Multistability of oscillatory thermocapillary convection in a liquid bridge.
A parametric investigation of the onset of chaos in a liquid bridge was numerically carried out for a medium Prandtl number liquid, Pr = 4, and unit aspect ratio under zero-gravity conditions. Spatiotemporal patterns of thermocapillary flow were successively studied beginning from the onset of instability up to the appearance of the nonperiodic flow and further on. Well-tested numerical code is used for solving the three-dimensional time-dependent Navier-Stokes equations in cylindrical coordinate system. Two-dimensional steady flow becomes oscillatory with azimuthal wave number m=2 as a result of Hopf bifurcation at Re(cr)(1)=630. A second independent solution with wave number m=3 was found to appear at Reynolds number Re(cr)(2) approximately 810. Two branches of three-dimensional periodic orbits, traveling waves with m=2 and m=3, coexist for Re>Re(cr)(2). Additional stable branches do not connect them. The different flow organizations reveal different behaviors in the supercritical area. The m=2 traveling wave always remains periodic, but the mode m=3 starts exhibiting chaotic features at Re approximately 4200. The onset of temporal nonperiodicity was shown to be associated with development of broadband noise in spectra and preceded by a quasiperiodicity. The flow stabilizes back to periodic with single frequency when Re exceeds a value Re approximately 5100. The window of periodicity exists up to at least Re=6000, the largest investigated value of the Reynolds number.
Shevtsova
V M
VM
MRC, CP-165/62, Université Libre de Bruxelles, 50, Avenue F. D. Roosevelt, B-1050 Brussels, Belgium. vshev@ulb.ac.be
Melnikov
D E
DE
Legros
J C
JC