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

Citation:

Fitzgerald, J. G., & Farrell, B. F. (2014). Mechanisms of mean flow formation and suppression in two-dimensional Rayleigh-Bénard convection. Physics of Fluids , 26, 054104.
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Abstract:

Two-dimensional laminar roll convection is capable of generating energetic horizontal
mean flows via a well-understood process known as the tilting instability. Less wellunderstood
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 advectionmechanism 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 thesemodels do not contain the
eddy-eddy advection mechanism. Instability suppression in such models is due to a
different mechanism involving vertical advection.We showthat 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.

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Last updated on 02/01/2019