Resonance patterns in spatially forced Rayleigh–Bénard convection

Abstract

We report on the influence of a quasi-one-dimensional periodic forcing on the pattern selection process in Rayleigh-Bénard convection (RBC). The forcing was introduced by a lithographically fabricated periodic texture on the bottom plate. We study the convection patterns as a function of the Rayleigh number (Ra) and the dimensionless forcing wavenumber (q f ). For small Ra, convection takes the form of straight parallel rolls that are locked to the underlying forcing pattern. With increasing Ra, these rolls give way to more complex patterns, due to a secondary instability. The forcing wavenumber q f was varied in the experiment over the range of 0.6q c < q f < 1.4q c , with q c being the critical wavenumber of the unforced system. We investigate the stability of straight rolls as a function of q f and report patterns that arise due to a secondary instability.

Rayleigh–Bénard convection with a melting boundary

“…Among the phenomena neglected in classical RB convection, the possibility of a nonplanar boundary is particularly interesting. The case of rough boundaries has been extensively studied due to its application to laboratory experiments (Du & Tong 2000) while the case of large-scale topographies can significantly change the nature of convection both close to onset (Kelly & Pal 1978;Weiss et al 2014) and in the super-critical regime (Toppaladoddi et al 2015;Zhang et al 2018). While the topography is usually fixed initially, many natural mechanisms can dynamically generate non-trivial topographies.…”

Leidenfrost Pattern Formation and Boiling

“…1. The experiments were conducted in a high-pressure Rayleigh-Bénard convection setup that has previously been used to study pattern formation in single phase fluids [12][13][14]. A detailed description of the setup is given in [12].…”

Non-monotonic resonance in a spatially forced Lengyel-Epstein model

“…[1][2][3][4][5][6][7][8][9][10][11][12][13] In 1D systems, this spatial resonance problem reduces to the capability of a system to adjust the actual wavenumber, k, of the pattern it forms to a fraction of an external wavenumber, k f , provided that fraction is close enough to the wavenumber, k 0 , formed by the unforced system. It is the spatial counterpart of temporally forced oscillations and shares with the latter the property of an increased yielding capability as the forcing strength is increased; the stronger the forcing, the wider the wavenumber range in which the system can lock its wavenumber to the forcing wavenumber.…”

“…This effect has been studied first in the context of forced oscillations, [14][15][16][17][18][19] and more recently in the context of spatial forcing of pattern-forming systems. 3,5,7,8,10 The new patterns that appear at sufficiently strong forcing are related, in part, to the multiplicity of stable phase-locked states that exist within the tongues, and to phase fronts that locally shift the phase from one state to another. In oscillatory systems, the front shifts the oscillation phase, whereas in non-oscillatory pattern-forming systems it shifts the periodic-pattern phase.…”