Issue
EPL
Volume 87, Number 5, September 2009
Article Number 54003
Number of page(s) 6
Section Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics
DOI http://dx.doi.org/10.1209/0295-5075/87/54003
Published online 22 September 2009
EPL, 87 (2009) 54003
DOI: 10.1209/0295-5075/87/54003

Bifurcation and chaos in zero-Prandtl-number convection

P. Pal1, P. Wahi2, S. Paul1, M. K. Verma1, K. Kumar3 and P. K. Mishra1

1   Department of Physics, Indian Institute of Technology - Kanpur, India
2   Department of Mechanical Engineering, Indian Institute of Technology - Kanpur, India
3   Department of Physics and Meteorology, Indian Institute of Technology - Kharagpur, India

mkv@iitk.ac.in

received 1 June 2009; accepted in final form 21 August 2009; published September 2009
published online 22 September 2009

Abstract
We present a detailed bifurcation structure and associated flow patterns near the onset of zero-Prandtl-number Rayleigh-Bénard convection. We employ both direct numerical simulation and a low-dimensional model ensuring qualitative agreement between the two. Various flow patterns originate from a stationary square observed at a higher Rayleigh number through a series of bifurcations starting from a pitchfork followed by a Hopf and finally a homoclinic bifurcation as the Rayleigh number is reduced to the critical value. Homoclinic chaos, intermittency, and crises are observed near the onset.

PACS
47.20.Bp - Buoyancy-driven instabilities (e.g., Rayleigh-Benard).
47.20.Ky - Nonlinearity, bifurcation, and symmetry breaking.
47.27.ed - Dynamical systems approaches.

© EPLA 2009