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Secondary instabilities of convection in a shallow cavity. (English) Zbl 0745.76018
Summary: Analysis of secondary instabilities of natural convection in a shallow cavity heated from a side has been carried out. For mercury with Prandtl number equal to 0.027 analysis of the primary instabilities by linear theory shows that an instability sets in as transverse cells at Grashof number equal to 9157.6. Instability resulting in oscillatory longitudinal rolls is also possible, their critical Grashof number being equal to 10608.4. The secondary instabilities of the equilibrium states of transverse cells for mercury have been determined. The results show roughly that stable transverse cells with wavelength shorter than the critical become unstable by subharmonic resonance, but the instability for longer cells sets in by a combination resonance. The instability as longitudinal oscillatory rolls reappears at larger values of Grashof number, although slightly delayed by the presence of the transverse cells.

MSC:
76E15 Absolute and convective instability and stability in hydrodynamic stability
76R10 Free convection
80A20 Heat and mass transfer, heat flow (MSC2010)
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[1] Laure, J. Méc. Théor. Appl. 6 pp 351– (1987)
[2] DOI: 10.1017/S0022112083001603 · Zbl 0528.76049
[3] DOI: 10.1175/1520-0469(1972)029 2.0.CO;2
[4] DOI: 10.1017/S0022112074002552 · Zbl 0282.76044
[5] Gershuni, J. Appl. Mech. Tech. Phys. 5 pp 706– (1974)
[6] Drummond, J. Fluid Mech. 148 pp 245– (1987)
[7] DOI: 10.1017/S0022112074001571 · Zbl 0291.76019
[8] Chait, J. Fluid Mech. 200 pp 189– (1989)
[9] DOI: 10.1017/S002211206700045X · Zbl 0144.47101
[10] DOI: 10.1063/1.866574 · Zbl 0641.76031
[11] Klaassen, J. Fluid Mech. 202 pp 367– (1989)
[12] DOI: 10.1017/S0022112067002538 · Zbl 0322.76020
[13] DOI: 10.1017/S0022112074002540
[14] Hurle, Phil. Mag. 13 pp 305– (1966)
[15] DOI: 10.1016/0375-9601(88)90560-9
[16] DOI: 10.1146/annurev.fl.20.010188.002415
[17] DOI: 10.1063/1.864226
[18] DOI: 10.1063/1.857405
[19] Stuart, Proc. R. Soc. Lond. A 362 pp 27– (1978)
[20] DOI: 10.1017/S0022112082000044 · Zbl 0479.76056
[21] DOI: 10.1017/S0022112083002931 · Zbl 0561.76055
[22] DOI: 10.1007/BF01022868 · Zbl 0233.76087
[23] DOI: 10.1017/S0022112084001762 · Zbl 0561.76037
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