Binary convection in slightly inclined elongated cells

Author

Mercader, M.; Batiste, O.; Alonso, Arantxa

Type of activity

Presentation of work at congresses

Name of edition

13th International Meeting on Thermodiffusion

Date of publication

2018

Presentation's date

2018-09-13

Book of congress proceedings

IMT'18 13th International Meeting on Thermodiffusion: London (United Kingdom): September 11-14, 2018: book of abstracts

First page

48

Last page

48

Abstract

We analyze the effect of adding a small inclination to a two dimensional horizontal bounded layer heated from below containing a binary mixture with negative separation ratio (water-ethanol mixtures). The horizontal component of gravity generates a parallel shear flow with a cubic profile that interacts with the convective flows generated by the vertical component. The primary bifurcation of this flow, for very small inclinations, is a Hopf bifurcation that gives rise to chevron and blinking sta...

We analyze the effect of adding a small inclination to a two dimensional horizontal bounded layer heated from below containing a binary mixture with negative separation ratio (water-ethanol mixtures). The horizontal component of gravity generates a parallel shear flow with a cubic profile that interacts with the convective flows generated by the vertical component. The primary bifurcation of this flow, for very small inclinations, is a Hopf bifurcation that gives rise to chevron and blinking states similar to those obtained without inclination [1]. As soon as the inclination is established a fold bifurcation in the base flow curve emerges. When the inclination increases, the Rayleigh number of this fold decreases. The location of the primary direct Hopf bifurcation and of the subsequent inverse Hopf bifurcation undergone by the base parallel flow for very small inclinations approach themselves and to the fold point, and eventually merge and disappear at a critical inclination. Thus, from this critical inclination, the primary bifurcation of the base flow is a fold.
The branches of localized states (convectons) obtained in the non inclined case [2,3] are notably affected. For very small inclinations, the odd convecton branch splits up, as expected from the breaking of symmetry that inclination implies. The branch of even solutions reconnects with the asymmetric rung states branch and breaks up into disconnected parts. For slightly larger inclinations, though still quite small, we have obtained small amplitude localized states of co-rotating rolls that configure a branch with complex gyrations when the large scale flow is continued by varying the Rayleigh number (see figure). Several disconnected branches connecting solutions of co-rotating rolls, counter-rotating rolls, and mixed solutions of co-rotating and counter-rotating rolls are also obtained. The snaking diagram of the counter-rotating rolls obtained without inclination is destroyed from a very small inclination.
REFERENCES
[1] O. Batiste, E. Knobloch, I. Mercader, and M. Net, Phys. Rev. E, 65, 016303 (2001).
[2] I. Mercader, O. Batiste, A. Alonso, and E. Knobloch, Fluid Dyn. Res., 42 025505 (2010).
[3] I. Mercader, O. Batiste, A. Alonso, and E. Knobloch, J. Fluid Mech., 667, 586 (2011).