Linear stability analysis of Rayleigh-Benard convection for cold water near its density maximum in a cylindrical container

In this paper, the onset of Rayleigh-Benard convection of cold water near its density maximum in a vertical cylindrical container and the stability of the steady axisymmetric flow were studied by using linear stability analysis. The results show that the critical Rayleigh number for the onset of convection increases with increasing the density inversion parameter Tm (Tm=(Phi(max)-Phi(c))/(Phi(h)-Phi(c)), where Phi(max) is the temperature at the maximum density, and Phi(h) and Phi(c) are the temperature at the bottom wall and top wall, respectively), and some new flow patterns not found in the Rayleigh-Benard convection of common fluids are presented. Within a certain range of density inversion parameters, the onset of convection is steady and axisymmetric. The steady axisymmetric basic flow is found to depend on the initial condition, and two distinctly different basic flow are obtained at identical parameters, due to the top-bottom symmetry breaking. For the upward basic flow, four different flow patterns are observed after the axisymmetry-breaking instability. In addition, a hysteresis phenomenon of the flow pattern transition is found when Tm=0.57. For the downward basic flow, six flow patterns are observed after the axisymmetry-breaking instability. In particular, it is found that there still exists stable axisymmetric flow beyond the second bifurcation in certain ranges of Rayleigh numbers. The energy analysis shows that both the primary instability and the axisymmetry-breaking instability are caused by the thermal-buoyancy mechanism. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This study investigates the onset of Rayleigh-Benard convection of cold water near its density maximum in a vertical cylindrical container and the stability of the steady axisymmetric flow through linear stability analysis. It is found that the critical Rayleigh number for the onset of convection increases with the density inversion parameter Tm, leading to new flow patterns. Different initial conditions result in distinct basic flows, and top-bottom symmetry breaking causes axisymmetry-breaking instability.