18] DOI: 10.1016/0017-9310(90)90070-B · doi:10.1016/0017-9310(90)90070-B
[19] DOI: 10.1016/0017-9310(91)90066-N · doi:10.1016/0017-9310(91)90066-N
[20] DOI: 10.1063/1.858671 · doi:10.1063/1.858671
[21] DOI: 10.1016/0021-9991(86)90265-2 · Zbl 0609.76037 · doi:10.1016/0021-9991(86)90265-2
[22] DOI: 10.1017/S0022112083003055 · Zbl 0599.76039 · doi:10.1017/S0022112083003055
[23] DOI: 10.1017/S0022112087001848 · Zbl 0632.76032 · doi:10.1017/S0022112087001848
[24] DOI: 10.1017/S0022112088003179 · Zbl 0656.76087 · doi:10.1017/S0022112088003179
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.