On the onset of multi-wave patterns in laterally heated floating zones for slightly supercritical conditions

Lappa, Marcello (2016) On the onset of multi-wave patterns in laterally heated floating zones for slightly supercritical conditions. Physics of Fluids, 28 (12). 124105. ISSN 1070-6631 (https://doi.org/10.1063/1.4971840)

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This analysis follows and integrates the line of inquiry started in past author’s works (Phys. Fluids, 15(3): 776-789, 2003, and Phys. Fluids 16(2): 331-343, 2004) about the typical instabilities of Marangoni flow and associated hierarchy of bifurcations in laterally heated floating zones with various shapes and aspect ratios. The main motivation for re-examining this kind of problems, which so much attention have attracted over the last twenty years, is the recent discovery (Kudo, Ueno and Kawamura, (2014), in Japanese, DOI: 10.1299/transjsme.2014tep0095) of a chaotic state in region of the space of parameters where on the basis of existing theories and earlier results for the classical liquid-bridge problem with organic fluids, the flow should be relatively regular in time and with a simple structure in space. Axisymmetric computations are used to obtain the steady basic state, and then the Navier Stokes equations are solved in their complete, three-dimensional, time-dependent and non-linear formulation to investigate the evolution of azimuthal disturbances. It is shown that the “apparent” doubling or quadrupling of the azimuthal wavenumber in the equatorial plane, previously reported for the case of floating zones of liquid metals, is replaced for high-Prandtl-number liquids by the complex interaction of disturbances with distinct spatial and temporal scales. These disturbances become critical at relatively comparable values of the Marangoni number. The unexpected multiplicity of waveforms and competition of spatial modes is explained according to the increased complexity of the considered system in terms of flow topology and structure with respect to the classical half-zone configuration.