Zero-Prandtl-number convection with slow rotation

Abstract

We present the results of our investigations of the primary instability and the flow patterns near onset in zero-Prandtl-number Rayleigh-Bénard convection with uniform rotation about a vertical axis. The investigations are carried out using direct numerical simulations of the hydrodynamic equations with stress-free horizontal boundaries in rectangular boxes of size $(2\pi /k_x)\times (2\pi /k_y)\times 1$ for different values of the ratio $\eta =k_x/k_y$. The primary instability is found to depend on $\eta$ and $Ta$. Wavy rolls are observed at the primary instability for smaller values of $\eta$ ($1/\sqrt{3}\le \eta \le 2$ except at $\eta =1$) and for smaller values of $Ta$. We observed Küppers-Lortz (KL) type patterns at the primary instability for $\eta =1/\sqrt{3}$ and $Ta\ge 40$. The fluid patterns are found to exhibit the phenomenon of bursting, as observed in experiments [Bajaj et al. Phys. Rev. E {\bf 65}, 056309 (2002)]. Periodic wavy rolls are observed at onset for smaller values of $Ta$, while KL-type patterns are observed for $Ta\ge 100$ for $\eta =\sqrt{3}$. In case of $\eta =2$, wavy rolls are observed for smaller values of $Ta$ and KL-type patterns are observed for $25\le Ta\le 575$. Quasi-periodically varying patterns are observed in the oscillatory regime ($Ta>575$). The behavior is quite different at $\eta =1$. A time dependent competition between two sets of mutually perpendicular rolls is observed at onset for all values of $Ta$ in this case. Fluid patterns are found to burst periodically as well as chaotically in time. It involved a homoclinic bifurcation. We have also made a couple of low-dimensional models to investigate bifurcations for $\eta =1$, which is used to investigate the sequence of bifurcations.

50 pages, 22 figures and 3 tables

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Cited by in corpus (4)

• Zero Prandtl-number rotating magnetoconvection
• Effects of a small magnetic field on homoclinic bifurcations in a low-Prandtl-number fluid
• Effect of horizontal magnetic field on Küppers-Lortz instability
• Overstable rotating convection in presence of vertical magnetic field