Extreme multiplicity in cylindrical Rayleigh-B\'enard convection: I. Time-dependence and oscillations

TL;DR

This paper investigates the complex behavior of Rayleigh-Benard convection in a cylindrical setup, revealing multiple stable states and oscillations under different boundary conditions, advancing understanding of pattern formation in fluid dynamics.

Contribution

It demonstrates the coexistence of various steady and oscillatory flow states in cylindrical Rayleigh-Benard convection with different boundary conditions at water-like Prandtl number.

Findings

Multiple stable flow states coexist at the same parameters.

Time-dependent oscillatory flows are observed.

Boundary conditions significantly influence flow patterns.

Abstract

Rayleigh-Benard convection in a cylindrical container can take on many different spatial forms. Motivated by the results of Hof, Lucas and Mullin [Phys. Fluids 11, 2815 (1999)], who observed coexistence of several stable states at a single set of parameter values, we have carried out simulations at the same Prandtl number, that of water, and radius-to-height aspect ratio of two. We have used two kinds of thermal boundary conditions: perfectly insulating sidewalls and perfectly conducting sidewalls. In both cases we obtain a wide variety of coexisting steady and time-dependent flows.