Mechanisms of mean flow formation and suppression in two-dimensional Rayleigh-Bénard convection

• Published in: Physics of fluids (1994) 2014-05, Vol.26 (5)
• Main Authors: Fitzgerald, Joseph G., Farrell, Brian F.
• Format: Article
• Language: English
• Subjects: Advection; Aspect ratio; Dependence; Domains; Fluid dynamics; Physics; Shutdowns; Tilting instability (fluids); Vortices; Wavelengths
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.4875814

Two-dimensional laminar roll convection is capable of generating energetic horizontal mean flows via a well-understood process known as the tilting instability. Less well-understood is the physical mechanism behind the strong dependence of this effect on the horizontal lengthscale of the convection pattern. Mean flows of this type have been found to form for sufficiently large Rayleigh number in periodic domains with a small aspect ratio of horizontal length to vertical height, but not in large aspect ratio domains. We demonstrate that the elimination of the tilting instability for large aspect ratio is due to a systematic eddy-eddy advection mechanism intervening at linear order in the tilting instability, and that this effect can be captured in a model retaining two nonlinearly interacting horizontal wavenumber components of the convection field. Several commonly used low-order models of convection also exhibit a shutdown of the tilting instability for large aspect ratio, even though these models do not contain the eddy-eddy advection mechanism. Instability suppression in such models is due to a different mechanism involving vertical advection. We show that this vertical advection mechanism is excessively strong in the low-order models due to their low resolution, and that the instability shutdown in such models vanishes when they are appropriately extended.